Investigations are more common to our work in science but they can prove invaluable in maths in helping pupils to understand mathematical reasoning. In these activities the pupils are presented with puzzles to solve and in doing so they will gain greater understanding of some key concepts.

__Activity One – Brackets__

**Suitable for Years 4 to 6**

Learning Objectives:

- Be able to recognise that a sum with several operations can give different answers depending on the order of operations.
- Learn that brackets in a sum indicate that this part of the sum must be completed first.

The use of brackets can materially alter the outcome of a sum and are the first action to be undertaken in the acronym ‘BIDMAS’ (brackets, indices, division, multiplication, addition and subtraction). They are used to help us understand the order of operations in a sum. For example…

3 + 9 x 4 – 3 =

In this sum, the logical way to approach it is to work from left to right so the answer would be 45 but we could equally see the answer could be 12 if the 3 is subtracted from the 4 first. If we multiply the 9 by 4 first then we can also get 36.

Write the sum out three times on the board as follows:

3 + 9 x 4 – 3 = 45

3 + 9 x 4 – 3 = 12

3 + 9 x 4 – 3 = 36

…and tell the pupils that we can use brackets to tell us which part of the sum to tackle first. Ask them to tell you where the brackets should go:

(3 + 9) x 4 – 3 = 45

(3 + 9) x (4 – 3) = 12

3 + (9 x 4) – 3 = 36

Now give them the accompanying worksheet Using Brackets and ask them to write out the sums using brackets in different places to give different answers for each. How many can they find?

__Activity Two – 2D and 3D Shapes__

**Suitable for Years 3 to 6**

Learning Objective:

- To be able to use known facts about 2D and 3D shapes to identify them correctly.
- To use different strategies to be able to solve mathematical problems.

In this activity the pupils get to guess the 2D and 3D shape from closely examining a small part of the shape and having to guess from that information, what shape they are being presented with. The activity is done most easily on an interactive whiteboard.

A SMART Notebook 11 file accompanies this activity but for those schools using other technology, screenshots are provided below to allow you to create your own. Previous lessons will need to have covered the properties of 2D and 3D shapes including the number and size of angles.

Ask the pupils to tell you what strategies they might use to help them guess the correct shape. These could include extending the lines they are given, comparing the information they have to actual 2D and 3D shapes or by measuring the angles they can see.

Ask the pupils if there are any other shapes that could possibly be hidden by the coloured tiles, for example, the arc revealed by the yellow square could also be a semi-circle or a sector whilst the pentagon and hexagon covered by the red and purple squares could also be triangles.

**Telling the Time**

Click below to download the Telling the Time worksheets:

Telling the Time Five Minutes Past

Telling the Time Five Minutes To

Telling the Time Half and Quarter Past