Formative Assessments

Generating Equivalent Expressions # Students are asked to write equivalent expressions using the Distributive Property.
Equal Sides, Equivalent Expressions # Students are asked to generate and justify an expression equivalent to a given one using the properties of operations.
Associative and Commutative Expressions # Students are asked to write expressions equivalent to a given one by using the Associative and Commutative Properties.

Lesson Plans

Extending the Distributive Property # In this lesson, students will build upon their arithmetic experiences with the distributive property to equate algebraic expressions through a series of questions related to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for moving the concrete learner to the abstract level and the use of matching cards.
This is an introductory lesson that only includes producing equivalent expressions such as 3(2 + x) = 6 + 3x.
Collectively Collecting # In this lesson, students will examine and experience collecting like terms through an analogy to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for transitioning a concrete experience to the abstract level and a card-matching activity.
Interpreting Algebraic Expressions # This lesson unit is intended to help you assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help you to identify and support students who have difficulty in recognizing the order of algebraic operations, recognizing equivalent expressions and understanding the distributive laws of multiplication and division over addition (expansion of parentheses).
Have You Met Your Match?-Understanding Equivalent Expressions # In this lesson, students will use the properties of operations to generate and identify equivalent algebraic expressions. Students will apply their prior knowledge of the distributive property and combining like terms to create equivalent algebraic expressions. The hands-on memory "match" game will engage students and support student understanding of algebraic thinking.
The Distributive Property # Introductory lesson on the distributive property using word problems as context for area models.

Original Student Tutorial

MacCoder's Farm Part 4: Repeat Loops # Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities. Click below to check out the other tutorials in the series.

Problem-Solving Tasks

Rectangle Perimeter 3 # The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.
Watch out for Parentheses # This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses.
Anna in D.C. #
Students solve a multi-step percent problem involving sales tax and tip. They are asked to find the original cost of a meal before tax and tip when given the total cost. The task highlights real-world applications of percent increase and can be solved through reasoning with ratios, division, or algebra.

Tutorials

Applying Arithmetic Properties with Negative Numbers # In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.
The Distributive Law of Multiplication over Addition # Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.
The Distributive Law of Multiplication over Subtraction # Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.
How to Use the Distributive Property with Variables # Learn how to apply the distributive property to algebraic expressions.
How to Simplify an Expression by Combining Like Terms # Students will simplify an expression by combining like terms.
How to Combine Like Terms # This tutorial is an explanation on how to combine like terms in algebra.
Combining Like Terms Introduction # This is an introduction to combining like terms in this tutorial.
Pre-Algebra - Associative & Distributive Properties of Multiplication # Take a look at the logic behind the associative and distributive properties of multiplication.
Pre-Algebra - Commutative & Associative Properties of Addition # A look behind the fundamental properties of the most basic arithmetic operation, addition
Pre-Algebra - Commutative Property of Multiplication # The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.

Video/Audio/Animation

How to Use the Distributive Property to Factor Out the Greatest Common Factor # Learn how to apply the distributive property to factor numerical expressions.