Solving proportion word problems using sentence stems

Teaching proportionality is a difficult task with any group of students, but with students who may be below their grade level in reading, teaching proportional relationships may seem to be nearly impossible.  After years of working with English learners in the math classroom, a simple sentence stem may be all you need to bridge the gap when teaching your proportions unit this school year.

My students were always looking for patterns in word problems—quick fixes that would “tell” them exactly what they were supposed to be doing.  As a teacher, this often made me crazy.  The story problems just did not work like that.  Once we started proportions, this student tactic was made even worse by the way the proportion problems were worded.  My kids needed a pattern—a mathematically correct pattern—for analyzing proportion problems.  They needed a signal that the problem that they were solving was not just about operations, but that they would need to find the information and set up a proportion.

How would they be able to tell when they are working on a problem that contained proportional relationships?

We were on the look out for questions that could fill this pattern:

When I have ________________, I also have ___________________.

Let’s look at an example from the proportionality interactive notebook set:

Two teachers supervise 70 students in the cafeteria during lunch time.  When five teachers are available during lunch time, how many students can be in the cafeteria?

Can this word problem fill in the sentence stem?  Yes, we can say that, “When I have 2 teachers, I also have 70 students.”  Practice this pattern again and again with your students.  Every time you are looking at a word problem, use this sentence stem with your students.  As you repeat the stem, write the ratio. 

Your students will start recognizing the ratio in word problems with this repeated practice.

Can your students write the proportion equation?

Once your students have mastered finding the ratio in the word problem, the next step is to add one more piece to the sentence stem.

When I have ___________________, I also have __________________, but I really have_________________.

Back to our previous example from the proportionality interactive notebook:

When I have 2 teachers, I also have 70 students, but I really have 5 teachers.

This new stem gives the students all the pieces they will need to write a proportionality equation.

Before long, your students will be able to recognize proportional situations in word problems and analyze those problems to write proportion equations.

Solving proportion word problems using sentence stems.

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