Solving Ratios with a Tape Diagram

Once students understand how the tape diagram works, they are ready to start solving ratio problems using this visual tool.  You can print and laminate ratio cards, or have students draw boxes.

We are going to look at 2 examples on how to use the tape diagram to solve ratio problems.  The first example is when we are given one of the parts and the second example is when we are given the total.

Example 1:  The ratio of boys to girls is 2:3.  If there are 10 boys, how many girls are there? 

Have students represent the ratio with their tape diagram cards and label boys and girls.

 

If there are 10 boys, that means each of the two cards must be worth 5.  Since all of the ratio cards have to be the same in order to have an equivalent ratio, put a 5 on every card.  This means that there must be 15 girls.

Example 2:  The ratio of cats to dogs in a shelter is 5:1.  If there are 24 animals, how many cats are there?   

Have students represent the ratio with their tape diagram cards and label cats and dogs.

This time, we were given the total number of animals.  That means that the 6 total cards is representing 24.  Therefore, each card must be worth 4, because 24 divided by 6 is 4.  Our final answer is 20 cats.

I hope this visual model is an effective strategy for your students!
~MN

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