Sub-goal C: Solve multiplication tasks using counting-based strategies
Counting-based strategies for multiplication involve conceiving of a group of individual items as a composite unit (a new unit made up of individual unit items) and iterating (repeating) that unit a specified number of times. The instructional resources promote counting in multiples (involving 2s, 5s, 3s, and 4s) to solve multiplication tasks, simultaneously keeping track of the number of groups, the number of items in each group and the total number of items. Tasks advance from visible materials, to screen materials, to the absence of materials. (Note: The goal across this module is not to automatize multiplication and division for 2s, 5s, 3s, and 4s, but rather, to use these multiples as a means for developing strategies that involve iterating and keeping track. Larger multiples are not emphasized because they involve long counts and can be better handled with other strategies.)
Home Communication and Engagement
Large Group
Instructional Activities
Equal-Sized Groups: Groups and Items Visible
Activity 7-C-L-1Purpose: Solve multiplication as repeated equal groups with groups and individual items visible using real world applications
Description: Students explore tasks involving visible equal-sized groups using real world applications.
Equal-Sized Groups: Groups Visible and Items Screened
Activity 7-C-L-2Purpose: Solve multiplication as repeated equal groups with groups visible and individual items screened using real world applications
Description: Students engage in tasks involving partially screened equal-sized groups using real world applications.
Equal-Sized Groups: Screened
Activity 7-C-L-3Purpose: Solve multiplication as repeated equal groups with groups and individual items not visible using real world applications
Description: Students engage in tasks involving fully screened equal-sized groups using real world applications.
Hidden Arrays
Activity 7-C-L-4Purpose: Solve multiplication problems with partially screened arrays using real world applications
Description: Students engage in finding the total when the groups are partially or fully screened using real world applications.
Exploring Multiplication
Activity 7-C-L-5Purpose: Solve multiplication as repeated equal groups involving contextual situations
Description: Students solve real world problems that involve repeated equal groups.
Small Group
Instructional Activities
Incrementing and Decrementing by Composite Units
Activity 7-C-S-1Purpose: Increment and decrement by composite units of 2s, 5s, 3s, and 4s
Description: Students increment and decrement in multiples
N-Groups: Visible
Activity 7-C-S-2Purpose: Solve multiplication as repeated equal groups with groups and individual items visible
Description: Students engage in tasks involving visible equal-sized groups.
N-Groups: Groups Visible and Items Screened
Activity 7-C-S-3Purpose: Solve multiplication as repeated equal groups when group items are not fully visible
Description: Students find the total by counting equal sized groups when the groups are fully visible with individual items screened.
N-Groups: Screened
Activity 7-C-S-4Purpose: Solve multiplication as repeated equal groups when individual items and groups are not visible
Description: Students determine the total by counting when the groups and group items are not visible.
Arrays: Visible
Activity 7-C-S-5Purpose: Solve multiplication as repeated equal groups with visible arrays
Description: Students determine the total through counting when the array is visible.
Arrays: Partially Screened
Activity 7-C-S-6Purpose: Solve multiplication as repeated equal groups when individual items are not fully visible
Description: Students find the total when group items are partially visible.
Arrays: Fully Screened
Activity 7-C-S-7Purpose: Solve multiplication as repeated equal groups when groups and individual items are not visible
Description: Students find the total when the groups and group items are not visible.
Multiplication: Screened Arrays and Expressions
Activity 7-C-S-8Purpose: Connect visual representation of an array for multiplication with the corresponding written expression
Description: Students determine the total of a screened array and connect the array to a written expression.
Building and Solving Arrays with Written Expressions
Activity 7-C-S-9Purpose: Connect visual representation of an array for multiplication with the corresponding written expression
Description: Students build arrays using n-tiles from a given written expression.
Number Battle with N-Tiles
Activity 7-C-S-10Purpose: Solve multiplication as repeated equal-sized groups involving visible arrays
Description: Students use n-tiles to create an array of a specified size and then determine the total number of dots.
Independent
Instructional Activities
Number Battle with N-Groups
Activity 7-C-I-1Purpose: Solve multiplication as repeated equal groups with screened groups and individual items
Description: Students will describe and create a collection of n-group cards using a multiplicative count to determine the total.
Multiplication Memory Match
Activity 7-C-I-2Purpose: Solve multiplication equal grouping problems with n-groups
Description: Students practice determining the number of dots in the context of n-groups when given total number of groups and how many dots in each group.
Number Battle with Arrays
Activity 7-C-I-3Purpose: Solve multiplication as repeated equal groups with arrays
Description: Students practice determining number of dots in an array when given the number of rows and how many in each row.
Array (N-Tiles) Game
Activity 7-C-I-4Purpose: Solve multiplication as repeated equal groups with arrays
Description: Students take turns rolling dice and building arrays on the Array (N-Tiles) Board.
© 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®.