Ratios and Proportions / Solving Proportions

Understanding

Students consider ratio problems that involve an additional constraint on the quantities. In particular, the two quantities involved add to a given sum as well as have a proportional relationship. Students look at the problem using a table, a graph and equations.

What to look for

Students might solve problems in this activity using double number lines, ratio tables, the unit rate, the equation, a graph, or drawing a diagram. The answers to the questions will vary. Ask students to note the advantages and disadvantages of using the various techniques.

Sample Assessment

A board is cut into two pieces in a ratio of 4:5. If the length of the board is 36 inches, how long is each piece?

Answer: 16 inches and 20 inches

The Big Idea

Proportions are tools for solving a variety of problems with two variables involved in a proportional relationship. Students need to examine situations carefully to determine if they describe a proportional relationship.

What are the students doing?

Students use unit rates, equations, graphs, and revisit ratio tables and double number lines to reason about problems involving proportionals. The importance of units in helping set up a problem and in thinking about the solution is stressed in several places.

What is the teacher doing?

A common error in setting up proportions is placing numbers in incorrect locations. For this reason students should pay particular attention to the units involved in setting up the problem.