How Many Cubes?
1 out of 3
This problem challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Problem
Take a look at the video below.
You might like to pause it every time Liz asks Bernard a question and think about how you would answer.
When Liz takes out some of the cubes from under the cloth, how many do you think there might be still under the cloth? Can you explain your thinking?
When Liz takes some more cubes out, what do you think now? How many cubes do you think there are altogether? How do you know?
You'll see that Bernard and Liz count how many cubes there are altogether.
When they put all the cubes back under the cloth and take two out, how many are still under the cloth? How do you know?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Working on this problem can encourage learners to work together, discuss ideas, test things out, and explore further. This is how it is to be a mathematician, working alongside other mathematicians.
This activity can do well to replace questions set out like; 3 + ? = 8, ? + 4 = 8 etc. Those written examples can be very confusing to decipher, whereas the early thinking of many children enables them to manage very confidently the more practical approach outlined in the video. This project will help to develop concepts of algebraic thinking.
Possible approach
You could invite children to watch the video, pausing each time a question is posed. Alternatively, you could recreate the video yourself to introduce the mathematics. Even if you use the video initially, you'll want to have cubes and a cloth available so you can explore the context further and set up additional challenges.
You can invite a child to take some of the cubes out from under the cloth and ask the group how many there are left. This encourages algebraic thinking. You could go further by saying "I'm covering up 15 cubes. How many would I have to take out for there to be 8 left under the cloth?". You could try giving children some cubes from under the cover, telling them how many are hidden altogether, and asking, "How many did I have to start with?".
Encourage pupils to think about what other children have said. When a child makes a suggestion, it can be useful to ask why they think that but repeating what they said word for word, without feeling the need to paraphrase. For example, a child might say "there should be 8 there" and the teacher might respond: "why do you say 'there should be 8 there'?".
Key questions
- Do you agree with what ... said?
- Why do you think there are four hidden?
- Tell me about that (thought).
- Do you all agree then that ...?
- How can we find out?
- What questions would you like to ask?