## Fundamentals of Algebra

Chapter 1
Abacus (operations)

Find simple sums or differences using an abacus

Base Blocks

Represent numbers in base 2, 3, 4, 5, or 10 using place-value models

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 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
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 Use a coordinate grid to locate shapes in two dimensions
Number Line Arithmetic Use a number line to visualize operations
Rectangle Multiplication Visualize the product of two factors using an array
Rectangle Multiplication of Integers Visualize the product of two integers

Chapter 2
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

Chapter 3
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

Chapter 4
Algebra Balance Scales-Negatives Solve simple linear equations with integers and one unknown using a balance scale
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

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
Money Make a dollar, calculate change, or make a specific amount using bills and coins
Rectangle Multiplication of Integers Visualize the product of two integers

Chapter 5
Factor Tree Find the prime factorization of one or two numbers
Fractions-Adding Add fractions with like and unlike denominators
Number Line Bars-Fractions Use adjustable color bars to illustrate arithmetic operations with fractions on a number line

Chapter 6
Converting Units Solve unit conversion problems or create your own
Fractions-Equivalent Recognize and generate equivalent forms of commonly used fractions

Chapter 7
Base Blocks Represent decimals through thousandths using place-value models
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
Fractions-Equivalent Recognize and generate equivalent forms of commonly used fractions
Fractions-Parts of a Whole Model commonly used fractions
Loan Calculator Explore the size of payments required to pay off a loan
Mastermind Use logical reasoning to discover the color sequence of 4 pegs
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

Chapter 8
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
Pie Chart Make circle graphs
Scatterplot Determine the line of best fit based on data entered
Venn Diagrams Explore the union and intersection of sets

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)
Fraction Pieces Manipulate fractional pieces of a circular or square region
Geoboard Color and make specific shapes
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
Pentominoes Make different figures using pentominoes, including congruent figures
Pie Chart Make circle graphs

Chapter 10
Coin Problem Find the counterfeit coin (light or heavy) in a set of identical coins
Factor Tree Find the prime factorization of one or two numbers
Geoboard Explore perimeter and area of regular and irregular shapes using a geoboard
Geoboard-Coordinate Explore inscribed parallelograms
Pattern Blocks Create various patterns of shape, including symmetrical patterns
Pentominoes Explore the perimeter of different pentominoes
Pythagorean Theorem Explore two proofs of the Pythagorean Theorem
Tessellations Form tessellations using different shapes

Chapter 11
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
Space Blocks Construct figures with a given surface area
Space Blocks Match nets with the appropriate solid figure

Chapter 12
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
Pascal's Triangle View number patterns or create your own
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

Chapter 13
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
Attribute Trains

Complete patterns of shapes, numbers, or colors

Fifteen Puzzle Move tiles around to arrange them in a specific pattern
Function Machine Explore the concept of a function using a function machine
Geoboard-Coordinate Find the slope of a line
Geoboad-Coordinate Construct reflections
Grapher Graph functions
Number Patterns Recognize patterns in number sequences
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
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 14
Algebra Balance Scales Solve simple linear equations with one unknown using a balance scale
Algebra Tiles Use algebra tiles to multiply and square binomials; factor polynomials; apply the Distributive Law