Mental Calculations

Question 1

Why is fluency important with mental calculation?

Answer 1

It is essential for efficient problem solving.

They can lead to efficient written methods which can be used to carry out a wider range of calculations.

Question 2

Why is conceptual understanding about number important?

Answer 2

If children don’t explore concrete visuals and materials of numbers in maths, they will have misconceptions. However, if they do have a conceptual understanding, they have a visual hook to go back to in their brain

Question 3

What are the mental calculation strategies?

Answer 3

Reordering
Transforming
Using doubles
Identifying near doubles (using the double +/- 1)
Partitioning
Compensating
Inverse operation
Finding the small difference
Empty number line

Question 4

Mental calculation strategy: Reordering

Answer 4

Re-arranging numbers to make the calculation easier
Such as putting the largest number first and counting on

Question 5

What is the commutative order?

Answer 5

Addition can be done in any order

Question 6

Mental calculation strategy: using doubles

Answer 6

Identifying doubles to calculate the total
25+25
20+20=40
5+5=10
40+10

Question 7

Mental calculation strategies: Identifying near doubles & using the double +/-1

Answer 7

8+9
8+10=18
18-1=17
8+9=17

Question 8

Mental calculation strategies: partitioning into tens and units

Answer 8

Taking apart the numbers in the calculation- children must have an understanding of place value to do this
24+35
20+30=50
4+5=9
50+9=59

Question 9

Compensating

Answer 9

Add or subtract 9 or 11= add/subtract 10 and adjust by 1
53+29
53+30-1^

Question 10

Mental calculation strategy: Transforming

Answer 10

Writing an equivalent calculation
59+24 is equivalent to ^60+23
103-13
^100-10

Question 11

Mental calculation strategies: Partitioning-bridging through multiples of 10

Answer 11

15+7= 15+5+2
23-7= 23-3-4

Question 12

Mental calculation strategy: Using the inverse operation

Answer 12

Addition and subtraction family
Multiplication and division family
4+6=10
6+4=10
10-6=4
10-4=6

3x5= 15
5x3= 15
15 divided by 3=5
15 divided by 5=3

Question 13

Mental calculation strategy:
Finding small difference

Answer 13

By counting up from the small number to the largest number
42-39=3
|____________________+3____|
39————————> 42

Question 14

What do children need to be confident in before they begin to use an empty number line?

Answer 14

They need to have lots of experience counting on and back using numbered tracks, lines, bread strings and partly numbered lines