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.

2 part ratio

3 part ratio

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.

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2. Fill in the gap in the total column for the ratio.

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3. Here we have set up a fraction, this fraction is the value of one part of the ratio.

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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.

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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.

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2. The fraction is set up, so find the value of one part.

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3. Find the amount of yellow buttons.

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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.

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2. Find the corresponding difference in the ratio.

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3. This is our fraction – find the value of one part.

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4. Total the ratio and multiply to find the amount of tiles.

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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.wp-1541602611227.jpg
  2. We group and total the corresponding parts of the ratio.wp-1541602664224.jpg
  3. This is our fraction – find the value of one part.
    wp-1541602707831.jpg
  4. Multiply to find the amount of men.
    wp-1541602759096.jpg

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.
      wp-1541603270039.jpg
    2. The fraction is set up, so find the value of one part.wp-1541603304763.jpg
    3. Find the value of ‘n’.wp-1541603359207.jpg

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.
      wp-1541603603257.jpg
    2. The fraction is set up, so find the value of one part.
      wp-1541603644737.jpg
    3. This is the amount of pounds.wp-1541603676206.jpg

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.wp-1541603779603.jpg
  2. The fraction is set up, so find the value of one part.wp-1541603818545.jpg
  3. Find the amount of miles.wp-1541603869240.jpg

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!”.

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