Robot Monsters
Robot Monsters printable sheet
Robot monsters need three different parts. They need a head, a body and legs.
Using some of these robot parts, make a robot monster!
You might like to print off and cut out the parts from the printable sheet at the top of this page. Alternatively (or as well), you could use the interactivity at the bottom of this page to try out your ideas.
The numbers show how tall the parts are in centimetres. How tall is your robot monster?
How tall is the tallest robot monster you can make?
What about the shortest robot monster?
What other heights could your robot monster be?
Can you find all the possible heights of a robot monster? How do you know you have found them all?
You could use the pieces from this sheet and try it out practically.
If a Robot Monster is going to be as tall as possible, which head will you choose? So which body and set of legs will you add?
To work out how many Robot Monsters you can make of different heights, why not start with one head and look at all the different ways you could add body and legs to it?
We had a couple of very full solutions to this problem. Jack and Alex from Woodfall Junior School wrote:
The biggest robot you can make is 22cm using 6cm head 8cm body and 8cm legs
The smallest robot you can make is 14cm using 3cm head 5cm body and 6cm legs
The bits that are left over using 4cm head 7cm body and 7cm legs that equals 18cm
They went on to say:
Head 
Body 
Legs 
Total height 
3 
5 
6 
14 
3 
5

7

15 
3 
5

8

16 
3 
7

6

16 
3 
7

7

17 
3 
7 
8

18 
3 
8

6

17 
3 
8 
7 
18 
3 
8 
8 
19 
6 
5 
6 
17 
6 
5

7

18 
6 
5

8

19

6 
7

6

19 
6 
7

7

20

6 
7 
8

21 
6 
8

6

20 
6 
8 
7 
21 
6 
8 
8 
22 
4 
8

8

20 
4 
8

7

19 
4 
8 
6 
18 
4 
7

8

19 
4 
7

6

17 
4 
7 
7 
18 
4 
5

8 
17 
4 
5

7 
16 
4 
5

6

15

We tried to use a systematic order to make sure we found all 27 monsters. We found all the monsters with 3cm heads first, then 6cm, then 4cm. We did the same with the bodies and legs.
Ruth from Swanborne House School commented:
There are 9 possible monster heights between 14cm and 22cm (14/15/16/17/18/19/20/21/22). To prove that you could make all of them we drew a diagram of all the possible combinations, starting from the three heads. We found that once we had drawn the first head + body and leg combination for the 3cm head, we could work out the other combinations for the 3cm head quite easily, because only the body measurement varied. Then we found it was easy to adjust from this to the other two heads, and we didn't need to do the full diagram.
Here is the diagram that Ruth sent:
Children from Seven Mills Primary School in the London borough of Tower Hamlets created robots with the body part cards but then used Numicon pieces to represent the height of each part. This meant that they were easily able to compare the heights of their robots and spot which ones were missing. Here are some photos to show what they did:
Three very good ways of solving this problem  well done!
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 the printable sheet available for pairs to use should they wish. 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?
Why not start with one head and look at all the different ways you could add body and legs to it?
How are you going to record what you have found out?
Possible support
Having the pieces printed out and/or using the interactivity will help all learners try out their ideas.
Possible extension
Learners could make their own robot monsters in different sizes or try Find the Difference or The Tall Tower.