Why do this problem ?

Possible approach

The problem assumes some familiarity with Cuisenaire rods, so if students are not familiar with the different colours and lengths, it may be worth spending some time first exploring a set of rods or using the online environment.

"I wonder how many different ways we could combine white rods (1) and red rods (2) to make the same length as the orange rod (10) ..."

Give students some time to think about the challenge, and then share their thoughts. The following might emerge:
"There are going to be loads of different ways"
"How are we going to be able to make sure we don't miss any?"

If no-one has suggested it: "Perhaps we could work on a simpler version of the problem to see if that helps. Let's see how many ways we could make the pink rod (4) out of whites and reds."
Once students have agreed on the five ways that a pink can be made from whites and reds, invite them to find the number of ways to make light green (3), yellow (5), and dark green (6). Then encourage them to make a prediction for black (7) and then test it out.

It is important to set aside enough time for students to think about and appreciate why each answer is the sum of the previous two. To draw out this insight, you might suggest that students organise their work into two categories: solutions that start with a red (what's left?) and solutions that start with a white (what's left now?)

Key questions

Possible extension

Students could try 1 Step 2 Step, which has the same mathematical structure but set in a different context.

Possible support