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Division inquiry

For notes and resources on this prompt see the main Inquiry Maths page.
Rich inquiry in a primary classroom
When Amanda Klahn used the prompt with her grade 4 (year 5) class, an extremely rich inquiry developed. Amanda structured the inquiry into three steps. Step 1 saw students post questions and comments to a wall on the class blog. The pupils focused on the meaning of the signs and the accuracy of the equations, speculated about or offered explanations for the underlying mathematics and wondered what would happen if they changed the prompt: 
  • I think 42 x 14 is the same as 84 x 7 because if you split 84 you get 42 and if you split 14 you get 7. 
  • Why does it say that 42 x 14 = 84 when the answer is really 588? 
  • I think the answer to 42 x 14 is the same as 84 x 7, and the same with division. 
  • I understand that 42 x 14 = 84 is not what it's trying to say. It's trying to say that 42 x 14 is the same as 84 x 7. 
  • Does it link to doubles? 
  • Now I see! 42 ÷ 84 = 2 and 7 ÷ 14 = 2. 
  • Maybe the equals sign with the line across means does not equal. 
  • I think the equals sign with the cross means the same thing. 
  • Would it work with subtraction and addition? 
  • What if you use decimals?
Step 2 involved students in responding to their peers' questions and comments. Below is an example of how a pupil tackled some of the issues raised in step 1:
Step 3 was teacher-driven inquiry. Amanda asked: "What could we do to 42 ÷ 14 to change the sign to an equals?" Here is an example of the responses:

Amanda teaches at the Western Academy of Beijing (China). You can follow her on twitter @KlahnAmanda.