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Solving Ratio and Proportion Word Problems using Patterns

solving ratio and proportion word problems using patterns and lesson freebie

Solving ratio and proportion word problems is challenging for many students.  Interpreting the word problem and deciding whether each value is the part or total is difficult.  To help students gain a better understanding of ratio and proportion word problems, a strategy that builds from concrete to abstract is essential.

Basic Patterns of Ratio and Proportion Word Problems

Proportional reasoning is a complex skill.  There is a very basic skill that your students have known since preschool that can help them create proportional reasoning.

If you have ever watched the educational cartoons, you have surely seen the characters solve simple puzzles using patterns.  They move along the path and announce, “Green, Green, Red, Green, Green, Red, Green, Green…  What comes next?”  This type of pattern is actually the foundation for proportional reasoning!

This pattern is actually a simple proportion.  Every time there are two greens, then there is also a red.  We can model patterns such as these using a hands-on tool like beads and ribbon, snap cubes, colored tiles, almost anything!

beads on a ribbon showing a patterns

Look at the blue and yellow beaded pattern in the picture above.  It has a pattern of 3 blue beads, 2 yellow, 3 blue, 2 yellow, and so on.  Have students create the pattern using a concrete model.  Use the model to create a ratio table for each iteration of the pattern.  Use sentence stems to describe the pattern:

Every time there are 3 blue beads there also must be 2 yellow beads. That means if there are ______ there also must be ______.

Begin with ratio and proportion problems that use small enough numbers to model concretely.  When the numbers get so large that your students cannot make the model you can use the next strategy.

Creating Strip Diagrams from Ratio Models

Using concrete models to represent ratio and proportion word problems works great when the numbers are relatively small.  What if you need to model a problem that needs to be scaled up 20 times, 50 times, or 500 times!  Obviously, the concrete model will not work well once the numbers get that large.  (Well, actually the model would still work perfectly, but it would be very time consuming to create!)

Now is the time to bridge toward some paper and pencil modeling.  Students will use the physical model to create a strip diagram that represents the ratio from the word problem.

Watch this quick video to see this process illustrated!

Ready to Teach Ratio and Proportion Word Problems?

If this method seems like a helpful tool for your students, you can download a free worksheet to help take your students through this process by filling out the email form below!

You may also want to try some of these ready to use printable or digital interactive notebooks to help guide your students through ratios, rates, and proportionality!

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