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- SpringBoard Mathematics: Course 3 (2014)
SpringBoard Mathematics: Course 3 (2014)
1: Investigating Patterns--Laws and Order
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
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
![Screenshot of Finding Patterns](/Assets/img/blank.gif)
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
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
2: Operations with Fractions--And the Beat Goes On
![Screenshot of Dividing Fractions](/Assets/img/blank.gif)
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
![Screenshot of Fractions with Unlike Denominators](/Assets/img/blank.gif)
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
![Screenshot of Multiplying Fractions](/Assets/img/blank.gif)
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
3: Powers and Roots--Squares and Cubes
![Screenshot of Balancing Blocks (Volume)](/Assets/img/blank.gif)
Balancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview
![Screenshot of Perimeter and Area of Rectangles](/Assets/img/blank.gif)
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
![Screenshot of Square Roots](/Assets/img/blank.gif)
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
4: Rational Numbers--Know When to Fold 'Em
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
Modeling Fractions (Area Models)
Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
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
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
6: Properties of Exponents--That's a Lot of Cats
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
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
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
7: Scientific Notation--A Traveler's Tale
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
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: Operations with Scientific Notation--How Big is that Planet?
![Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits](/Assets/img/blank.gif)
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
9: Writing Expressions--Pebbles in the Sand
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
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
![Screenshot of Using Algebraic Expressions](/Assets/img/blank.gif)
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
10: Solving Equations--Bags and Cubes
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
11: Exploring Slope--High Mountain Ratio
![Screenshot of Distance-Time and Velocity-Time Graphs](/Assets/img/blank.gif)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
12: Slope-Intercept Form--Leaky Bottle
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
13: Proportional Relationships--Vary Interesting
![Screenshot of Beam to Moon (Ratios and Proportions)](/Assets/img/blank.gif)
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
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
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
14: Graphing Systems of Linear Equations--System of Trees
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
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
15: Solving Systems of Linear Equations Algebraically--What's the Point?
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Standard Form)](/Assets/img/blank.gif)
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
16: Angle-Pair Relationships--The Winning Angle
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
18: Introduction to Transformations--Move It!
![Screenshot of Reflections](/Assets/img/blank.gif)
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
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
19: Rigid Transformations and Compositions--All the Right Moves
![Screenshot of Quilting Bee (Symmetry)](/Assets/img/blank.gif)
Quilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview
![Screenshot of Rock Art (Transformations)](/Assets/img/blank.gif)
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
20: Similar Triangles--Mirrors and Shadows
![Screenshot of Similar Figures](/Assets/img/blank.gif)
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
21: Dilations--Alice's Adventures in Shrinking and Growing
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Perimeters and Areas of Similar Figures](/Assets/img/blank.gif)
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
22: The Pythagorean Theorem--Stop the Presses
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
23: Applying the Pythagorean Theorem--Diamond in the Rough
![Screenshot of Distance Formula](/Assets/img/blank.gif)
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
24: Converse of the Pythagorean Theorem--Paper Clip Chains
![Screenshot of Classifying Triangles](/Assets/img/blank.gif)
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
25: Surface Area--Greenhouse Gardens
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
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
26: Volume of Solids--Castles in the Sand
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
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
27: Introduction to Functions--It's All Related
![Screenshot of Function Machines 1 (Functions and Tables)](/Assets/img/blank.gif)
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
![Screenshot of Function Machines 2 (Functions, Tables, and Graphs)](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
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
28: Comparing Functions--Which Car Wins?
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
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
29: Constructing Functions--Hold On to Your Hats
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
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
30: Linear Functions--Get in Line
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
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
31: Linear and Non-Linear Functions--Measure Up
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
32: Scatter Plots and Association--Cracker Snacker
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
33: Bivariate Data--Sue Swandive
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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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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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