Many of our resources in all categories involve mathematical reasoning, but we also have a special area, called Reasoning/Problem Solving for each year group which really concentrates on this important aspect of Mathematics.
We have just published four new sets of resources for Year 5 Reasoning on:
• Ordering decimals
One way to put decimals in order of size is to set up a table with the decimal point in the same place for each number; this makes it much easier to compare decimals to see which is the larger (e.g. 0.65, 5.6, 0.605 etc).
• Finding half way between two decimals
There are several ways of finding a number half way between two others and this applies equally well to decimals.
One way is to add the two numbers and then divide the answer by 2.
Another way is to find the difference by subtracting the smaller number from the larger number. Halve the difference and add this to the smaller number.
Which method to use would depend on the numbers involved and it is a good idea to ask children why they have chosen a particular method.
• Word problems with decimals
Here is a typical word problem involving decimals:
Liz chooses a number less than 20. She divides it by 2 and then adds 10. She then divides this result by 5. Her answer is 3.7. What was the number she started with?
Questions like this depend on knowing that addition is the opposite of subtraction and multiplication is the opposite of division. The reasoning comes in as the calculation is worked through step by step; if her answer is 3.7 and she had divided by 5 then multiplying by 5 will complete the first step…. and so on.
1. Start at the end with the final answer which was 3.7.
Multiply 3.7 by 5 (because Liz divided by 5). 3.7 x 5 = 18.5
2. Take away 10 from 18.5 (because Liz added 10) 18.5 – 10 = 8.5
3. Multiply 8.5 by 2 (because Liz divided her number by 2) 8.5 x 2 = 17
4. The number Liz started with was 17.
5. Check by dividing 17 by 2, adding 10 and dividing by 5
• Ordering fractions
Ordering fractions with different denominators needs a good understanding of equivalent fractions and the questions are quite hard (e.g. order five ninths, two sixths, two thirds and one twelfth). It is important to change the fractions so that the denominators are all the same. If these prove difficult it would be well worth looking at our Fractions category to get further practice.