Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Area Model
- Commutative Property of
- Rectangular Array
Purpose and Instructional Strategies
The purpose of this benchmark is for students to build a conceptual understanding of what multiplication is and how it relates to division. Because the expectation of this benchmark is at the explore level, instruction should focus on building an understanding of multiplication and division facts from 0 to 144 using manipulatives (e.g., counters), visual models (e.g., rectangular arrays, equal groups), discussions, estimation and drawings (e.g., rectangular arrays, equal groups) (MTR.2.1).
- 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 Task 1
- 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.
Instructional Item 1
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
- 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