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

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

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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

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Developing a Whole School Approach to Mental Computation

Day 1 – Basic Facts Milestones for Addition and Subtraction Dr Paul Swan and David Dunstan

1

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Proficiency and Content Strands

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Consider

28 + 3 37

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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

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A closer look

  • 20 + 30 +8 + 7
  • How do you add 20 and 30?
  • How do you add 8 and 7?
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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)
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Basic Facts

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  • 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
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Basic Facts

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+ 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 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 × 0 1 2 3 4 5 6 7 8 9 10 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 0 10 20 30 40 50 60 70 80 90 100

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Fluency

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  • 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.

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Working Memory

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  • 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)

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Understandings

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Maths Language

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Tools

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Tools

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"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.
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Disposition

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Place Value

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Efficient Mental Strategies

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  • Strategies that use less

steps

  • Counting in ones not

efficient

  • Recall (retrieval) of

single-digit facts helps

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Mental Computation

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  • Definition
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Milestones

  • What are the

expectations?

  • When do they need

to know them?

  • How will we know

they’ve got it?

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Milestones

  • What are the

expectations?

  • When do they need

to know them?

  • How will we know

they’ve got it?

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How will we know?

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Foundation

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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

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Year One

  • Start of Yr 1 recap Foundation 2 – 4 weeks
  • Learn 64 addition facts in year 1
  • Highlight
  • Addition property of

zero

  • Commutative property
  • Part part whole
  • Link to subtraction

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+ 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 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

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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

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Count on zero

  • Addition Property of Zero

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Commutative Property

  • Shake and Spill
  • Call red first
  • Number Window
  • On my side of the window …

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Subtraction

  • Count back

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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

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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

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Build to Ten

  • Use ten eg bonds of ten
  • Rainbow facts?
  • Tool
  • Ten Frame
  • Five frame, ten strip
  • Two colour counters

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Partition board

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Cuisenaire Partitioning Ten

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Build to games

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LULU Game

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Ken Ken

  • Apply knowledge of basic number acts
  • Problem Solving

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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 PS Reasoning See p. 18

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Doubles

  • Double Dominoes
  • Cubes
  • Link to Near Doubles

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Near Doubles

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Dominoes game

  • Separate all the doubles and near doubles.
  • Turn over (face down)
  • Pick one up
  • State Total
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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

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Bridge Ten

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Bridge Ten

  • Introduce new tool
  • Empty Number Line

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Link Add and Subtraction

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Celebrity Heads

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18 18 12 12 6

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Language of Subtraction Difficult

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E.L.P.S

Experience Language Picture Symbols

Liebeck, P . (1991). How children learn mathematics. Penguin

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1 2 4 8

1 2 4 8

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9 Card Bingo

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Tug of War (Choice of tasks)

  • Beads and six sided dice
  • Language of maths
  • Part part whole (20)
  • Commutative property
  • Turn around facts

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Games

  • 7 Card Game, p. 44 Mathematics Games with School Friendly Cards
  • Observe strategies being used.
  • Flipper p. 28/29 Card Capers
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ROWCO

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Year 3

  • First 2 – 4 weeks review Yr 1 and 2 facts
  • Consider a Normed Test
  • Westwood One Minute Basic Facts Test

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Westwood One Minute Basic Facts Tests

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Westwood Analysis

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My Basic Number Facts Book Milestones Assessment

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