teaching multiplication & division centre for excellence cluster of schools combined staff...
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NSW Department of Education & Training NSW Public Schools – Leading the Way Counting and grouping Counting Grouping Coordinating 3TRANSCRIPT
Teaching Multiplication & Division
Centre for Excellence cluster of schoolsCombined staff meetings
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
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
Multiplication & Division in the classroom
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Counting and grouping
Counting
Grouping
Coordinating
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NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Terminology
• Composite units
a set of items are treated spatially (visually) or numerically (abstractly)
as a unit
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
4 groups of 3
counting grouping
4 threes
coordinating
3333
Thinking groups - not items
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
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.
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NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Key concepts in Multiplication and Division
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
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?
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
What are the key concepts in multiplication & division?
Repeated addition Commutative property Associative property Inverse relationship mult/division
Key concepts
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
• 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
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Concrete Visual
Abstract 3 + 3 + 3 + 3 = 12
4 groups of 3 = 12
Key concepts – Repeated addition
x
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
• Commutative Property of Multiplication - it doesn’t matter which number is first.
3 x 4 = 12 4 x 3 = 12
Key concepts – Commutative Property
3 x 4 = 4 x 3
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Concrete Visual
Abstract - 3 x 4 = 4 x 3
Key concepts – Repeated addition Key concepts – Commutative Property
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Distributive Property
2 x 14 = 2 x (10 + 4) = (2 x 10) + (2 x 4) = 20 + 8
= 28
Key concepts – Distributive Property
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Concrete Visual
Abstract 12 x 2 = 24 12 2 x
Key concepts – Distributive Property
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Splitting the product into known parts.
8 x 7 = 7 x 7 = 49 8 x 7 = 49 + 7 8 x 7 = 56
Key concepts – Distributive Property
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Key concepts – Inverse relationships
3 x 4 = 12 12 ÷ 3 = 4
Division start with the total items.
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Repeated addition Commutative property Distributive property Inverse relationship
mult/division
Key concepts
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Deep Understanding
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• 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 8If 5 x 8 = 40Then 4 x 8 must equal 32
What is the answer to 9 x 3?Double 9 is 18,18 + 2 is 2020 + 7 is 27
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Concrete /Manipulatives
• Counters• Base 10 material• Pencils• Blocks• Egg cartons
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
• Arrays• Numberline• 100 chart
Visuals
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Visuals - Arrays
• Classroom tools – arrays
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Learning Object – The Array
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Learning object - Arrays: factor families
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Counting-On website
NSW Department of Education & TrainingNSW Public Schools – Leading the Way www.det.nsw.edu.au
Count Me In Too website