Multiplication & Division: Strategies & Basic Facts

Overview

Learning Goal

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.

Pre-Requisite Knowledge

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

See Instructional Resources
Multiplication and division with 2s and 10s is an attainable early goal for most students. Using 2 as a factor links to knowledge for doubles and using 10 as a factor relates to base-10 knowledge. These facts become important reference points for learning other facts. The instructional resources provide opportunities to develop fluency with these basic facts.

  1. 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)

  2. 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.

Sub-goal B

Purchase the module to unlock this Description.
Purchase the module to unlock this Student Knowledge Check.

Sub-goal C

Purchase the module to unlock this Description.
Purchase the module to unlock this Student Knowledge Check.

Sub-goal D

Purchase the module to unlock this Description.
Purchase the module to unlock this Student Knowledge Check.
Math Recovery Purple Book

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)

Math Recovery Red Book

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)  

 

© 2022 US Math Recovery Council®. All rights reserved. Permission is hereby granted for individual use only to support student learning. No other part of this product may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the written permission of the US Math Recovery Council®.