## Foundations of Algebra

Chapter 1
Base Blocks

Represent whole numbers through thousands using place-value models

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
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
Pythagorean Theorem Explore two proofs of the Pythagorean Theorem

Chapter 3
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
Function Machine Explore the concept of a function using a function machine
Rectangle Multiplication of Integers Visualize the product of two integers

Chapter 4
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
Rectangle Multiplication of Integers Visualize the product of two integers

Chapter 5
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
Rectangle Multiplication Visualize the product of two factors using an array

Chapter 6
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
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
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
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
Geoboard Explore perimeter and area of regular and irregular shapes using a geoboard
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
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
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
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
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