This past week C25 have been tackling some really tricky maths problems, where they have been required to convert worded problems, to pictorial models, to mathematical calculations, to finally find an answer!
We’ve been required to multiply and divide integers (whole numbers) by fractions, and divide/multiply fractions by fractions, which many of us wanted to know how to do after our grapple! However, we have found using bar models has really helped.
The activity set out was a card sort, Where students had to find all 3 matching cards, and work out the answer at the end. Some superstars realised that there was more than one calculation that they could use to complete a problem. eg. 3 ÷ 1/3 would give me the same answer as 3 x 3, so as long as we multiplied/divided (depending on the inverse operation) by the reciprocal, we’d be able to work out our answers.
Once each pair had completed their activity, we then went on a bit of a gallery walk, and peer critiqued our work, making suggestions and corrections when we disagreed with other table’s answers. It was fantastic to hear students use our mathematical keywords, such as reciprocal, inverse operation, denominator and numerator in their answers. The collaboration on this task was really impressive, and I heard some fantastic discussions filled with mathematical reasoning.
I was especially impressed with students who used bar models to represent their solutions. This provided everyone with a really intuitive, visual representation of what 1/2 ÷ 1/4 looked like, and why the answer was 2!