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South Carolina - Mathematics: 8th Grade
SC--College- and Career-Ready Standards | Adopted: 2015
8.NS: : The Number System
8.NS.1: : Explore the real number system and its appropriate usage in real-world situations.
8.NS.1.a: : Recognize the differences between rational and irrational numbers.
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Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
8.NS.1.b: : Understand that all real numbers have a decimal expansion.
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Comparing and Ordering Decimals
Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview
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Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Sums and Differences with Decimals
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line. 5 Minute Preview
8.NS.2: : Estimate and compare the value of irrational numbers by plotting them on a number line.
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Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.NS.3: : Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.

Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
8.F: : Functions
8.F.1: : Explore the concept of functions.
8.F.1.a: : Understand that a function assigns to each input exactly one output.

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
8.F.1.c: : Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
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Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview

Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
8.F.1.d: : Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.

Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
8.F.1.e: : Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview

Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
8.F.2: : Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.
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Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
8.F.3: : Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.F.3.a: : Define an equation in slope-intercept form (y = mx + b) as being a linear function.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.F.3.b: : Recognize that the graph of a linear function has a constant rate of change.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.F.3.c: : Provide examples of nonlinear functions.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.F.4: : Apply the concepts of linear functions to real-world and mathematical situations.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.4.a: : Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.4.b: : Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.4.c: : Construct a function in slope-intercept form that models a linear relationship between two quantities.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.4.d: : Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.4.e: : Explore the relationship between linear functions and arithmetic sequences.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
8.F.5: : Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.5.a: : Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview

Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.5.b: : Sketch the graph of a function from a verbal description.

Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview

Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
8.F.5.c: : Write a verbal description from the graph of a function with and without scales.

Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Improper Fractions and Mixed Numbers
Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
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Multiplying with Decimals
Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview

Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
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Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Using Algebraic Equations
Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview
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Using Algebraic Expressions
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview
8.EEI: : Expressions, Equations, and Inequalities
8.EEI.1: : Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.
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Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
8.EEI.2: : Investigate concepts of square and cube roots.
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.EEI.2.a: : Find the exact and approximate solutions to equations of the form x² = p and x³ = p where p is a positive rational number.
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.EEI.2.b: : Evaluate square roots of perfect squares.
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview

Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.EEI.2.d: : Recognize that square roots of non-perfect squares are irrational.
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
8.EEI.3: : Explore the relationship between quantities in decimal and scientific notation.
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Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
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Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.3.a: : Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ≤ a < 10 and b is an integer.
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Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
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Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.3.b: : Translate between decimal notation and scientific notation.
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Number Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
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Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.3.c: : Estimate and compare the relative size of two quantities in scientific notation.
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
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Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.4: : Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.

Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
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Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.4.a: : Multiply and divide numbers expressed in both decimal and scientific notation.
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Multiplying with Decimals
Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview
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Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview

Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview

Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.4.b: : Select appropriate units of measure when representing answers in scientific notation.
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview

Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.4.c: : Translate how different technological devices display numbers in scientific notation.
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Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview

Unit Conversions 2 - Scientific Notation and Significant Digits
Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview
8.EEI.5: : Apply concepts of proportional relationships to real-world and mathematical situations.

Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
8.EEI.5.a: : Graph proportional relationships.
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Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
8.EEI.5.b: : Interpret unit rate as the slope of the graph.
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Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
8.EEI.5.c: : Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.
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Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
8.EEI.6: : Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships.
8.EEI.6.a: : Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.EEI.6.b: : Derive the slope-intercept form (y = mx + b) for a non-vertical line.
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.EEI.6.c: : Relate equations for proportional relationships (y = kx) with the slope-intercept form (y = mx + b) where b = 0.
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
8.EEI.7: : Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.
8.EEI.7.a: : Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
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Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
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Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
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Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.EEI.7.b: : Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b).
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Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview

Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.EEI.7.c: : Generate linear equations with the three types of solutions.
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
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Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.EEI.7.d: : Justify why linear equations have a specific type of solution.
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.EEI.8: : Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.
8.EEI.8.a: : Graph systems of linear equations and estimate their point of intersection.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
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Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
8.EEI.8.b: : Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an

Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
8.EEI.8.c: : Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview

Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an

Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
8.EEI.8.d: : Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.
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Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview

Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an

Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
8.GM: : Geometry and Measurement
8.GM.1: : Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).
8.GM.1.a: : Verify that lines are mapped to lines, including parallel lines.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.1.b: : Verify that corresponding angles are congruent.
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Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.1.c: : Verify that corresponding line segments are congruent.
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2: : Apply the properties of rigid transformations (rotations, reflections, translations).
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2.a: : Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2.b: : Reflect geometric figures with respect to the x - axis and/or y - axis.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2.c: : Translate geometric figures vertically and/or horizontally.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2.d: : Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.2.e: : Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.3: : Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.3.a: : Use coordinate geometry to describe the effect of transformations on two-dimensional figures.

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.GM.3.b: : Relate scale drawings to dilations of geometric figures.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
8.GM.4: : Apply the properties of transformations (rotations, reflections, translations, dilations).

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
8.GM.4.a: : Dilate geometric figures using scale factors that are positive rational numbers.

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
8.GM.4.b: : Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.

Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
8.GM.4.c: : Given two similar figures, describe the series of transformations that justifies this similarity.

Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
8.GM.4.d: : Use proportional reasoning to find the missing side lengths of two similar figures.

Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
8.GM.5: : Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview

Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
8.GM.5.a: : Discover that the sum of the three angles in a triangle is 180 degrees.

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview

Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
8.GM.5.b: : Discover and use the relationship between interior and exterior angles of a triangle.

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview

Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
8.GM.5.c: : Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview

Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
8.GM.5.d: : Recognize that two similar figures have congruent corresponding angles.

Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview

Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview

Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
8.GM.6: : Use models to demonstrate a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview

Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
8.GM.7: : Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
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Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview

Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview

Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview

Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
8.GM.8: : Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.

Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview

Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview

Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
8.GM.9: : Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.
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Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview

Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview

Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
8.DSP: : Data Analysis, Statistics, and Probability
8.DSP.1: : Investigate bivariate data.
8.DSP.1.a: : Collect bivariate data.
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Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
8.DSP.1.b: : Graph the bivariate data on a scatter plot.
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Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
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Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.1.c: : Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.2: : Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.3: : Apply concepts of an approximate line of best fit in real-world situations.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.3.a: : Find an approximate equation for the line of best fit using two appropriate data points.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.3.b: : Interpret the slope and intercept.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.3.c: : Solve problems using the equation.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
8.DSP.4: : Investigate bivariate categorical data in two-way tables.
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Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
8.DSP.4.a: : Organize bivariate categorical data in a two-way table.
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Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
8.DSP.4.b: : Interpret data in two-way tables using relative frequencies.

Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
8.DSP.4.c: : Explore patterns of possible association between the two categorical variables.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
8.DSP.5: : Organize data in matrices with rational numbers and apply to real-world and mathematical situations.
8.DSP.5.c: : Add and subtract matrices of the same size.
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
Correlation last revised: 9/16/2020
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
How Free Gizmos Work
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Start teaching with 20-40 Free Gizmos. See the full list.
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Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
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All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
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