Developing a Whole School Approach to Mental Computation Day 2 - PowerPoint PPT Presentation

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 |

Key Ideas • Strategies versus recall • Understandings • Sequence and pre-requisites www.drpaulswan.com.au |

Expectations 36 x 2 x 25 men ental? al? www.drpaulswan.com.au |

Facts & Understandings 25 is related to 100 36 is 4 x 9 4 x 9 = 9 x 4 Commutative property 9 x 4 x 25 I can do the 4 x 25 bit first 9 x 100. That is easy! • 36 x 25 www.drpaulswan.com.au |

Doubling and Halving 36 x 25 Halve x double 18 x 50 Halve x double 9 x 100 www.drpaulswan.com.au |

Pre - requisites • Trigger number (25) • Double and halve strategy • Number Sense • Strategies • Bank of facts www.drpaulswan.com.au |

Factors and properties of number 36 x 25 4 x 9 x 25 (why not 6 x 6 x 25?) 9 x 4 x 25 (property?) 9 x (4 x 25) 9 x 100 www.drpaulswan.com.au |

36 x 25 • What is going wrong? www.drpaulswan.com.au |

Multiplication & Division • How do you teach • How do children learn tables? • Teaching vs testing www.drpaulswan.com.au |

Learning a new set of multiplication facts • 18 x table • What do we know? • 0 x 18 = 18 • 1 x 18 = 18 • What strategies can we use to derive more? • Doubling • 1 x 18 = 18 • Double • 2 x 18 = 36 • What would 4 x 18 =? • What about 8 x 18? www.drpaulswan.com.au |

Learning the 18 x Table • What would 10 x 18 =? • Can I work out 5 x 18? • What facts have I worked out • 1 x 18 • 2 x 18 • 4 x 18 • 5 x 18 • 8 x 18 • 10 x 18 • Can I work out 3 x 18, 6 x 18, 9 x 18 • What different strategies could I use? • Could I become fluent? www.drpaulswan.com.au |

Plan - Milestones • What are the expectations? • When do they need to know them? • How will we know they’ve got it? Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 13

AC: Basic facts x ÷ (Year 2) 1. “Lots of” 2. “Groups of” www.drpaulswan.com.au |

AC: Basic facts x ÷ (Year 2) 3. Array model understanding of multiplication. 4 rows of 3 3 rows of 4 Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 15

AC: Basic facts x ÷ (Year 3) Yr 3 ACMNA056 • Recall multiplication facts of two, three, five and ten and related division facts. Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 16

Connected Chart Factor • Factor Factor Product x 0 1 2 3 4 5 6 7 8 9 10 Factor 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 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 Product 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au |

Multiplication property of zero • 21 facts 0 x 0, 0 x 1, 0 x 2, 0 x 3, 0 x 4, 0 x 5, 0 x 6, 0 x 7, 0 x 8, 0 x 9 0 x 10 and related facts x 0 1 2 3 4 5 6 7 8 9 10 10 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 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 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au |

Grid paper: Arrays www.drpaulswan.com.au |

Multiplication property of one 19 new facts: x 0 1 2 3 4 5 6 7 8 9 10 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 4 0 4 8 12 16 20 24 28 32 36 40 • 1 x 5, 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 10 0 10 20 30 40 50 60 70 80 90 100 • and related facts www.drpaulswan.com.au |

Commutative Property of Multiplication • Each fact is related, that is 4 x 3 produces the same result as multiplying 3 x 4 x 0 1 2 3 4 5 6 7 8 9 10 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 10 0 10 20 30 40 50 60 70 80 90 100 www.drpaulswan.com.au |

x2 Facts • Relate to doubles addition facts (Year 2) Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 22

x5 and x10 facts Ideal time to introduce: • Halving x 0 1 2 3 4 5 6 7 8 9 10 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 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 9 0 9 18 27 36 45 54 63 72 81 90 10 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

Exposure to Doubling Five rows of 4 Five rows of 2 Ten rows of 2 www.drpaulswan.com.au |

x3 Facts • Page 40 Tackling Tables www.drpaulswan.com.au |

Array Game • See Tackling tables p. 32 - 33 www.drpaulswan.com.au |

Strategy: Relate to a known fact • 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 |

Calculation in NAPLAN 2010 Yr 5 q 24 www.drpaulswan.com.au |

Start of Yr 4 • 2 – 4 weeks review of: • addition and subtraction facts • 2, 3, 5 and 10 facts • Assess www.drpaulswan.com.au |

What to do in Year 4 • Facts to be learned in Yr 4 x 0 1 2 3 4 5 6 7 8 9 10 10 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 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 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 | 30

What number facts Year 4? • Recall multiplication facts to 10 x 10 (ACMNA075) • 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 |

Connection to Division • Factor Factor Product Cards Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 32

Multispin, Spindiv & Race Car Rally 2, 3, 5 www.drpaulswan.com.au |

Division - Sharing (Partition) • The number of groups is known • The size of each group is found by a process of sharing Sharing Pr Prob oblem • There are 18 bananas in a bunch • Three people will share them • How many for each person? www.drpaulswan.com.au |

Quotition (repeated subtraction) • The size of each group is known • The number of groups is found by a process of repeated subtraction (quotition) Quotiti tion Pr Prob oblem: • There are 18 sunflowers • Three flowers are to be placed in each vase • How many vases are needed? www.drpaulswan.com.au |

Recording the operation -uses arrays 18 divided by 3 6 ) 3 www.drpaulswan.com.au |

Array for Division 18 divided by 6 3 ) 6 www.drpaulswan.com.au |

Language • Sharing language eventually replaced by the more formal language of ‘divided by’ • ‘goes into’ (gzinta) and ‘how many … in’ typically link to the repeated subtraction idea of division. • Note ÷ symbol and ) symbol read in different ways. (read left to right, right to left) www.drpaulswan.com.au |

Thinking about the recording Number each gets Number ) Number to sharing be shared www.drpaulswan.com.au |