Tape diagrams are a great visual tool for understanding ratios. Students can easily draw tape diagrams or you can print and laminate tape diagram cards and have students write on them with dry erase markers. I like using the tape diagram cards because sometimes students have a hard time making equal size boxes.
Have students represent the ratio 2:3 using the tape diagram cards or by drawing 2 boxes and underneath, 3 boxes.
When we write on the tape diagram cards, we must write the same number in each card in order to keep our ratios equivalent. This is super important! Let’s write 2 in each box. That would give us 4 in the top ratio and 6 in the bottom ratio. Therefore, a ratio of 4:6. That means that the ratio of 2:3 equals the ratio of 4:6.
If we write a 3 in each box, that would give us a ratio of 6 to 9. If we write a 4 in each box, that would give us a ratio of 8:12. All of the ratios when simplified equal 2:3.
Let’s look at another example. Represent the ratio 6:5.
Have students write a number of their choice in the boxes to represent equivalent ratios. Have students share their results. Some possible answers would be 12:10, 18:15, 24:20.
Discuss with students how it is important to keep the order of the ratio the same. If the first number is larger than the second, it should stay that way when you find your equivalent ratios. Also, we do not convert ratios into mixed numbers.
Once students have a strong understanding of how the tape diagram works, they are ready to start solving ratio problems using the tape diagram.