Math Tips from Homework Help: Proportional Reasoning

Blog Post created by teachontarioteam on Apr 23, 2015

kevin_bio_pic_75x75.jpgKevin Williams is the Program Consultant for K-8 Numeracy with the Dufferin Peel Catholic District School Board, and a senior tutor with Homework Help, the free online math resource for kids in grades 7 to 10.



Proportional reasoning is not an easy one to explain.  The Ontario Math Curriculum defines proportional reasoning as “reasoning based on the use of equal ratios”.  In Paying Attention to Proportional Reasoning, John Van de Walle describes it as “the ability to think about and compare multiplicative relationships between quantities”. So, for example, it’s thinking about the number 10 being two times as much as 5, as opposed to 5 more than 5.






Proportional relationships are formally introduced to Ontario students in Grade 4. But there’s lots of work in the early grades that can support the development of proportional reasoning.  Comparing money amounts is one way that this can happen.












In Grades 4 and beyond, students begin to work with ratios, rates, fractional equivalence and percent.  It is developing the idea of multiplicative thinking as opposed to additive thinking.  Here’s what that means:







Supporting Proportional Reasoning with Your Child:


So how do you help your child develop proportional reasoning? Here are some tips:


  1. Highlight ratios as they exist in everyday life:

    Making juice: What is the ratio of water to juice (e.g. 3 cans of water for 1 can of frozen concentrate). What happens if you are making two batches? Three batches?  How much more water do you need?

    Buying groceries: Ask your kids to comparison shop, reminding them that the lowest price is not always the best deal – they need to compare the amount of product against the price to make a good decision. Which is the better deal for the Cheetos displayed here?


    Driving in the car: Point out speed signs and ask your kids to figure out what would be the maximum speed for a half hour? For two hours?speedlimit.JPG

  2. Explore measurement conversions.

    ►Measure your child’s arm length, or foot using centimetres.  How many millimetres is that?  Skip the tricks or apps to do this – have your child work from the fact that in 1cm there are 10mms.

  3. Explore equivalent fractions.

    ►Use the multiplication table to help your child see the relationship with equivalent fractions. For example , if you look at ½ as a fraction, and now look to the right, each pair of numbers represents an equivalent fraction.
    multiplication table.jpg

  4. Explore scales on maps.

    For example, on a map, 1 cm may represent 50 kilometres. Have your child figure out different distances based on the scale. How many kilometres is half a centimeter, two-thirds?