ALEX Resources

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Learning Activities (1) Building blocks of a lesson plan that include before, during, and after strategies to actively engage students in learning a concept or skill. Classroom Resources (2)

ALEX Learning Activities  
   View Standards     Standard(s): [MA2019] REG-7 (7) 7 :
7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
[DLIT] (7) 33 :
27) Identify data needed to create a model or simulation of a given event.

Examples: When creating a random name generator, the program needs access to a list of possible names.

Subject: Mathematics (7), Digital Literacy and Computer Science (7)
Title: Balancing Act

In this activity, students will create equivalent expressions using an online tool. Students are provided two expressions and asked to find the value of the variable to make the two expressions equal. Then, students are provided an expression and a value of the variable and asked to generate a different expression equal to the original expression. Through the online digital tool, students are able to substitute values and develop strategies for creating equivalent expressions. This provides a great opportunity for students to investigate how to solve problems using multiple methods.

Balancing Act Student Response Page

ALEX Learning Activities: 1

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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] (7) 6 :
6 ) Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7-NS3]

[MA2019] REG-7 (7) 7 :
7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
[MA2019] REG-7 (7) 9 :
9. Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.
Subject: Mathematics (7), Mathematics (7)
Title: Grade 7 Mathematics Module 2, Topic C: Applying Operations With Rational Numbers to Expressions and Equations

In Module 2, Topic C, students problem-solve with rational numbers and draw upon their work from Grade 6 with expressions and equations (6.EE.A.2, 6.EE.A.3, 6.EE.A.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7). They perform operations with rational numbers (7.NS.A.3), incorporating them into algebraic expressions and equations. They represent and evaluate expressions in multiple forms, demonstrating how quantities are related (7.EE.A.2). The Integer Game is revisited as students discover “if-then” statements, relating changes in player’s hands (who have the same card-value totals) to changes in both sides of a number sentence. Students translate word problems into algebraic equations and become proficient at solving equations of the form px + q = r and p(x + q) = r, where p, q, and r, are specific rational numbers (7.EE.B.4a). As they become fluent in generating algebraic solutions, students identify the operations, inverse operations, and order of steps, comparing these to an arithmetic solution. The use of algebra to represent contextual problems continues in Module 3.

   View Standards     Standard(s): [MA2019] REG-7 (7) 6 :
6. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
[MA2019] REG-7 (7) 7 :
7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
Subject: Mathematics (7)
Title: Grade 7 Mathematics Module 3, Topic A: Use Properties of Operations to Generate Equivalent Equations

To begin Module 3, students will generate equivalent expressions using the fact that addition and multiplication can be done in any order with any grouping and will extend this understanding to subtraction (adding the inverse) and division (multiplying by the multiplicative inverse) (7.EE.A.1). They extend the properties of operations with numbers (learned in earlier grades) and recognize how the same properties hold true for letters that represent numbers. Knowledge of rational number operations from Module 2 is demonstrated as students collect like terms containing both positive and negative integers.

An area model is used as a tool for students to rewrite products as sums and sums as products and can provide a visual representation leading students to recognize the repeated use of the distributive property in factoring and expanding linear expressions (7.EE.A.1). Students examine situations where more than one form of an expression may be used to represent the same context, and they see how looking at each form can bring a new perspective (and thus deeper understanding) to the problem. Students recognize and use the identity properties and the existence of inverses to efficiently write equivalent expressions in standard form (2x + (-2x) + 3 = 0 + 3 = 3)(7.EE.A.2). By the end of the topic, students have the opportunity to practice Module 2 work on operations with rational numbers (7.NS.A.1, 7.NS.A.2) as they collect like terms with rational number coefficients (7.EE.A.1).

ALEX Classroom Resources: 2

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