Teach-Primary-18.3

• Where might you start, and why? • Now that we know that shape, how will that help? What does that tell us? How do we know? • How are you keeping track of what you have done? the semi-circle’s value larger than 12. So, I settled on 2. After filling out the spots where the squares and semi-circles were used, I started creating a key which would state all the values I had found. Note Ginny started with the first calculation, using the additional information given in the question to support her reasoning. It would be worth stopping everyone for a brief mini plenary before that if you notice some interesting and efficient ways to record. 3 | SHARING YOUR SOLUTIONS You might also like to share examples of solutions from other learners and compare them to the ones your class has suggested. Here’s the beginning of a solution submitted to NRICH by Ginny: I started with the first sentence, which is the square times square times square equals semi-circle one. I used the process of elimination to figure it out. It couldn’t have been 1, since then multiple shapes would have the same number. And it couldn’t have been 3, because that would’ve made • Pupils could make up their own problem based on Shape Times Shape that also uses shapes as symbols. Just as in the NRICH example, they could write their own solution as well. • The children could also write a list of hints and tips for others to help them get started on their problem. • Ask chilren to try out their own problem on friends or family members, and perhaps develop it further based on their feedback. • You could publish a selection of the final versions of the children’s own problems on your school website or in your newsletter. • As a class or year group, you could create a maths activity book containing everyone’s problems, with an answer section at the back. EXTENDING THE LESSON In contrast, Syzmon, Charlie and Hattie submitted this solution, which began by using different calculations from Ginny’s: We realised that any time the isosceles triangle featured, the answer was the isosceles triangle, so it must be 0. Then we figured out that the only cubed number below 12 was 2 because 1 would make it be another square as the answer, when it was a half-circle. That made the half-circle have a value of 8. We knew that something times 2 equalled 8 so we then realised that the oval must be 4. Next, we did the rectangle times rectangle and worked out that it was 3 because the only number squared that we could use was 3, as we had already used 2. Did your learners use either of these approaches? Perhaps they found another way to solve the challenge? NRICH is a maths outreach project, which is a collaboration between the Faculties of Education and Mathematics, based at the University of Cambridge. NRICH resources are free for teachers to use with their classes. “Listen out for clear reasoning, based on learners’ knowledge of number properties” USEFUL QUESTIONS www.teachwire.net | 75