Post on 17-Dec-2015
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.
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
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?
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?
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?
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.