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# 2.5 Commutativity (part 2), doubling and halving

Created on 27 February 2019 by ncetm_administrator
Updated on 28 February 2019 by ncetm_administrator

## Introduction

Explore how one multiplication equation can have two different grouping interpretations (e.g., an equation from the two times table can be interpreted in terms of groups of two, or two equal groups); make connections between the two times table, doubling and halving.

## Teaching points

• Teaching point 1: The same multiplication equation can have two different grouping interpretations. Problems about two/five/ten equal groups can be solved using facts from the two/five/ten times table. (commutativity)

• Teaching point 2: If two is a factor, knowledge of doubling facts can be used to find the product; problems about doubling can be solved using facts from the two times table.

• Teaching point 3: Halving is the inverse of doubling; problems about halving can be solved using facts from the two times table and known doubling facts.

• Teaching point 4: Products in the ten times table are double the products in the five times table; products in the five times table are half of the products in the ten times table.

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