General Information
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Associative Property of Multiplication
- Commutative Property of Multiplication
- Distributive Property
- Factor
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to be able to state (recall) their multiplication and division facts in an effortless manner. This work builds on prior multiplication and related division fact strategy work from grade 3 (MA.3.NSO.2.4). Students also understand that multiplication is commutative and that the Distributive Property can be used to break more complex facts into easier ones.- To help reach the automaticity of multiplication and related division facts, the related concepts should be considered to be foundational. These concepts may be addressed during the exploration or procedural reliability stage (MA.3.NSO.2.4) of the benchmark progression.
- Multiplication by zeroes and ones
- Doubles (2s facts)
- Double and Double Again (4s)
- Doubling three times (8s)
- Tens facts (relating to place value, 5 × 10 is 5 tens or 50)
- Five facts (half of tens or connect to the analog clock)
- Skip counting (counting groups of __ and knowing how many groups have been counted)
- Square numbers (the physical and visual representation of these facts make a square; e.g., 3 × 3)
- Nines (10 groups less 1 group; e.g., 9 × 3 is 10 groups of 3 minus 1 group of 3 so 30– 3 = 27)
- Decomposing into known facts (6 × 7 is a double - 6 × 6 - plus one more group of 6)
- Elevens (10 groups and 1 group more; e.g., 11 × 5 is 10 groups of 5 plus 1 group of 5 so 50 + 5 = 55)
- Decomposing using the Distributive property (12 × 6 = (10 × 6) + (2 × 6) = (60) + (12) = 72)
- Throughout K-5 instruction, it is not recommended to use timed fact fluency assessments to learn and practice facts.
Common Misconceptions or Errors
- Many students have difficulty with multiplication and related division facts when teachers rely solely on memorization of facts. It is important that strategy work and conceptual understanding is the foundation of instruction for multiplication and division facts.
Strategies to Support Tiered Instruction
- Instruction includes building strategies and conceptual understanding to recall facts to find unknown multiplication facts by using known facts.
- For example, if students do not know the product for 9 × 12 have them use a known fact such as 10 × 12. The known fact of 10 × 12 = 120 can be used to find the product of 9 × 12 by subtracting one more group of 12 from the product of 120 to find the product of 108.
- For example, if students do not know the product for 6 × 7 have them use a known fact such as 5 × 7. The known fact of 5 × 7 = 35 can used to find the product of 6 × 7 by adding one more group of 7 to the product of 35 to find the product of 42.
- Instruction includes building strategies and conceptual understanding to recall facts to find unknown division facts by using known multiplication facts.
- For example, if students do not know the quotient for 121 ÷ 11 have them think about how many groups of 11 equal 121. Have students write the problem as a missing factor problem __ × 11 = 121 to help use multiplication facts to find the quotient. Students can also use known multiplication facts to solve: 10 groups of 11 is 110 and one more group of 11 equals 121 so 121 ÷ 11 equals 11.
- For example, if students do not know the quotient for 45 ÷ 5 have them think about how many groups of 5 equal 45. Have students write the problem as a missing factor problem ___ × 5 = 45 to help use known multiplication facts to find the quotient.
Instructional Tasks
Instructional Task 1 (MTR.5.1)
- Explain how the 2s facts, 4s facts, and 8s facts for multiplication are related.
Instructional Items
Instructional Item 1
Select all the true equations.- a. 11=132÷11
- b. 7×12=84
- c. 56=7×7
- d. 49÷7=7
- e. 6×11=66