Standard #: MA.3.AR.2.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.2.2 
• MA.3.NSO.2.4 
• MA.3.AR.1.2

 

Terms from the K-12 Glossary

• Equation 
• Expression

 

Vertical Alignment

Previous Benchmarks

• MA.2.AR.2.2

 

Next Benchmarks

• MA.4.AR.2.2

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to find an unknown value represented by a symbol or letter in a multiplication or division equation, continuing the work from Grade 2, where students found unknown values in addition and subtraction equations. 

• Instruction that emphasizes the relationship between related facts in a fact family helps students use known values to solve for unknown values. For example, a fact family could be used to help students determine the unknown value in the equation 72 ÷ ? = 9 (MTR.5.1). 

• Students can use any of these related facts to determine that the unknown value is 8. Teachers should encourage students to use such equations to justify their solutions (MTR.6.1). 
• In the primary grades, students used fact families to find missing addends and understand the relationship between addition and subtraction. 
• Understanding and using related facts to solve for unknown values is an important algebraic understanding for using inverse operations to solve equations in future mathematics courses (MTR.5.1).

 

Common Misconceptions or Errors

• By Grade 3, many students expect the solutions of equations to be an expression on the right side of the equal sign. When students determine unknown values in multiplication or division equations, give examples with the product or quotient on the left side.

 

Strategies to Support Tiered Instruction

• Instruction includes opportunities to explore the meaning of the equal sign within the context of multiplication and division. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” supporting the understanding that the product and quotient can be on either the left or the right side of the equal sign. Multiple examples are provided for students to solve for the unknown with the product or quotient on both the left and right sides of the equation. The teacher uses the same equations written in different ways to reinforce the concept. 
  • For example, the teacher shows the following equations, asking students to solve for the unknown. Students explain why each equation is true after solving, repeating with additional examples. 

• Teacher provides opportunities to explore the meaning of the equal sign within the context of multiplication and division using visual representations (e.g., counters, drawings, base-ten blocks) to represent the equations. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” supporting the understanding that the product and quotient can be on either the left or the right side of the equal sign. Multiple examples are provided for students to solve for the unknown with the product or quotient on both the left and right sides of the equation, using the same equations written in different ways to reinforce the concept. 
  • For example, the teacher shows the following equations, asking students to solve for the unknown and explain why each equation is true after solving. Students use counters, drawings, or base-ten blocks to represent the equation, repeating with additional operations.

 

Instructional Tasks

Instructional Task 1 

Sam is having trouble deciding whether the value of $n$ that makes the equation below true is 4 or 36. Which number is correct? Show your thinking using an equation or array.