### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Greater Than or Less Than?

## Greater Than or Less Than?

Use the symbols and numbers below to make the above number sentence correct.

<             >                1              1                    2                   3

For example:

5.31 > 5.21

How many different sentences can you make?
How will you know when you have found them all?

#### Why do this activity?

This challenge encourages the class to think about the value of digits in decimal numbers and use symbols < and > to compare them.
It also encourages them to think about finding all possible solutions to a problem.

#### Possible approach

It may be useful to begin the lesson by reminding the children about place value and sharing models and images to support this understanding.

The activity could be introduced using a similar challenge but with numbers with which the class are more familiar. So it might be set up as:

<                    >                       4                     4                    5                      6

And the class could be encouraged to come up with possible solutions to the problem. This will be an opportunity to review understanding of the symbols < and > as well as to introduce the idea of there being more than one possible solution to the problem.

Discuss with the children how they were comparing the numbers. Remind them that they look at the most significant digit first (10s) and then the next digit (1s).

As you take ideas from the class, their responses could be organised in a systematic way. It might look like this:

44<56
44<65
45<46
45<64
46>45
46<54
54>46
54<64
56>44
64>45
64>54
65>44

Ask the class to identify how you have organised the work. What has been your system?
Can they find any pairs (ie 11<23 and 23>11)?

You can then move on to the problem using decimal points.

#### Key questions

Which number is greater? How do you know?
Have you found all of the possible options? How do you know?

#### Possible extensions

Extension 1: Try the activity again using different digits. You could roll a dice to generate these. How many solutions do you think there will be this time? Does it make a difference if the digits are unique?
Extension 2: Include a 0 in the digits. Does that make it harder or easier to compare the numbers?
Extension 3: Change the number of digits and/or the position of the decimal point. For example, try

or

Extension 4: As well comparing the numbers, find the difference between them.

#### Possible support

A place value chart may be helpful as the children consider the value of each digit.