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<big>How children work out answers in their heads

Mental Calculation

(so, how do children work things out?)

A few points to note:

We are keen to develop children's mental calculation skills across the school.
It is important that a child can understand number operations and make simple calculations and estimations before learning more formal written methods.
Instead of telling a child how we would solve a problem, a good way for adults to understand how a particular child thinks mathematically, is to ask them how they would try to find an answer.
Whilst we do teach, systematically, particular ways of calculating, children are encouraged to use the method which they understand best.
There is no right or wrong way to find an answer, though we would always encourage an efficient method which the child feels comfortable with.
Once we understand the language that the child uses, it is easier for us, as adults, to support, teach and communicate with them about their maths.

Children's comments:

5 + 3 =

"I just know it!"

"I use my fingers, starting at 5, and count on 3."

5 + 11 =

"I start with the biggest number, 11, and add on 5."

"I take 1 off the 11 and add it to the 5. Then I just add 10 and 6."

25 + 13 =

"I add up the tens (20 +10) to make 30, then the units(5 +3) to make 8. Then 30 + 8 = 38"

"I do 25 +10 = 35, then add the 3, makes 38."

10 - 3 =

"I stick out ten fingers and put three of them down."

"I know my number bonds to 10 so I know it's 7."

"I put 10 in my head, hold up 3 fingers and count back 3."

26 - 13 =

"I start with the big number (26) take away the ten, making 16, then take away the three,making 13."

" I start at 13 and count on 7 to make the 20, then count on 6 to make 26. 7 + 6 = 13!"

quarter of 12 =

"I halve 12 then halve it again."

"I draw 12 spots then chop them into 4 sets."

"I use my tables to see how many 4s make 12."

"I just know it!"

35 x 4 =

"I double 35, then double it again."

"I do 30 + 30 + 30 + 30 making 120, then add on 5 + 5 + 5 + 5, making 140."

"I do 4 x 30 = 120, then 4 x 5 = 20. Then I add the 120 and 20 making 140."

"I know that 4 x 25 is 100, so I add 4 x 10. 100 + 40 = 140."

3478 ÷ 100 =

"I just move the decimal point along two places to the left."

"I could only do it on a calculator!"

any other suggestions much appreciated!