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Explore effective teaching strategies for multiplication and division concepts in the classroom. Discover key concepts such as repeated addition, commutative property, distributive property, and inverse relationships. Enhance students' deep understanding through concrete manipulatives and visual aids.
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Teaching Multiplication & Division Centre for Excellence cluster of schools Combined staff meetings NSW Department of Education & Training NSW Public Schools – Leading the Way www.det.nsw.edu.au
Multiplication & Division in the classroom In groups/pairs discuss • What does teaching Multiplication & Division look like in my classroom? • What do I already know about how students learn to multiply and divide? • Share
Counting and grouping Coordinating Grouping Counting 3
Terminology • Composite units a set of items are treated spatially (visually) or numerically (abstractly) as a unit
3 3 3 3 Thinking groups - not items 4 groups of 3 counting grouping 4 threes coordinating
Background notes Some students persist with counting by ones and have difficulty in progressing to grouping strategies By focusing on groups, rather than individual items, students learn to treat the groups as composite units. 6
Teaching Key concepts • In our Explicit teaching part of the lesson how do we ensure deep understanding of the concept? • How do we teach concepts? • What are the key ideas?
Key concepts What are the key concepts in multiplication & division? • Repeated addition • Commutative property • Associative property • Inverse relationship mult/division
Key concepts – Repeated addition • Repeated addition - Multiplication is a fast way of adding a series of numbers 3 + 3 + 3 + 3 = 12 (Division – repeated subtraction)
Key concepts – Repeated addition Concrete Visual Abstract 3 + 3 + 3 + 3 = 12 4 groups of 3 = 12 x
Key concepts – Commutative Property • Commutative Property of Multiplication - it doesn’t matter which number is first. 3 x 4 = 12 4 x 3 = 12 3 x 4 = 4 x 3
Key concepts – Commutative Property Key concepts – Repeated addition Concrete Visual Abstract - 3 x 4 = 4 x 3
Key concepts – Distributive Property Distributive Property 2 x 14 = 2 x (10 + 4) = (2 x 10) + (2 x 4) = 20 + 8 = 28
Key concepts – Distributive Property Concrete Visual Abstract 12 x 2 = 24 12 2 x
Key concepts – Distributive Property Splitting the product into known parts. 8 x 7 = 7 x 7 = 49 8 x 7 = 49 + 7 8 x 7 = 56
Key concepts – Inverse relationships 3 x 4 = 12 12 ÷ 3 = 4 Division start with the total items.
Key concepts • Repeated addition • Commutative property • Distributive property • Inverse relationship mult/division
Deep Understanding Students who understand how to coordinate composite units are able to make efficient use of known facts What is the answer to 8 x 4? 8 x 4 is the same as 4 x 8 If 5 x 8 = 40 Then 4 x 8 must equal 32 What is the answer to 9 x 3? Double 9 is 18, 18 + 2 is 20 20 + 7 is 27 19
Concrete /Manipulatives • Counters • Base 10 material • Pencils • Blocks • Egg cartons
Visuals • Arrays • Numberline • 100 chart 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0
Visuals - Arrays • Classroom tools – arrays
