Year 4

We can explain to someone else how we solve problems and puzzles

Year 4 Unit 1

What we are learning:

• Many children (and adults) are naturally ‘visual’ mathematicians. When they are asked to solve a problem they first need to visualise the problem. They may visualise the problem in their head or need to draw the problem out using simple pictures or a diagram. This should be encouraged.
• A diagram is a line drawing created to demonstrate a mathematical idea.
• We live in a world full of mathematical puzzles and problems, for instance, ‘If I am cooking rice for 4 people and the recommended amount of rice per person is 60g, how much rice should I cook?’ Children will generally respond better to real-life maths puzzles and problems than those presented as writing within a book.
• There is often more than one right answer to a problem. Presenting your child with problems where there is more than one right answer will provide the opportunity for you to discuss why a particular solution has been chosen.

ACTIVITY 1: I AM THINKING OF A NUMBER

ACTIVITY SHEETS

Downloads:

Activity sheet: I am thinking of a number PDF

ACTIVITY 2: FIND THE AGE

Activities you can do at home:

Play “I am thinking of a number”. Use the 100-square provided as a visual prompt if needed. Take it in turns to think of a number between 1 and 100
– write this number down – but don’t show anyone else. Now provide clues as to what this number is:
The number I am thinking of is greater than 50 but less than 70. Allow some thinking time. Ask your child to write down possible solutions. The number I am thinking of is an odd number. Your child will now need to cross some of their original solutions out.
The number I am thinking of is NOT a multiple of 5. Again some solutions can be deleted.
The number I am thinking of has a digit sum (The total when adding the digits together) of less than 10. We should be closer to the solution now.
The number I am thinking of is a multiple of 3. The solution can only be 51 or 63 now.
Guess which number I am thinking of!
By not giving a clue to reveal the actual number ‘I am thinking of’, the opportunity for discussion and explanation has been created. Encourage your child to use their jottings to explain their thinking.

Make up some puzzles that involve age totals and differences, i.e. Jack and Jill have a total age of 30. The difference in their ages is 4 years.
Jack is the eldest. How old are Jack and Jill?
Guide your child to look for all the possible solutions where the total age is 30. They may find it useful to draw a table:

Encourage your child to be systematic in their problem solving. In this instance start with Jack being 29 and work backwards.
Then look for all the solutions where the difference in their ages is 4 years. There is only one solution that fulfils all the criteria.
Ask your child to explain how they know this is the correct solution. Guide them to talk through each of the criteria – using the table to support their explanation.

Good questions to ask:

Can you explain how you solved this?
If you were telling me how to solve this, what would you tell me to do first, second etc?
Is there any other way of solving this?
Which method might give us the solution fastest?

If your child:

Finds is difficult to explain their thinking
Try the following:
Simplify the problem so that it is easier to explain – the object is to explain the method for solving it, not just to get it right
Break their explanation down into stages by asking questions: what do you know? What do you need to find out first? What will you do next?
You explain how you would solve a problem and see if your child can follow your method