Addition and Subtraction Workshop

1
Addition and Subtraction Workshop

• Addition and Subtraction Workshop

Fiona Fox and Charlotte Rawcliffe Numeracy
Facilitators
2
Knowledge Warm-up

• Equipment
• A squeezie Box
• Activities
• -Read the number
• -Number before / after
• -Ten more / less
• -Doubles
• -How many more to make 10
• -Multiply by
• What other key concepts could be developed
• using the Squeezie Box?

3
Objectives

• Revise the Strategy framework stages.
• Understand the teaching model used for teaching
  strategy.
• Explore equipment and activities used to teach
  addition subtraction strategies.
• Know how to use planning sheets, Numeracy Book 5
  and other supportive resources to help teach
  addition subtraction.

4
Reflection

• Reflect on your numeracy lessons, routines and
  classroom organisation.
• Share with the person beside you
• One thing you have started doing
• One thing you have stopped doing
• One thing you would like to do in your maths
  programmes

5
How would you solve these?
3 5
How would you solve these?
How would a child at stages 2, 3 and 4 solve this
problem?
7 9
How would a child at stages 3 4 and 5 solve this
problem? How would a child at stages 4 and 5
solve this?
42 - 7
6
How would you solve these?
How would you solve these?

• 7 9

How would a child at stage 3, 4 and 5 solve this
problem?
42 - 7
How would a child at stage 4 and 5 solve this
problem? How would a child stage 6 and 7 solve
this?
27 54
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A Teaching Progression

• Start by
• Using materials, diagrams to illustrate and solve
  the problem
• Progress to
• Developing mental images to help solve the
  problem
• Extend to
• Working abstractly with the number property

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The Strategy Teaching Model
Existing Knowledge Strategies
Using Number Properties
Using Imaging
Using Materials
Using Materials
New Knowledge Strategies
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Using Materials and Imaging
Hands Tens frames Abacus Place Value
Material Number Lines
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Imaging Phases

• First Phase of Imaging
• Look but dont touch!
• Second Phase of Imaging
• Shielding materials ,scaffolding.
• Third Phase of Imaging
• No materials at all.

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A lesson using the teaching model

• Watch the DVD of a lesson using the teaching
  model.
• In your thinking groups answer the following
  questions
• What did you notice about how the teaching model
  was utilised?
• How was folding back evident in the lesson?
• How were childrens misconceptions addressed
  during the lesson?

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Importance of Place Value

• What is place value?
• Where does place value
• start?
• What place value equipment
• have you currently got in your
• school?
• Order the equipment from
• least abstract to most abstract.

• Place value Hats
• Large numbers Roll Over Page 43.

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Maths Thinking Groups

• What is the purpose of a thinking group?
• Each person is given a chance to share their
  thinking and solution to a problem.
• Group members listen to each other. Only one
  person talks at a time.
• Everyone must be able to understand and explain
  others thinking and solutions.
• Group members must be prepared to explain their
  own thinking.

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Introduction to Book 5

• Each strategy stage is separated into 2 parts
  Learning experiences to move from one stage to
  next and learning experiences for each stage.
• Refer to the required knowledge check before
  transitioning students.
• If the group are not ready to move from one stage
  to the next you may need to broaden their
  experiences.
• Refer to the teaching model progression for each
  lesson.

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A Strategy Teaching Lesson

• Start of Lesson Consider strategy stage of group
• Required knowledge check
• Diagnostic Snapshot (Can they already do it?)
• Teaching
• - Teaching Model (materials, imaging, number
  properties)
• Consider thinking groups modelling book
• End of Lesson
• Feedback Whos got it? Who hasnt? Set
  practice.
• Consider next teaching and learning steps.

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A Strategy Lesson.

• Break into two groups to explore an add/sub
  lesson
• Junior Teachers Senior Teachers
• Stage 4 Stage 6
• Stage 5 Stage 7

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Practice - 10 days of activities

• Questions on the board / Modeling Book
• Create a game (Snakes Chances, Jigsaw, Bingo)
• Play each others games
• Diary writing / class book entry
• Solving story problems
• Writing and checking story problems
• Swapping story problems
• Resource Book e.g. Figure it Out
• Worksheet
• If this is the answer - what could the question
  be?

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Stage 6 AA

• Advanced Additive
• There are 53 people on the bus.
• 29 people get off
• How many people are now on the
• bus?

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53 - 29

• Tidy Numbers using Compensation

53 - 30 1 24
20
53 - 29

• Place Value Partitioning

53 - 20 - 3 - 6 24
21
53 - 29
29 1 20 3 53

• Reversibility

22
53 - 29

• Equal Additions

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Summary of Strategies
Tidy numbers using Compensation 53 - 30 1
Place Value Partitioning 53 - 20 - 9
53 - 29
Reversibility 29 ? 53
Equal Additions 54 - 30
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Why are mental strategies important?
Why bother teaching mental strategies, why cant
I just learn the written form?

• Merely following a procedure - rule following
• Lack of real understanding - mistakes are made
  or wrongly applied to problem solving
• Need mental ability to estimate check answers
• It is often quicker to work something out
  mentally

25

• So, which strategy is best?

It depends on what the question is!!
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?

• 385 - 99

478 - 56
1002 - 987
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Stage 8 AP

• Advanced Proportional
• To use a range of mental partitioning strategies
  to solve proportion (fraction), ratio and decimal
  problems.

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Proportional Problem

• If 30 children pay a total of 75 dollars in entry
  fees to Rainbows End, how much money will 18
  children pay?

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Strategies for solving Proportional problems
3075 is the same as 25 therefore multiply
both by 9 1845
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Long term unit plans (Bk 3, pg.16).

• AC- EA
• This would be appropriate for children who are
  transitioning from AC to EA,
• OR
• Those who need to broaden the EA stage before
  moving onto the next stage.
• In other words, AC - EA implies the EA stage
• Where would you start each of your groups?

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Objectives

• Revise the Strategy framework stages.
• Understand the teaching model used for teaching
  strategy
• Explore equipment and activities used to teach
  addition subtraction strategies
• Know how to use planning sheets, numeracy book 5
  and other supportive resources to help teach
  addition subtraction.

32
Thought for the day

• And, if it all just seems too much..
• STRESSED
• backwards spells
• DESSERTS!