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Big Ideas Math: Modeling Real Life, Grade 6

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Big Ideas Math: Modeling Real Life, Grade 6 View details

2. Using Tape Diagrams

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Exercise 6 Page 117

Remember that 1 part in a tape diagram can represent different values.

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Practice makes perfect

We want to describe 2 different ways that we can represent the given ratio using a tape diagram. In this ratio, the first quantity is 3 times the second quantity. 3&* 4 &⇓ & 12: 4 To do this, we should draw two tapes, one for each quantity in the ratio, so that the lengths of these tapes represent the relationship described by the ratio. First, let's draw 2 tapes in which each part represents 1 unit. This means that the first tape will have 12 parts and the second tape will have 4 parts.

We can see that the length of the first tape is 3 times the length of the second tape. However, one part in the tape diagram does not necessarily have to represent 1 unit. Let's suppose that each part in a tape diagram represents 4 units. We can calculate the number of parts needed for each tape by dividing the original quantity from the ratio by the value of one part. 12/4& = 3 [0.3em] 4/4& = 1 The first tape will have 3 parts and the second tape will have only 1 part.

Notice that these are only two example ways to represent the given ratio using a tape diagram. We can draw more tape diagrams as long as the first tape is 3 times longer than the second tape.

Subchapter links

Try It p.116-117

Self-Assessment for Concepts & Skills p.117

Self-Assessment for Problem Solving p.118

Review & Refresh p.119

Concepts, Skills, & Problem Solving p.119-120