Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Commutative property of multiplication
- Associative property of multiplication
- Distributive property of multiplication
Purpose and Instructional Strategies
The purpose of this benchmark is for students to utilize skills from the exploration stage of multiplication and division (MA.3.NSO.2.2
) to develop an accurate, reliable method that aligns with the student’s understanding and learning style. Procedural fluency of multiplication facts with factors up to 12 and their related division facts is not expected until Grade 4 (MTR.2.1, MTR.3.1).
- This benchmark provides the opportunity for students to generalize patterns they see within the tools used during the exploration stage (e.g., rectangular arrays, equal groups) to then identify multiplication and related division facts (MTR.4.1).
- Instruction that builds procedural reliability should connect multiplication understanding with the properties of multiplication (commutative, associative and distributive). The patterns students recognize help them relate facts to one another, and to use the related facts to find the products and quotients of unknown facts. In this benchmark, students should be able to explain how they know facts and how they can find products of unknown facts (MTR.5.1). For example, students should recognize that 4 x 6 and 6 x 4 have the same product of 24 and identify this pattern as evidence of the commutative property of multiplication. This can also be discovered through arrays for multiplication using objects or drawings, where students can observe that the arrays contain the same total number of squares, but the orientation of the array has just rotated so the rows and columns are switched as shown below (MTR.5.1).
Common Misconceptions or Errors
- This benchmark does not support students’ memorization of multiplication and division facts. Memorization does not indicate work toward multiplication and division fact fluency. Students should be able to explain how they know multiplication and division facts, and how they can find products and quotients of unknown facts.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to experience the properties of multiplication and division. Students use and apply properties to build procedural fluency. Students should understand that multiplication and division both involve grouping equal sets of numbers or objects.
- For example, the teacher shows students an array of 8 × 6 = 48 and has them describe what they see with rows and columns. This learning can be connected to the concept of “groups of” objects, 8 groups of 6 is the same as 8 jumps of 6 on the number line.
- Teacher provides opportunities to build and manipulate what a multiplication fact looks like and then relates how it looks as division.
- For example, students model 3 x 4 as 3 rows of 4 with counters.
- The teacher then relates the multiplication model to division by separating the rows into groups. 12 = 4 groups of 3 counters, or 12 divided by 4 = 3.
Instructional Task 1
- Part A. Show how to find the product of 6 × 7 in two different ways.
- Part B. Identify the related division facts from your equation in Part A.
Instructional Item 1
- What is the product of 11 and 4?
Instructional Item 2
- Provide two division facts that have a quotient of 8.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.