Claire Lee devised this inquiry for her year 6 class. Using the prompt 40 x 40 = 39 x 41 + 1, she reports that the inquiry involved high levels of motivation, rich activities and the introduction of many new topics:
"I had seen someone's work about asking students to start with 2 x 2 then look at 1 x 3 and it built from there. One of the things I loved was the way students started to change the prompt. They predicted that moving two numbers, for example 40 x 40 = 38 x 42, would mean you had to add 2 but then quickly picked up that there would be a square number pattern. We got a lot of new material out of it: square roots, exponents, some simple multiplication of two digit numbers and place value. I am really enjoying using the idea of a prompt to start the lessons."
The prompt can develop into proving that the difference between n2 and (n - 1)(n + 1) is always one. It is possible to bridge between number and algebra through the same approach to multiplication. The grid method for finding the product of two double-digit numbers can be used to find the product of two algebraic expressions (see below). The method has the advantage of showing the structure of the calculation.
Claire is a Year 6 Coordinator and class teacher. You can follow her on twitter@cpl1909.
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