WAR Against Ratio

I have created a frame to help scaffold ratio problems.  It wasn’t until a student said “Should I use that war thing?” that I noticed the acronym.

Below are two examples of the frame.  The first is a two-section ratio, the second is a three-section ratio.  More sections could be added by adding extra columns.  I will demonstrate how this frame can be used to solve ratio and proportion problems, including:

1. Share into a ratio
2. Given an amount
3. Given a difference
4. Given a combination of amounts
5. Unit ratio
6. Currency conversions
7. Unit conversions

Share into a ratio

Carl and Mel share £56 into the ratio 4:3.  How much do they each get?

1. Set up the the frame with the information I have been given. 2. Fill in the gap in the total column for the ratio. 3. Here we have set up a fraction, this fraction is the value of one part of the ratio. 4. Now that one part is known, we can easily find out how much money Carl and Mel get by multiplying by the number of parts. Given an amount

There are red, yellow and blue buttons in a jar in the ratio 7 : 4 : 9.  There are 36 blue buttons.  How many yellow buttons are there?

1. Set up the table – this time we don’t know the total but do know the amount of blue buttons. 2. The fraction is set up, so find the value of one part. 3. Find the amount of yellow buttons. Given a Difference

Sandra has white, red and blue tiles in the ratio 4:3:1.  She has 6 more white tiles than red tiles.  How many tiles do she have in total?

1. Set up the table – we put the difference in between the unknown values. 2. Find the corresponding difference in the ratio. 3. This is our fraction – find the value of one part. 4. Total the ratio and multiply to find the amount of tiles. Given a combination of amounts

Men, women and children visit a cinema in the ratio 6:5:7.  On Tuesday 72 women and children visited the cinema.  How many men visited?

1. Set up the table – we know the total of two amounts so we indicate that by grouping them. 2. We group and total the corresponding parts of the ratio. 3. This is our fraction – find the value of one part. 4. Multiply to find the amount of men. Unit ratio

A breakfast cereal is made with oats and fruit in the ratio 5:4.  Write the ratio in the form 1:n.

1. Set up the table (a total doesn’t make sense here) – we put ‘1’ in the amounts row. 2. The fraction is set up, so find the value of one part. 3. Find the value of ‘n’. Currency conversions

£1:\$1.50, convert \$30 into pounds.

1. Set up the table (a total doesn’t make sense here) – we know the amount of dollars so that goes in the dollars column. 2. The fraction is set up, so find the value of one part. 3. This is the amount of pounds. Unit conversions

3 miles = 5 kilometres, how many miles is 45 km?

1. Set up the table (a total doesn’t make sense) – we know the amount of km so that goes in the km column. 2. The fraction is set up, so find the value of one part. 3. Find the amount of miles. I have found this to be a useful frame for scaffolding these types of problems for students that are having trouble grasping these concepts.  I was particularly happy when, after a recent assessment, a low attaining student was asked, “How did you get 24?”, his reply “I used war!”.