Developing a Whole School Approach to Mental Computation Day 1 - PowerPoint PPT Presentation

Developing a Whole School Approach to Mental Computation Day 1 – Basic Facts Milestones for Addition and Subtraction Dr Paul Swan and David Dunstan www.drpaulswan.com.au | 1

Proficiency and Content Strands Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 2

Consider 28 + 3 37 www.drpaulswan.com.au |

Three Strategies: 28 + 27 • Split one 20 + 37 + 8 • Or 28 + 30 + 7 • Split both 20 + 30 + 8 + 7 Adjust and compensate 30 + 27 – 2 www.drpaulswan.com.au |

A closer look • 20 + 30 +8 + 7 • How do you add 20 and 30? • How do you add 8 and 7? www.drpaulswan.com.au |

8 and 7 • 8 + 8 – 1 (Near doubles) • Relies on knowing doubles • Adjust and compensate • 7 + 7 + 1 (Near doubles) • 8 + 2 + 5 (bridge ten) • Relies on make to ten strategy • Ability to partition (7 = 2 and 5) www.drpaulswan.com.au |

Basic Facts • Single digit addition • (0 + 0 to 9 + 9) • Related subtraction • 7 + 2 = 9, 9 – 2 = 7, 9 – 7 = 2 … • Single digit multiplication • (0 x 0 to 9 x 9 AC 10 x 10) • Related division facts Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 9

Basic Facts + 0 1 2 3 4 5 6 7 8 9 × 0 1 2 3 4 5 6 7 8 9 10 10 0 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 4 5 6 7 8 9 10 1 0 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 2 0 2 4 6 8 10 12 14 16 18 20 3 3 4 5 6 7 8 9 10 11 12 3 0 3 6 9 12 15 18 21 24 27 30 4 4 5 6 7 8 9 10 11 12 13 4 0 4 8 12 16 20 24 28 32 36 40 5 5 6 7 8 9 10 11 12 13 14 5 0 5 10 15 20 25 30 35 40 45 50 6 6 7 8 9 10 11 12 13 14 15 6 0 6 12 18 24 30 36 42 48 54 60 7 7 8 9 10 11 12 13 14 15 16 7 0 7 14 21 28 35 42 49 56 63 70 8 8 9 10 11 12 13 14 15 16 17 8 0 8 16 24 32 40 48 56 64 72 80 9 9 10 11 12 13 14 15 16 17 18 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 | 10

Fluency • Efficiency • Few simple steps • Accuracy • Flexibility • Choose between appropriate strategies . Russell, J. Developing Computational Fluency with Whole Numbers. • Teaching Children Mathematics 7 (Nov 2000): 154–58. Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 11

Working Memory • Working memory is likely to be required to a greater extent for procedural as compared to retrieval strategies (Cragg et al 2017) • Different strategies tax working memory to different extents. Hecht (2002) Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 12

Understandings Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 13

Maths Language Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 14

Tools Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 15

Tools "Mathematical tools should be seen as supports for learning … This requires more than watching demonstrations; it requires working with tools over extended periods of time, trying them out, and watching what happens. Meaning does not reside in tools; it is constructed by students as they use tools p.10” Hiebert, J., Carpenter, T.P ., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P . (1997). Making sense: Teaching and learning mathematics with understanding . Portsmouth, NH: Heinemann. Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 16

Disposition Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 17

Place Value Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 18

Efficient Mental Strategies • Strategies that use less steps • Counting in ones not efficient • Recall (retrieval) of single-digit facts helps Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 19

Mental Computation • Definition Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 20

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 | 21

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 | 22

How will we know? Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 23

Foundation Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 24

Foundation • Which is the Bigger Number? • Missing number • 4, 6, …, • 4, …., 6 • …, 5, 6 • Count on from any number. • Relies on counting principles • Addition may be performed in any order • Commutative property of addition Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 25

Year One • Start of Yr 1 recap Foundation 2 – 4 weeks • Learn 64 addition facts in year 1 • Highlight + 0 1 2 3 4 5 6 7 8 9 • Addition property of 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 zero 2 2 3 4 5 6 7 8 9 10 11 • Commutative property 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 • Part part whole 5 5 6 7 8 9 10 11 12 13 14 • Link to subtraction 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 26

Count on from the larger number • Know the larger number • Count from any number • Count on from the next number • Commutative Property • Turn-around facts • Watch for language issues Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 27

Count on zero • Addition Property of Zero Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 28

Commutative Property • Shake and Spill • Call red first • Number Window • On my side of the window … Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 29

Subtraction • Count back Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 30

Link addition and subtracton • Need to know a bank of facts • Link to • Shake and Spill (red first) • Number Window • Partition Board • Celebrity Heads • Develop Fact Families Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 31

Year Two • First 2 – 4 weeks • Review basic number facts • Count on from the larger 1, 2, 3 or 0 • Link to subtraction • Fact families • Part Part Whole Flashcards • See p. 20 FSiM: Number - Understand Operations Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 32

Build to Ten • Use ten eg bonds of ten • Rainbow facts? • Tool • Ten Frame • Five frame, ten strip • Two colour counters Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 33

Partition board www.drpaulswan.com.au |

Cuisenaire Partitioning Ten www.drpaulswan.com.au |

Build to games Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 36

LULU Game Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 37

Ken Ken • Apply knowledge of basic number acts • Problem Solving Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 38

Domino Trains When dominoes are joined the number of dots must match Make some Domino Trains Shortest Train Longest Train How many different trains can you make? How will you know when you have found them all? Involves: Number and all proficiencies Understanding Fluency See p. 18 PS Reasoning www.drpaulswan.com.au |

Doubles • Double Dominoes • Cubes • Link to Near Doubles Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 40

Near Doubles Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 41

Dominoes game • Separate all the doubles and near doubles. • Turn over (face down) • Pick one up • State Total www.drpaulswan.com.au |

Mary’s Game • 0 1 2 3 4 5 6 7 8 9 10 11 12 • 0 1 2 3 4 5 6 7 8 9 10 11 12 • p. 20 Dice Dilemmas • Improves speed and accuracy Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 43

Bridge Ten Dr Paul Swan and David Dunstan Developing a Whole School Approach www.drpaulswan.com.au | 44