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Mental Maths Strategies

Workshop 1: Addition and Subtraction

2014

1

Overview

Workshop 1

• May 2014

• Addition and subtraction strategies

Workshop 2

• School year 2014/2015

• Multiplication and division strategies

2

Support Materials

PDST Workshop Booklet PDST Mental Maths Handbook

3

What is Mental Maths?

• Sorting activity

• Teacher Reflection

4

Key Messages

1. Concrete and pictorial exploration of number is the foundation of mental maths strategy development

2. Pupils should devise, communicate and reflect on various mental maths strategies

3. The teacher’s role is to facilitate mathematical thinking

5

Objectives

• To broaden participants perception of mental maths

• To reflect on how pupils are encouraged to engage in mathematical thinking

• To actively engage participants in identifying and naming mental maths strategies for addition and subtraction

6

8+8=

121+122=

In your class, which do your pupils use most often?

• rapid recall of known facts

• application of known facts

7

Number Facts or Mental Maths

“Rapid recall of number facts is one aspect of mental calculation but there are others. This involves presenting children with calculations in which they have to work out the answer using known facts and not just recall it from a bank of number facts that are committed to memory.”

(Crown, 2010, p.12)

8

Solid Foundations

• Being able to confidently add and subtract any pair of two-digit numbers mentally is an important starting point for mental maths.

9

6 aspects of maths that involve mental calculation

Recalling Facts

Applying Facts

Hypothesising and

Predicting

Designing and Comparing Procedures

Interpreting Results

Applying Reasoning

10

Crown, 2010

Teacher as Facilitator

• Starts by assessing the knowledge of the group

• Information flows in many different directions

• Facilitators elicit a variety of methods from pupils

• Facilitators encourage pupils to critically evaluate solution methods

11

A Range of Methods…

“To help children to learn and draw on a range of mental methods, you need to raise their awareness and understanding of the range of possible strategies, develop their confidence and fluency by practising using the strategies, and help them to choose from the range the most efficient method for a given calculation.”

(Crown, 2010, p.15)

12

I just know it

Stages of Progression

• Counting Strategies – using object counting (for example blocks or fingers) or verbal counting to determine the answer.

• Reasoning Strategies – using known information to logically determine an unknown combination.

• Mastery – efficient (fast and accurate) production of answers.

13 Arthur Baroody (2006)

Mental Strategies for + and -

COUNTING

14

Name the strategy…

• 160 + 170

• 404 – 200

15

Handbook p.19, 20

Name the strategy…

• 164 + 206

• 150 - 28

16

Handbook p. 21

Name the strategy…

• 65 + 7

• 1.4 + 1.7

17

Handbook p.21, 22

Name the strategy…

• 58 + 47 – 38

• 4.7 + 5.6 – 0.7

18

Handbook p. 22

Name the strategy…

• 109 + 256

• 96 - 55

19

Handbook p.23, 24

Name the strategy…

• 6.8 - 4.9

20

• 5.7 + 3.9

Handbook p. 24, 25

Name the strategy…

• 6.30am + 40 minutes

• 15.20pm – 3h 40 minutes

21

Handbook p.26 - 27

Name the strategy…

• 1088 – 975

• 124 – 97

22

Handbook p.28-29

Name the strategy…

• 51 – 26

• 2448 – 298

• 209 – 151

23

Handbook p.29 - 31

Addition and Subtraction Strategies

Counting forwards

and backwards Doubles/near

doubles Facts of 10

Bridging through ten(s)

Reordering Partitioning by

place value

Compensating Bridging through

60 (time)

Subtraction

• Think addition

• Keeping a constant difference

24

The Test !

No pressure

You can work with a partner to figure them out

25

Mastering the Basic Facts

Do:

1. Ask students to self-monitor

2. Focus on self improvement

3. Drill in short time segments

4. Work on facts over time

5. Involve families

6. Make drill enjoyable

7. Use technology

8. Emphasise the importance of quick recall of facts

Avoid:

1. Using lengthy timed tests

2. Using public comparisons of mastery

3. Proceeding through facts in order from 0 to 9

4. Moving to memorisation too soon

5. Using facts as a barrier to good mathematics

26

Van de Walle, p. 188

Steps to Success for Pupils with SEN…

1. Recognise that more drill will not work

2. Provide hope

3. Inventory – the known and unknown facts for each student in need

4. Diagnose strengths and weaknesses

5. Focus on reasoning strategies

6. Build in success

7. Provide engaging activities for drill

Van de Walle (p.186/187) 27

Reflect again

Activity 1 : Re-sort statements

Activity 2: Reflection booklet pg 5

28

PDST Supports

• Session 2 Term 1 2014

• www.pdst.ie