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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
Related Courses
Related Access Points
Related Resources
Educational Games
Educational Software / Tool
Lesson Plans
Perspectives Video: Experts
Perspectives Video: Teaching Idea
Problem-Solving Task
Student Center Activities
Teaching Ideas
Worksheets
STEM Lessons - Model Eliciting Activity
This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.
Student Resources
Educational Games
This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.
Type: Educational Game
This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.
Various levels of difficulty make this game appropriate for multiple age and ability levels.
Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.
Multiplication/Division: The multiplication and addition of whole numbers.
Percentages: Identify the percentage of a whole number.
Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.
Type: Educational Game
Educational Software / Tool
In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Educational Software / Tool
Parent Resources
Perspectives Video: Experts
Explore strategies students may use to solve basic multiplication problems and ways to support their understanding by watching this video.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Perspectives Video: Expert
Explore strategies students may use to solve basic division problems and ways to support their understanding in this video.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Perspectives Video: Expert
Problem-Solving Task
The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.
Type: Problem-Solving Task
Student Center Activities
In this game, students develop fluency with addition or multiplication facts and strengthen number sense through fast-paced problem-solving.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
In this game, students develop fluency with counting sequences and number patterns and strengthen number sense through movement, rhythm, and voice modulation while also practicing active participation and listening skills.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
Teaching Idea
This guide offers five practical strategies to help after-school providers support meaningful, low-pressure math experiences that lead to deeper understanding and better long-term outcomes for K-5 students.
Type: Teaching Idea
Worksheets
Division Flash Cards Related to Multiplication through 12 x 12
Type: Worksheet
Division Flash Cards Related to Multiplication with Single Digit Numbers
Type: Worksheet
Multiplication Flash Cards through 12 x 12
Type: Worksheet
