Standard #: MA.3.NSO.2.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.2.3
• MA.3.NSO.2.4 
• MA.3.AR.1.1
• MA.3.AR.1.2
• MA.3.AR.2.1 
• MA.3.AR.2.2 
• MA.3.AR.3.2
• MA.3.GR.2.2 
• MA.3.GR.2.3
• MA.3.GR.2.4

Terms from the K-12 Glossary

• Area Model 
• Commutative Property of Multiplication 
• Dividend 
• Divisor 
• Equal sign
• Equation 
• Expression 
• Factors 
• Rectangular Array
• Whole Number

Vertical Alignment

Previous Benchmarks

• MA.2.AR.3.2

Next Benchmarks

• MA.4.NSO.2.1

Purpose and Instructional Strategies

• Instruction should relate multiplication to repeated addition work that began in Grade 2. In Grade 2, students used repeated addition to find the total number of objects using rectangular arrays and equations (MA.2.AR.3.2). 
• Students should explore multiplication and division through word problems, writing expressions and drawing models that match the problems’ contexts (MTR.2.1, MTR.3.1). 
• In division, students should see examples of sharing, or partitive division (where the number of groups are given and students determine the number in each group), as well as measurement, or quotative division (where the number in each group is given and students determine the number of groups). 
• Instruction should relate division facts to known multiplication facts (e.g., fact families). Fact families can be explored through arrays and equal groups (MTR.5.1).

Common Misconceptions or Errors

• Students may have difficulty relating word problems and real-world scenarios to models, expressions, and equations. For example, students may not differentiate the number of groups versus the number in each group in multiplication, which then impacts their models, expressions, and equations. 
• Students may be confused by measurement (or quotative) division when the amount in each group is given and the number of equal-sized groups is found.

Strategies to Support Tiered Instruction

• Instruction includes demonstrating the use of counters, arrays, and skip counting to model groups of objects, including the use of real-world scenarios to support students’ understanding of the number of groups versus the size of each group. Students represent their models with equations to reinforce the concept of multiplication. 
  • For example, a farmer is planting rows of sunflowers. He plants 6 rows with 5 sunflowers in each row. How many sunflowers does he plant? 

• For example, there are 3 tables in the library. There are 4 students sitting at each table. How many students are sitting at tables in the library? 

• Instruction includes demonstrating the use of counters and arrays to model division problems where the amount in each group is given and the number of equal-sized groups is found. The teacher provides real-world scenarios to represent the number of objects in each group and the number of groups Students form a group based on the context of the problem continuing to form groups of that size until the total is reached. Students can skip counting to keep track of how many counters they have used, representing their models with equations to reinforce the concept of division. 
  • For example, Renee is setting up chairs in the library. She is placing 24 chairs into rows. If she places 6 chairs in each row, how many rows of chairs will she have? 

• For example, there are 15 students working on an art project. The art teacher divides them into groups of 3 students to work on the project. How many groups are there?

Instructional Tasks

Instructional Task 1 (MTR.3.1, MTR.7.1)

• Build 12×9 with place value blocks or counters.
• Part A. How would you solve for the product? What strategy did you use to solve the problem?
• Part B. Now build 9×12with place value block or counters. What is the product of 9×12? How did you see it?
• Part C. Draw a model for 9×12 or solve using a different strategy.

• There are 32 photos that need to be organized into a photo album. What are all the possible ways to display the photos on the pages of the album? Each page must have an equal number of photos. Use manipulatives, models, or equations to help you figure out all the possible combinations.

• Tina has 4 shelves on her bookshelf. Each row has 6 books. How many books are on Tina’s bookshelf in all? Draw a model and write an equation to represent your answer.

• Mateo goes to the grocery store with his dad to buy some fruit. The prices of the fruit are shown above.
  
  • Part A. Mateo’s dad buys 6 bags of grapes. Write an equation that represents how many grapes he bought.
  • Part B. Mateo’s dad also buys 4 bags of apples and 5 bags of oranges. Did he spend more money on apples or oranges? Explain how you know.
  • Part C. Mateo sees his friend Jeremy at the grocery store. Jeremy’s mom buys 7 bags of grapes and 5 bags of apples. How much more does she spend on apples than grapes? How do you know?

Instructional Items

• What expression equals 7 x 6?
  a. 6 + 6 + 6 + 6
  b. 6 + 6 + 6 + 6 + 6
  c. 6 + 6 + 6 + 6 + 6 + 6
  d. 6 + 6 + 6 + 6 + 6 + 6 + 6

• Elizabeth has 28 pairs of earrings that she wants to put into her jewelry organizer. Each drawer of the organizer holds 4 pairs of earrings. How many drawers will she need to organize all of her earrings?

Instructional Item 4 

• A total of 56 chairs are in the cafeteria for an assembly. The principal arranges the chairs into 8 rows with the same number of chairs in each. Which equation shows the quotient as the number of chairs that will be in each row? 
  • a. 56÷8=7 
  • b. 56÷8=48 
  • c. 56÷8=64 
  • d. 56÷8=6