Why do this problem?
requires learners to see the connections between numbers in a set and so find the rest of the set. They will need to make and test hypotheses, and justify their reasoning.
You could start by using this interactivity
during a 'warm-up' activity. Choose a particular property and drag one number with that property onto the left side of the grid. Invite the group to work out what the property is that you have chosen by calling out other numbers, which you then place on the appropriate side of the grid. Can they decide
upon the 'rule' in as few guesses as possible?
The class could then work in pairs on the problem itself so they can talk through their ideas with a partner. They will need this sheet of information about the numbers, which can be cut up into cards to make it easy to use. Observing how children record as they work
on this challenge will be very informative for you. This special hundred square could help some learners to record if they are struggling to find their own way. The different groups of numbers, the red set, the blue set and the black set could be recorded like
Using a hundred square to record (whether it is the special one or a 'standard' one) will reveal patterns and therefore may help children work out their properties.
Discussion at the end of the lesson could include not only the sets of numbers that have been found, but also the ways that the children approached the problem. What did they do first? What were their first ideas? How did they decide whether these initial hypotheses could be right? How did they record their thinking? Did they work in a systematic way? How did they know that their solution
What is the same about these numbers? What do these numbers have in common?
What do you know about this number? Is that true of any of the others in the set?
How will you keep track of your thinking?
Can you see a pattern on the hundred square?
Can you see any gaps in that pattern?
Why do those numbers make that pattern?
Learners could do the much harder Ben's Game
or make up their own clues for sets of numbers for others to try.
Some learners might need you to suggest using a hundred square and they could start by putting the numbers in the "red set" onto it. Can they find the rest of the numbers in this set? They might start by trying this slightly more straightforward related problem