Addition and Subtraction Workshop

Addition and Subtraction Workshop

Susan McDougall and Amanda Caldwell

(With thanks to Fiona Fox and Charlotte Rawcliffe)

Numeracy Facilitators

Addition and Subtraction Workshop

Addition and Subtraction Workshop

Susan McDougall and Amanda Caldwell

(With thanks to Fiona Fox and Charlotte Rawcliffe)

Numeracy Facilitators

Whakatauki

E tu kahikatea, hei whakapae ururoaAwhi mai, awhi atu, tatou, tatou e.

Kahikatea stand together, their roots intertwine, strengthening each other.

We all help one another and together we will be strong.

Knowledge Warm-up:No Name Game

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.

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

This strategy - What stage?

• How wou ld you solve these?3 + 5 =

7 + 9 =

42 - 7

27 + 54

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

Using Number Properties

Using Imaging

Using Materials

New Knowledge & Strategies

Existing Knowledge & Strategies

Using Materials

The Strategy Teaching Model

Hands Tens frames

Abacus Place Value Material

Number Lines

37 87 90

+ 50+ 3

1010

1223

Using Materials and Imaging:

Imaging Phases:

First Phase of Imaging;• Look but don’t touch!

Second Phase of Imaging:• Shielding materials ,scaffolding.

Third Phase of Imaging:• No materials at all.

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 children’s misconceptions addressed during the lesson?

Rachel’s Millions

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.

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.

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: Who’s got it? Who hasn’t? Set practice.

- Consider next teaching and learning steps.

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

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?

Stage 6 AAAdvanced Additive

There are 53 people on the bus.29 people get off

How many people are now on thebus?

53 - 30 + 1= 24

53 - 29Tidy Numbers using Compensation

53 - 20 - 3 - 6 = 24

53 - 29• Place Value Partitioning

29 + 1 + 20 + 3 = 53

53 - 29• Reversibility

5329

1

1

5430

= 24

53 - 29

• Equal Additions

Tidy numbers using Compensation

53 - 30 + 1

53 - 29

Place Value Partitioning

53 - 20 - 9

Equal Additions54 - 30

Reversibility29 + ? = 53

Summary of Strategies

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.

Why bother teaching mental strategies, why can’t I just learn the written form?

• written form is following a procedure - rule following - some students just learn method without understanding

• mistakes are made or wrongly applied to problem solving

• Need mental ability to estimate & check answers first

• It is often quicker to work something out mentally

•Written form sometimes is the most suitable way but not always

Why are mental strategies important?

So, which strategy is best?

It depends on what the question is!!

?

385 - 99

478 - 56

1002 - 987

Stage 8 AP:

Advanced Proportional

To use a range of mental partitioning strategies to solve proportion (fraction),

ratio and decimal problems.

Proportional Problem:

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

will 18 children pay?”

30:18 = 10/6

10 parts of 75 =7.5 p/ part

6 parts @ 7.5 p/part = 45

18 /30 is the same as 3/5 so it is 3/5 of 75 which is 45because 1/5 is 15

30 children gives $751 child gives $2.5018 x 2.518 children gives $45.00

30:75 is the same as

2:5 therefore

multiply both by 918:45

Strategies for solving Proportional problems:

Long term unit plans (Bk 3, pg.16).

AC- EAThis 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?

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.

Thought for the day:

“And, if it all just seems too much…..

STRESSEDbackwards spells

DESSERTS!