Proportional reasoning is one of the biggest math ideas students will develop over the junior years. It applies to almost all areas of the curriculum, and is considered a critical concept for success in secondary math.

Despite this, the curriculum has a few expectations dealing with rates and ratios under a *Proportional Relationships* heading, and then leaves other proportional problems as unconnected ideas in number sense and other strands.

Proportional reasoning is, most simply, the ability to compare two things using multiplicative thinking, and then apply this to a new situation. It is also frequently defined as just the ability to compare quantities multiplicatively.

Here’s a good example.

In 30 minutes, Bob reads 60 pages of a book. How long should it take him to read 150 pages? |

You can compare pages to minutes (pages are twice as much as minutes), and then apply this understanding to the new situation of 150 pages.

You could also compare the 60 pages to 150 pages (2 and a half times more), and then apply this relationship to the amount of time.

There are several other strategies students will naturally use for problems like these – I’ll try to get a set of student samples posted.

The research for developing proportional reasoning skills indicates several strategies, most of which are the opposite to approaches in most textbooks.

1.** Proportional reasoning is best developed in investigative problem solving lessons.**

In the junior grades most texts show students ratios, then rates, and then maybe has them solve unit rate problems. Larger proportional reasoning problems of the type above might appear in this chapter but usually are in the multiplication / division section with no reference to proportional reasoning skills.

2. **Student understand best when multiple strategies are shared and discussed.**

3. **Problems should start with high context, hands on situations.**

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If it takes him 30mins to read 60 pages,

1h=120pages

So to read 30 pages half 30 which is 15

Therefore it’s gonna take her 15 minutes to read 30 pages

It takes 1h 15 minutes to read 150 pages

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