### Three Squares

What is the greatest number of squares you can make by overlapping three squares?

### Two Dice

Find all the numbers that can be made by adding the dots on two dice.

### Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

# Robot Monsters

## Robot Monsters

You are going to make Robot Monsters.

Here are their heads which all have blue backgrounds:

Here are their bodies which all have yellow backgrounds:

Here are their legs which all have green backgrounds:

What is the tallest Robot Monster that you can make using one head, one body and one set of legs?

What is the shortest one you can make using one head, one body and one set of legs?

How tall would the Robot Monster be that was made from the three bits left over after you had made the tallest and the shortest?

How many Robot Monsters which are all different heights can you make with the nine pieces (all with one head, one body and one set of legs)?

You could print off and cut up the Robot Monster head, body and leg cards from this sheet. Alternatively (or as well), you could use this interactivity to try out your ideas:

### Why do this problem?

This problem involves measurement that really focuses on number work - addition, ordering numbers and combinations. Manipulating the pictures can also help pupils to explore the different combinations systematically.

### Possible approach

This problem featured in an NRICH Primary webinar in September 2021.

You could start by showing the whole group the pictures in the problem by displaying the interactivity on the board. Explain that each Robot Monster needs a head, a body and a pair of legs. You could ask how tall the robot would be using a certain combination of head, body and legs, which you (or a child) could drag in place on the screen. Some learners might count squares to find the height, some might use the ruler (which can be dragged horizontally), some might add the three measurements. Spend some time sharing the different methods your class has used. (If you click on the Settings purple cog, you have the option to hide the ruler if you prefer.)

Once the group has got the idea of a Robot Monster, you could introduce the challenges in the problem. You could have pictures from this sheet (Word docPDF) available for pairs to use should they wish. The doc version has the exact measurements, whereas the PDF does not. (If these pictures are printed onto card and laminated they will make a lasting resource.) If possible, you could also have tablets/computers on hand so learners can choose to use the interactivity themselves. It is helpful if the children can work in pairs so that they are able to talk through their ideas with a partner.

At the end of the lesson you could discuss the tallest and shortest robots as a whole group, and all the different combinations they have found. You can use the interactivity (or pieces printed onto card and fixed onto the board) to illustrate the different combinations, and to draw out ways of working systematically so that you can be certain all solutions have been found.

### Key questions

If a Robot Monster is going to be as tall/short as possible, which head will you choose?
If a Robot Monster is going to be as tall/short as possible, which body and set of legs will you choose?
Can you think of a good way to find all the different heights you can make?