Foundations of Algebra |
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Chapter 1 |
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| Base Blocks |
Represent whole numbers through thousands using place-value models |
| Base Blocks Addition |
Add whole numbers through thousands using place-value models |
| Base Blocks Decimals |
Add decimals in base 2, 3, 4, 5, or 10 using place-value models |
| Base Blocks Decimals |
Add decimals through thousandths using place-value models |
| Base Blocks Subtraction | Subtract whole numbers through thousands using place-value models |
| Color Chips-Addition | Use colored chips to model and solve addition equations with integers |
| Color Chips-Subtraction | Use colored chips to model and solve subtraction equations with integers |
| Diffy | Choose between whole numbers, integers, fractions, decimals, or money amounts to find the difference between the pair of numbers on each side of a square |
| Factor Tree | Find the prime factorization of one or two numbers |
| Fractions-Adding | Add fractions with like and unlike denominators |
| Number Line Arithmetic | Use a number line to visualize operations |
| Number Line Bars | Use adjustable color bars to illustrate arithmetic operations on a number line |
| Number Line Bars-Fractions | Use adjustable color bars to illustrate arithmetic operations with fractions on a number line |
| Rectangle Multiplication of Integers | Visualize the product of two integers |
Chapter 2 |
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| Pythagorean Theorem | Explore two proofs of the Pythagorean Theorem |
Chapter 3 |
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| Algebra Balance Scales | Solve simple linear equations with one unknown using a balance scale |
| Algebra Balance Scales-Negatives | Solve simple linear equations with integers and one unknown using a balance scale |
| Base Blocks | Represent decimals through thousandths using place-value models |
| Base Blocks Decimals |
Add decimals in base 2, 3, 4, 5, or 10 using place-value models |
| Color Chips-Addition | Use colored chips to model and solve addition equations with integers |
| Color Chips-Subtraction | Use colored chips to model and solve subtraction equations with integers |
| Diffy | Choose between whole numbers, integers, fractions, decimals, or money amounts to find the difference between the pair of numbers on each side of a square |
| Fractions-Adding | Add fractions with like and unlike denominators |
| Function Machine | Explore the concept of a function using a function machine |
| Rectangle Multiplication of Integers | Visualize the product of two integers |
Chapter 4 |
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| Base Blocks Decimals |
Add decimals in base 2, 3, 4, 5, or 10 using place-value models |
| Color Chips-Addition | Use colored chips to model and solve addition equations with integers |
| Color Chips-Subtraction | Use colored chips to model and solve subtraction equations with integers |
| Diffy | Choose between whole numbers, integers, fractions, decimals, or money amounts to find the difference between the pair of numbers on each side of a square |
| Fractions-Adding | Add fractions with like and unlike denominators |
| Rectangle Multiplication of Integers | Visualize the product of two integers |
Chapter 5 |
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| Algebra Tiles | Use algebra tiles to multiply and square binomials; factor polynomials; apply the Distributive Law |
| Base Blocks Decimals |
Add decimals in base 2, 3, 4, 5, or 10 using place-value models |
| Color Chips-Addition | Use colored chips to model and solve addition equations with integers |
| Color Chips-Subtraction | Use colored chips to model and solve subtraction equations with integers |
| Diffy | Choose between whole numbers, integers, fractions, decimals, or money amounts to find the difference between the pair of numbers on each side of a square |
| Factor Tree | Find the prime factorization of one or two numbers |
| Fractions-Adding | Add fractions with like and unlike denominators |
| Rectangle Multiplication | Visualize the product of two factors using an array |
Chapter 6 |
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| Algebra Balance Scales-Negatives | Solve simple linear equations with integers and one unknown using a balance scale |
| Conway's Game of Life | Observe what happens to a given pattern of cells through successive generations |
| Counting All Pairs | Plot points on a coordinate grid |
| Geoboard-Coordinate | Find the slope of a line |
| Grapher | Graph functions |
| Scatterplot | Determine the line of best fit based on data entered |
Chapter 7 |
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| Converting Units | Solve unit conversion problems or create your own |
| Fill and Pour | Solve unit conversion problems or create your own |
| Fractions-Comparing | Recognize and generate equivalent forms of commonly used fractions to compare fractions |
| Golden Rectangle | Explore the golden ratio |
Chapter 8 |
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| Percent Grids |
Represent, name, and explore percentages using hundreds grids. |
| Base Blocks | Represent decimals through thousandths using place-value models |
| Fractals-Iterative | Draw any of 6 iterative fractals |
| Fractals-Koch and Sierpinski | Explore the Koch snowflake and the Sierpinski carpet fractals |
| Fraction Bars | Explore the relationhip between fractions |
| Fraction Pieces | Manipulate fractional pieces of a circular or square region |
| Fractions-Comparing | Recognize and generate equivalent forms of commonly used fractions to compare fractions |
| Fractions-Equivalent | Recognize and generate equivalent forms of commonly used fractions |
| Fractions-Naming | Identify the fraction that represents the model |
| Fractions-Parts of a Whole | Model commonly used fractions |
| Fractions-Visualizing | Model commonly used fractions using various shapes |
| Loan Calculator | Explore the size of payments required to pay off a loan |
| Percentages | Find the percent of a number |
| Percentages | Find what percent one number is of another |
| Percentages | Find the original number when a percent of it is known |
| Savings Calculator | Calculate the interest and total savings on single or regular deposits |
| Tight Weave | Explore Sierpinski Carpet |
Chapter 9 |
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| Attribute Blocks | Sort shapes using color, shape, and size |
| Attribute Trains |
Complete patterns of shapes, numbers, or colors |
| Congruent Triangles | Construct triangles from various combinations of sides and angles (SSS, SAS, ASA, SSA) |
| Fifteen Puzzle | Move tiles around to arrange them in a specific pattern |
| Geoboard | Color and make specific shapes |
| Geoboard | Subdivide, combine, and transform shapes using a geoboard |
| Geoboard-Circular | Draw and compare two-dimensional shapes using a circular geoboard |
| Geoboard-Circular | Construct central angles and find the measures of each angle in a triangle using a circular geoboard |
| Geoboard-Coordinate | Explore inscribed parallelograms |
| Pentominoes | Make different figures using pentominoes, including congruent figures |
| Pie Chart | Make circle graphs |
| Pinwheel Tiling | Manipulate right triangles to make Pinwheel Triangles |
| Tangrams | Build different shapes from a tangram |
| Tessellations | Form tessellations using different shapes |
| Venn Diagrams | Explore the union and intersection of sets |
Chapter 10 |
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| Geoboard | Explore perimeter and area of regular and irregular shapes using a geoboard |
| Geoboad-Coordinate | Construct reflections |
| Geoboard-Coordinate | Use a coordinate grid to locate shapes in two dimensions |
| Geoboard-Coordinate | Explore inscribed parallelograms |
| Ladybug Leaf | Use action buttons to direct a ladybug to a leaf |
| Ladybug Mazes | Use action buttons to direct a ladybug through a maze |
| Pentominoes | Explore the perimeter of different pentominoes |
| Transformations-Composition | Explore the effect of two transformations of a figure |
| Transformations-Dilation | Create figures with pattern blocks and explore dilations |
| Transformations-Reflection | Create figures with pattern blocks and explore reflections |
| Transformations-Rotation |
Create figures with pattern blocks and explore rotations |
| Transformation-Translation |
Create figures with pattern blocks and explore translations |
| Triominos | Flip or rotate triangular triominoes to build different figures |
Chapter 11 |
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| Attribute Trains |
Complete patterns of shapes, numbers, or colors |
| Color Patterns | Recognize, describe, and extend color patterns |
| Fibonacci Sequence | Pick a starting value and explore the terms in the Fibonacci Sequence |
| Grapher | Graph functions |
| Mastermind | Use logical reasoning to discover the color sequence of 4 pegs |
| Number Patterns | Recognize patterns in number sequences |
| Pascal's Triangle | View number patterns or create your own |
| Pattern Blocks | Create various patterns of shape, including symmetrical patterns |
| Polyominoes | Create patterns and explore creating different shapes with squares |
| Sieve of Eratosthenes | Explore patterns and relationships involving multiples |
Chapter 12 |
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| Fill and Pour | Manipulate two containers of liquid to achieve a target volume in one container |
| Geoboard-Isometric | Construct three-dimensional shapes |
| How High? | Explore the conservation of volume by pouring a liquid from a container to a differently shaped container |
| Platonic Solids | Manipulate solid figures to identify the number faces, vertices, and edges; explore Euler's Formula |
| Platonic Solids | Explore Euler's Formula |
| Platonic Solids-Duals | Manipulate five different dual platonic solids |
| Platonic Solids-Slicing | Visualize the intersection of a plane figure with a solid figure |
| Space Blocks | Construct figures with a given surface area |
Chapter 13 |
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| Bar Chart | Make a bar graph |
| Box Plot | Create box-and-whisker plots and histograms from data |
| Histogram | Create box-and-whisker plots and histograms from data |
Chapter 14 |
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| Box Model |
Model probability experiments, such as tossing a number cube or flipping a coin |
| Coin Tossing | Use a random generator to model tossing a coin repeatedly and recording the results |
| Hamlet Happens | Explore simulations of random experiments |
| Number Puzzles | Arrange numbers in positions in a diagram so that all numbers in a line add up to a given value |
| Peg Puzzle | Switch the pegs on the left with the pegs on the right |
| Spinners | Spin a spinner and record the results |
| Stick or Switch | Explore the probabilty of winning a "Let's Make a Deal" game |
| Towers of Hanoi | Move a stack of disks from one peg to another in the fewest moves |
| Whammy Awards | Explore 5 different voting schemes |
