Addition & Subtraction: Counting-based Strategies

Overview

Learning Goal

Develop advanced counting-based strategies for addition and subtraction

Learning Goal Description

Early approaches to addition and subtraction typically involve counting-based strategies. This involves determining quantities and performing operations by coordinating a sequence of number words with the items being counted. The learning progression includes tasks involving visible collections, screened collections, contextual problems, and numerical expressions. Sequences of tasks support the development of increasingly sophisticated counting-based strategies. These counting-based approaches precede the development of non-count-by-one strategies and basic fact knowledge for addition and subtraction.

Pre-Requisite Knowledge

Students should have fluency with forward and backward number word sequences and numeral identification to at least 20. Students should have initial knowledge of finger patterns and regular spatial patterns. Students should be able to count visible items to determine the numerosity for a single collection up to 20. (see Ready Set Math module Early Numeracy: Words, Symbols, and Quantities)

Sub-goal A : Solve addition tasks with items available

See Instructional Resources
Using items to solve addition tasks initially involves counting from one, by ones. The total for two collections of items can be found by associating each number word in sequence with one, and only one, item. The last number word in the count tells how many. The instructional resources provide opportunities to engage students in counting to add two visible collections.

  1. Ask students to find the total for two collections of items with the items visible and available to manipulate (e.g., [Present unorganized collections of counters.] Here are 9 blue counters and here are 5 red counters. How many counters are there altogether?)

If students are not successful, check first to see if they can count a single collection and have facility with the number words sequence to support the counting. If so, the resources for this sub-goal can provide support in designing instruction for counting visible items to solve addition tasks.

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 4 & 6)

The knowledge developed in this module can support the development of non-counting strategies for addition and subtraction in the range to 10. 

(see Ready Set Math module Addition & Subtraction to 10: Strategies and Basic Facts) 

 

Consideration should also be given to early learning for place value. 

(see Ready Set Math module Place Value: Counting Involving Base-10 Units) 

© 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®.