No one would argue against knowing number facts and that being able to calculate efficiently is vitally important. But there is much more to maths than this. It is no use being able to calculate accurately if you do not know what calculation to carry out – most of the maths we use in the real world does not come as a neatly displayed calculation.

Three of the key elements in this are:

• choosing the appropriate operation(s) to solve word problems and number puzzles
• deciding whether the calculations can be done mentally or need formal written methods
• explaining and recording how the problem was solved

Year 4 Intelligent practice

Intelligent practice is a feature of mathematics which is growing in popularity. A key aspect of this is to provide activities and questions so that, rather than just reproducing one mechanical process children are encouraged to think about the relationships between numbers.

For example:

• 4 + 4 + 4 + 4 =
• 4 x 4 =
• 5 + 3 + 5 + 3 =
• 16 ÷ 4 =
• 160 ÷ 4 =
• 32 ÷ 4 =

Whilst going through these six questions children can use and reflect on their knowledge of number, with such concepts as:

Knowing that adding a number four times is the same as multiplying the number by 4.

Knowing that adding two numbers either side of a middle number can also be worked out by doubling the middle number. (5 + 3 is the same as double 4).

Knowing that if 4 x 4 = 16 then 16 ÷ 4 = 4. Knowing that if 16 ÷ 4 = 4 then the answer to 160 ÷ 4 will be ten times greater.

The arrangement of these questions in small groups of 6 draws children’s attention to the many relationships between numbers and makes it easier for them to work out quite hard calculations ‘in their heads’.

Our Intelligent Practice worksheets can be found in the Year 4 Four Operations category.

Year 4 Reasoning and Problem Solving 

Year 4 Intelligent Practice