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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