Multiplication & Division: Strategies & Basic Facts
Develop multiplicative reasoning and generalized strategies in a pathway to fluency with multiplication and division basic facts
Learning Goal Description
Multiplicative reasoning involves the mental coordination of equal groups and “groups of groups.” This reasoning can lead to the development of multiplicative strategies grounded in quantitative connections. The learning progression includes building knowledge for foundational factors, using this knowledge to reason about other factors, generalizing these relationships, and building automaticity. This approach to coordinating groups supports learning in other mathematics domains such as fractions and algebraic reasoning.
Students should have facility with forming and counting equal groups. These students are likely to solve multiplication and division tasks using repeated addition and subtraction. Students should have knowledge of combinations and partitions as used for non-count-by-one strategies for addition and subtraction to 20. (see Ready Set Math modules Multiplication and Division: Counting-based Strategies and Addition and Subtraction: Strategies and Basic Facts to 20)
Sub-goal A : Develop automaticity for multiplication and division with 2s and 10s
Ask students to solve multiplication tasks involving factors of 2 and 10 (e.g., Present written tasks such as 2 x 8, 4 x 2, 2 x __ = 12, 10 x 6, 3 x 10, __ x 10 = 70)
Ask students to solve division tasks involving factors of 2 and 10 (e.g., Present written tasks such as 6 ÷ 2, 16 ÷ 2, 14 ÷ 7, 12 ÷ __= 2, 70 ÷ 10, 30 ÷ 3, 80 ÷ __= 10)
If students are not successful or count by ones to solve, consider instruction focusing on counting-based strategies for multiplication and division (see Ready Set Math module Multiplication and Division: Counting-based Strategies). If students are successful but are not fluent or need to count in multiples to solve, the resources for this sub-goal can support designing instruction to develop automaticity with these factors.
Wright, R. J., Stanger, G., Stafford, A. K., & Martland, J. (2015). Teaching number in the classroom with 4-8 year olds (2nd ed.). London: Sage Publications, Ltd. (Chapter 8 & 9)
Wright, R. J., Ellemor-Collins, D., & Tabor, P. D. (2012). Developing number knowledge: Assessment, teaching & intervention. London: Sage Publications, Ltd. (Chapter 6)
The knowledge developed in this module relates well with learning mental strategies for 2-digit addition and subtraction.
(see Ready Set Math module Addition and Subtraction to 100: Mental Strategies)
Consideration should also be given to early learning for fractions.
(see Ready Set Math module Fractions: Part Whole and Fractions: Fractions as Measures)
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