Teach-Primary-Issue-19.7

Exploring complex concepts in maths shows pupils that there’s often more than one way to find the solution to a problem... W e want children to have opportunities to be playful in mathematics. We want them to experiment, persevere through challenge, search different possibilities and spot patterns. This is the true nature of what it means to be a mathematician. How, though, can this be done in areas of maths that seem to be more procedural, like multiplication? And how can lessons be structured so that all children can engage in problem-solving, rather than just the highest attaining children? Here, we will look at a ‘big mathematical idea’ and consider the different ways that it can be explored. We will also consider how we can gradually sequence tasks so that all pupils can be supported and challenged. The sum and the product Before this task, we must ensure that children understand the terms ‘sum’ and ‘product’. This can be done by giving an example: “The sum of 6 and 2 is 8 (6+2=8). The product of 6 and 2 is 12 (6×2=12)”. Ask the children to consider these calculations. What do they notice this time? 5 × 5 = 6 × 4 = 7 × 3 = 8 × 2 = Now, the products are not the same. When a pair of factors increases/decreases by 1, the product becomes smaller! Is this always true? The children could create some of their own example Then, we must check for understanding before the children engage in the main task. For example, “What is the sum of 5 and 3? What is the product of 5 and 3?”. When children are secure with this terminology, we are ready to progress. Next, we can give children these calculations and ask them what they notice: 5 + 5 = 6 + 4 = 7 + 3 = 8 + 2 = Of course, the sum of each pair of numbers is the same. When one addend increases by 1 and the other addend decreases by 1, the sum of the pair of numbers stays the same. questions to test this theory. Or we could ask them to predict which calculation will have the larger product: 6 × 6 or 7 × 5? Then, a more open challenge can be introduced. Usually, I would introduce the task in stages, so it’s not too overwhelming when it’s first presented. Can children find an answer? A different answer? Or maybe even work systematically to find all the possible answers? You can also create new follow-up questions, such as by changing the word in the question from ‘less’ to ‘more’. The same ‘big idea’ can be explored with older children, working in a larger number range. For example, when we look at this sequence of questions, the same pattern is revealed: 10 × 10 = 100 11 × 9 = 99 12 × 8 = 96 13 × 7 = 91 14 × 6 = 84 What’s the BIG IDEA? GARETH MET CALFE “These tasks will enable pupils to experience what it means to be a true mathematician” Step 2: I think of two numbers. The sum of my numbers is 12. The product of my numbers is less than 30. What could my numbers be? Step 1: I think of two numbers. The sum of my numbers is 12. The product of my numbers is less than 30. What could my numbers be? 50 | www.teachwire.net