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36 x 25 Strategies versus recall Understandings mental? Sequence - PDF document

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31/07/2019 Developing a Whole School Approach to Mental Computation Day 2 Basic Facts Milestones for Multiplication and Division Dr Paul Swan and David Dunstan www.drpaulswan.com.au | 1 2 Key Ideas Expectations 36 x 25 Strategies

  1. 31/07/2019 Developing a Whole School Approach to Mental Computation Day 2 – Basic Facts Milestones for Multiplication and Division Dr Paul Swan and David Dunstan www.drpaulswan.com.au | 1 2 Key Ideas Expectations 36 x 25 • Strategies versus recall • Understandings mental? • Sequence and pre-requisites www.drpaulswan.com.au | www.drpaulswan.com.au | 3 4 Facts & Understandings Doubling and Halving 36 x 25 ��� � �� � �� �� ��� � �� ��� Halve x double ��� � �� �� �� � �� �� �� �� �� �� � ��� � �� �� � � �� �� ����� � 18 x 50 �� �� �� �� �� � � ���� ��� � ��� �� �� ��� �� � � � � � �� Halve x double �� �� ���� � ���� � � �� ����� 9 x 100 • 36 x 25 www.drpaulswan.com.au | www.drpaulswan.com.au | 5 6 1

  2. 31/07/2019 Pre - requisites Factors and properties of number 36 x 25 • Trigger number (25) • Double and halve strategy 4 x 9 x 25 (why not 6 x 6 x 25?) • Number Sense • Strategies 9 x 4 x 25 (property?) • Bank of facts 9 x (4 x 25) 9 x 100 www.drpaulswan.com.au | www.drpaulswan.com.au | 7 8 36 x 25 Multiplication & Division • What is going wrong? • How do you teach • How do children learn tables? • Teaching vs testing www.drpaulswan.com.au | www.drpaulswan.com.au | 9 10 Learning a new set of multiplication Learning the 18 x Table facts • 18 x table • What would 10 x 18 =? • Can I work out 5 x 18? • What do we know? • What facts have I worked out • 0 x 18 = 18 • 1 x 18 • 1 x 18 = 18 • 2 x 18 • What strategies can we use to derive more? • 4 x 18 • 5 x 18 • Doubling • 8 x 18 • 10 x 18 • 1 x 18 = 18 • Can I work out 3 x 18, 6 x 18, 9 x 18 • Double • 2 x 18 = 36 • What different strategies could I use? • Could I become fluent? • What would 4 x 18 =? • What about 8 x 18? www.drpaulswan.com.au | www.drpaulswan.com.au | 11 12 2

  3. 31/07/2019 Plan - Milestones AC: Basic facts x ÷ (Year 2) • What are the expectations? 1. “Lots of” • When do they need to know them? • How will we know they’ve got it? 2. “Groups of” Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 13 www.drpaulswan.com.au | 13 14 AC: Basic facts x ÷ AC: Basic facts x ÷ (Year 2) (Year 3) 3. Array model understanding of multiplication. Yr 3 ACMNA056 • Recall multiplication facts of two, three, 4 rows of 3 five and ten and related division facts. 3 rows of 4 Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 15 Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 16 15 16 Multiplication property Connected Chart of zero Factor • Factor Factor Product • 21 facts 0 x 0, 0 x 1, 0 x 2, 0 x 3, 0 x 4, 0 x 5, x 0 1 2 3 4 5 6 7 8 9 10 Factor 0 x 6, 0 x 7, 0 x 8, 0 x 9 0 x 10 and related 0 0 0 0 0 0 0 0 0 0 0 0 facts 1 0 1 2 3 4 5 6 7 8 9 10 x 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 6 9 12 15 18 21 24 27 30 1 0 1 2 3 4 5 6 7 8 9 10 4 0 4 8 12 16 20 24 28 32 36 40 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 9 12 15 18 21 24 27 30 5 0 5 10 15 20 25 30 35 40 45 50 4 0 4 8 12 16 20 24 28 32 36 40 6 0 6 12 18 24 30 36 42 48 54 60 5 0 5 10 15 20 25 30 35 40 45 50 7 0 7 14 21 28 35 42 49 56 63 70 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 8 0 8 16 24 32 40 48 56 64 72 80 9 0 9 18 27 36 45 54 Product 63 72 81 90 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au | www.drpaulswan.com.au | 17 18 3

  4. 31/07/2019 Multiplication Grid paper: Arrays property of one 19 new facts: x 0 1 2 3 4 5 6 7 8 9 10 • 1 x 1, 0 0 0 0 0 0 0 0 0 0 0 0 • 1 x 2, 1 0 1 2 3 4 5 6 7 8 9 10 • 1 x 3, 2 0 2 4 6 8 10 12 14 16 18 20 • 1 x 4, 3 0 3 6 9 12 15 18 21 24 27 30 • 1 x 5, 4 0 4 8 12 16 20 24 28 32 36 40 5 0 5 10 15 20 25 30 35 40 45 50 • 1 x 6, 6 0 6 12 18 24 30 36 42 48 54 60 • 1 x 7, 7 0 7 14 21 28 35 42 49 56 63 70 • 1 x 8, 8 0 8 16 24 32 40 48 56 64 72 80 • 1 x 9, 9 0 9 18 27 36 45 54 63 72 81 90 • 1 x 10 10 0 10 20 30 40 50 60 70 80 90 100 • and related facts www.drpaulswan.com.au | www.drpaulswan.com.au | 19 20 Commutative Property x2 Facts of Multiplication • Each fact is related, that is 4 x 3 produces • Relate to doubles addition facts (Year 2) the same result as multiplying 3 x 4 x 0 1 2 3 4 5 6 7 8 9 10 4 rows of 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 9 12 15 18 21 24 27 30 4 0 4 8 12 16 20 24 28 32 36 40 3 rows of 4 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au | Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 22 21 22 x5 and x10 facts Exposure to Doubling Ideal time to introduce: • Halving x 0 1 2 3 4 5 6 7 8 9 10 • Doubling 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 Five rows of 4 Five rows of 2 3 0 3 6 9 12 15 18 21 24 27 30 4 0 4 8 12 16 20 24 28 32 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 Ten rows of 2 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 23 www.drpaulswan.com.au | 23 24 4

  5. 31/07/2019 x3 Facts Array Game • Page 40 Tackling Tables • See Tackling tables p. 32 - 33 www.drpaulswan.com.au | www.drpaulswan.com.au | 25 26 Strategy: Relate to a known fact Calculation in NAPLAN • Implies that students have learned some facts • Askew, M. (1998). Teaching primary mathematics: A guide for newly qualified and student teachers. London: Hodder & Stoughton KNOWN NUMBER FACTS HELP BUILD ARE USED TO MORE DERIVE NUMBER FACTS ����� �� � �� �� �� Askew, M. (1998). Teaching primary mathematics: A guide for newly qualified and student teachers. London: Hodder & Stoughton. www.drpaulswan.com.au | www.drpaulswan.com.au | 27 28 Start of Yr 4 What to do in Year 4 • 2 – 4 weeks review of: • Facts to be learned in Yr 4 x 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 • addition and subtraction facts 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 • 2, 3, 5 and 10 facts 3 0 3 6 9 12 15 18 21 24 27 30 • Assess 4 0 4 8 12 16 20 24 28 32 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 36 42 48 54 60 7 0 7 14 21 28 35 42 49 56 63 70 8 0 8 16 24 32 40 48 56 64 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au | Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 30 29 30 5

  6. 31/07/2019 What number facts Year 4? Connection to Division • Recall multiplication facts to 10 x 10 (ACMNA075) • Factor Factor Product Cards • Use known multiplication facts to calculate related division facts • Develop efficient mental … strategies for x and ÷ (no remainder) (ACMNA076) • Using known facts and strategies such as commutativity, doubling and halving and connect to division www.drpaulswan.com.au | Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 32 31 32 Multispin, Spindiv & Race Car Rally Division - Sharing (Partition) 2, 3, 5 • The number of groups is known • The size of each group is found by a process of sharing Sharing Problem • There are 18 bananas in a bunch • Three people will share them • How many for each person? www.drpaulswan.com.au | www.drpaulswan.com.au | 33 34 Recording the operation Quotition (repeated subtraction) -uses arrays • The size of each group is known 18 divided by 3 6 • The number of groups is found by a process of repeated subtraction ) (quotition) 3 Quotition Problem: • There are 18 sunflowers • Three flowers are to be placed in each vase • How many vases are needed? www.drpaulswan.com.au | www.drpaulswan.com.au | 35 36 6

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