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1. Mental computation underpins numeracy
1. Mental computation underpins numeracy
One crucial area that must be developed as mathematics understanding develops is mental computation. This refers to a someone's ability to work out something 'in their head' or mentally, without having to draw, write or use a calculator.
Often people think that this refers to learning 'times tables' but this is only one small part of mental computation. To find out more about this see the resources on the final page.
2. Mental computation is important because:
2. Mental computation is important because:
mental computation is the most common form of calculation required by adults
mental computation processes are used in about 85% of maths in the real world (numeracy)
it is crucial for estimation
it is needed to check whether answers / responses are correct (think cash register, estimates of cost and time etc)
it is the easiest and most efficient way of doing many problems
it allows us to see how numbers work and use that knowledge in other problems
it supports creativity and problem solving
Research shows it can improve students' development of number, while an early introduction to formal written methods can harm it.
3. What needs to be taught?
3. What needs to be taught?
There are lots of sub-skills which need to be taught explicitly as part of mental computation. These can assist students when they are undertaking any problems.
There are lots of sub-skills which need to be taught explicitly as part of mental computation. These can assist students when they are undertaking any problems.
They need one and two digit strategies such as:
Doubling, adding multiples of ten, adding numbers that end in 5
Number pairs (inside the tens frame and above eg 8+5) Back through 10 - For example, 52 – 8 = ? can be solved by calculating 52 – 2 = 50 then 50 – 6 = 44.
Equal differences - for example what is the difference between 8 and 13? Well I can work that out by asking what is the difference between 10 and 15? (you find two numbers that are equally close to your original numbers and work out the difference between them). You could also do 5 and 10 in this example.
Near doubles - 9 + 8 is nearly 9+9
Up through ten - 19+9 = 20+8
Splitting arrays - 9x6 is the same as 3x6 + 3x6 + 3x6 or 6x6 + 3x6 or 9x3+9x3 (distributive law or property)
Using 10s - 5000+4000 = 5+4 000; 5000x4000 = 5x4 000 000
Aggregation (eg: 28+35: 28+5=33,33+30=63),
Wholistic addition (eg: 28+35: 30+35=65, 65-2=63)
Separation right to left (eg: 28+35: 8+5=13, 20+30=50, 13+50=63)
Separation left to right (eg: 28+35: 20+30=50, 8+5=13, 50+13=63)
Rounding to add (58+63+81 = 60+60+80 -2+3+1)
Rounding to multiply (59x61 is about 60 by 60 so my answer will be about 3600) - it is important to know an estimate of a written algorithm too
etc etc
3a. Activity: Mental computation strategies
3a. Activity: Mental computation strategies
Open this link https://drive.google.com/file/d/1tdXwrY_jJ-B8byfxVrwNW6TSbToU7Ooi/view and view the problems. Work through them with a partner or by yourself. We will share some of our thoughts after tackling them.
4. Times Tables
4. Times Tables
Mental computation skills are not just knowing your times tables. Times tables are one very small part of mental computation. If children are using mental computation skills they are working out a problem without using written records.
For example, they might look at two prices and work out which is the best value for money. Or consider the difference between traveling on an Express train and an all stops train. we will revisit Mental Computation skills in Links between processes and strategies (page 1c)
Always Remember Your Times Table (6 to 10) Using Fingers
Multiplication www.youtube.com/watch?v=x2Nr-f02AUY
Times Tables are taught as one element of Mental Computation. They are only one small part. They rely on rote learning rather than using strategies based on understanding of number.
Times Tables are taught as one element of Mental Computation. They are only one small part. They rely on rote learning rather than using strategies based on understanding of number.
There are a range of ways to teach and support the learning of times tables. You might need to support students by:
undertaking activities where they see the patterns in particular times tables
helping them learn tricks such as whether a number is divisible by 9, 2, 5 or 10
http://www.softschools.com/math/topics/the_divisibility_rules_3_6_9/
http://www.softschools.com/math/topics/divisibility_rules_2_4_8_5_10/
using fingers to learn their tables.
5. Resources for Mental Computation
5. Resources for Mental Computation
To help you understand what strategies to teach when, there are a range of good resources available. Frequently the students you are supporting will have poor mental computation skills and you will need to support them to improve.
There are some good websites (see below), videos, a range of books, and posters that can be used in classrooms and referred to by students.
Activity: How will you support this learning?
Activity: How will you support this learning?
Talk to a partner and review some of the strategies:
on the website above
from the Mental Computation books on the Resources page,
Consider how you might support students to understand some of the mental computation strategies being developed below:
Year 3 / 4 - arrays activity with 24 or 36 https://topdrawer.aamt.edu.au/Mental-computation/Activities/How-many-possible-ways
Year 2 / 3 - partial arrays https://topdrawer.aamt.edu.au/Mental-computation/Activities/Partial-arrays
Kinder - Year 1 - https://drive.google.com/file/d/0B75cP9HMyXqtcjUwYmlLdXJyQlk/view - page 11, 13, 15, 17 activities
Year 4/ 5 - https://drive.google.com/file/d/0B75cP9HMyXqtekx4OHFqV2pka3M/view - page 22, 23
Year 5/ 6 - https://drive.google.com/file/d/0B75cP9HMyXqtekx4OHFqV2pka3M/view - page 21, 22, 23 but change the numbers to 100s and 1000s
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