Ratios with Tape Diagrams (6th Grade)

What is it?

A ratio compares two amounts. "3 red for every 2 blue" is the ratio 3:2 of red to blue. A tape diagram draws each amount as a row of equal boxes, so the ratio is easy to see: 3 boxes in the red row and 2 boxes in the blue row. When you know the real count for one row, split it among its boxes to find what one box is worth. The other row uses the same box value.

Step by step: 3 red for every 2 blue

1. There are 3 red for every 2 blue. Draw a row of 3 boxes for red and a row of 2 boxes for blue, all the same size.
2. The ratio of red to blue is 3:2.
3. Now suppose there are 15 red. The 3 red boxes hold 15 in all.
4. Find the value of one box: 15 ÷ 3 = 5. Every box is worth 5.
5. The blue row has 2 boxes: 2 × 5 = 10. There are 10 blue.
6. Check: 15 red and 10 blue is still 3 red for every 2 blue, because 15 ÷ 5 = 3 and 10 ÷ 5 = 2.

Common mistakes

• Adding instead of scaling. With 15 red, adding 12 to both would give 14 blue, but the boxes must stay equal in size.
• Switching the order. 3 red to 2 blue is 3:2, not 2:3.
• Giving the red row and the blue row different box sizes. Every box in a tape diagram is worth the same amount.

Your turn

Here is a problem to try. Pause and let your child work it out before you check.

There are 4 red for every 5 blue. If there are 20 red, how many blue are there?

Answer: 25 blue. The 4 red boxes hold 20, so each box is 20 ÷ 4 = 5. The blue row has 5 boxes: 5 × 5 = 25.

Practice at home

Use two colors of snack or blocks. Make a ratio like 2 red for every 3 green, then repeat the same pattern to double and triple it and count the totals. Ask your child to draw the tape boxes first and then say what each box is worth.