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  • Inside Algebra (2011)

Inside Algebra (2011)

1: Variables and Expressions

1.1: Translate verbal expressions into mathematical expressions and vice versa

Map showing a car route between U.S. state capitals, highlighting vehicle options and gas stations for a road trip.

Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 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


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1.2: Evaluate expressions using the order of operation

Expression calculator displayed on screen, illustrating the order of operations for evaluating mathematical expressions.

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview


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1.3: Solve open sentences by performing arithmetic operations

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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2: Exploring Rational Numbers

2.1: Graph rational numbers on the number line

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview


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2.2: Add and subtract rational numbers

Image of various colored tables focusing on the topic of adding fractions with fraction tiles.

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview


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A computer screen displaying a number line with dynamic arrows illustrating the addition of real numbers.

Adding on the Number Line

Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview


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A computer screen displaying graphic models for adding and subtracting fractions with unlike denominators.

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview


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A computer screen displaying a number line illustrating sums and differences of decimal numbers using area models.

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


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2.3: Compare and order rational numbers

Computer screen displaying types of numbers: Fraction, Decimal, Percent with Area and Grid Models.

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview


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Computer screen displaying area grids and a number line for comparing percents, fractions, and decimals greater than 1.

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview


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2.4: Multiply and divide rational numbers

Computer screen displaying an area model for dividing fractions, with adjustable numerators and denominators.

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview


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A computer screen displays a math worksheet on dividing mixed numbers with step-by-step feedback for corrections.

Dividing Mixed Numbers

Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview


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A computer screen displaying a coordinate system for multiplying fractions using an area model with adjustable vertical and horizontal areas.

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview


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A math worksheet that shows multiplying mixed numbers with step-by-step feedback for corrections.

Multiplying Mixed Numbers

Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview


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Graphing calculator displaying a dynamic area model for multiplying two decimals on a shaded grid.

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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2.5: Find the principal square root of a number

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


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3: Solving Linear Equations

3.1: Solve linear equations with addition and subtraction

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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3.2: Solve linear equations with multiplication and division

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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3.3: Solve linear equations using one or more operations

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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3.4: Solve problems that can be represented as equations

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


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Map showing a car route between U.S. state capitals, highlighting vehicle options and gas stations for a road trip.

Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview


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3.5: Solve proportions that have a missing part

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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Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


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Perimeters and Areas of Similar Figures

Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview


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Proportions and Common Multipliers

Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview


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3.6: Use proportions to solve percent problems

Percent of Change

Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview


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Percents and Proportions

Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview


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4: Graphing Relations and Functions

4.1: Graph ordered pairs and relations

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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Points in the Coordinate Plane

Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change 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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4.2: Identify the domain, range, and the inverse of a relation

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


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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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4.3: Determine the range for a given domain of a relation

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


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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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4.4: Graph linear equations

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


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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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4.5: determine whether a relation is a function, and find a value for a given function

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


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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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5: Analyzing Linear Equations

5.1: Determine the slope given a line on a graph or two points on the line

Slope

Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview


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5.2: Write the equation of a line in standard form given two points on the line

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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5.3: Draw a best-fit line, and find the equation of the best-fit line for a scatter plot

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


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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


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5.4: Write linear equations in slope-intercept form to find the slope, x-intercept, and y-intercept, and sketch the graph

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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6: Solving Linear Inequalities

6.1: Solve and graph the solution set of inequalities with addition and subtraction

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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6.2: Solve and graph the solution set of inequalities with multiplication and division

Exploring Linear Inequalities in One Variable

Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview


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6.4: Solve and graph the solution set of compound inequalities and inequalities involving absolute value

Compound Inequalities

Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview


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Absolute Value Equations and Inequalities

Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview


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6.5: Graph inequalities in the coordinate plane

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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7: Solving Systems of Linear Equations and Inequalities

7.1: Solve systems of equations by graphing

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 (x, y) point to be a solution of one equation, or of a system of two equations. 5 Minute Preview


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7.2: Determine whether a system of equations has one solution, no solutions, or infinitely many solutions

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


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7.4: Solve systems of equations by eliminating one variable

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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7.5: Solve systems of inequalities by graphing

Systems of Linear Inequalities (Slope-intercept form)

Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview


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8: Exploring Polynomials

8.1: Multiply and divide monomials and simplify expressions

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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8.3: Add and subtract polynomials and express the answer so the powers of the terms are in descending order

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview


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9: Using Factoring

9.3: Factor quadratic trinomials of the form ax2 + bx + c, and solve equations by factoring

Modeling the Factorization of ax2+bx+c

Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview


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9.4: Factor quadratic polynomials that are perfect squares or differences of squares, and solve equations by factoring

Factoring Special Products

Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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10: Exploring Quadratic and Exponential Functions

10.1: Graph parabolas, and find the coordinates of the vertex and axis of symmetry

Parabolas

Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview


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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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10.2: Estimate the roots of a quadratic equation by graphing he associated function

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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10.3: Solve quadratic equations by factoring or using he quadratic formulas

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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10.4: Graph exponential functions, and solve problems using the graphs

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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Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 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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11: Exploring Rational Expressions and Equations

11.3: Divide a polynomial by a binomial

Dividing Polynomials Using Synthetic Division

Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview


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12: Exploring Radical Expressions and Equations

12.1: Simplify and perform operations with radical expressions

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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12.3: Use the Pythagorean t=Theorem to solve problems

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


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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


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12.4: Find the distance between two points in the coordinate plane

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


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12.5: Find the unknown measures of the sides of similar triangles.

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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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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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


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