Solving Problems about Proportional Relationships


Activity #1

Compare Relationships from a Table.

A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.

  • Use the information below to answer the questions that follow.

(1.) Order the people from greatest to least in terms of total number of comments checked.

(2.) Order the people from greatest to least in terms of how fast they checked the comments.

(3.) Write equations for each job applicant that allow you to easily decide who is working the fastest.

  • Make a table that allows you to easily compare how many comments the four job applicants can check.

Activity #2

Solve Problems Involving Proportional Relationships.

Lin and her brother were born on the same date in different years. Lin was 5 years old when her brother was 2.

  • Find their ages in different years by filling in the table and answer the question below.

(1.) Is there a proportional relationship between Lin’s age and her brother’s age?

(2.) Explain your reasoning.

(3.) For each situation below, explain whether you think the relationship is proportional or not. Explain your reasoning.

(a.) The weight of a stack of standard 8.5 x 11 copier paper vs. number of sheets of paper

(b.) The weight of a stack of different-sized books vs. the number of books in the stack.

Every package of a certain toy also includes 2 batteries.

(1.) Are the number of toys and number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.

(2.) Use t for the number of toys and b for the number of batteries to write two equations relating the two variables.

(i.) b =

(ii.) t =

Activity #3

Model Pairs of Proportional Relationships.

  • Check the box “show grid” in the applet below.​
  • Check the box “Enter x value” in the applet below.​
  • Type a whole number in the box for x. ​
  • Before you press the enter key on your keyboard, make a guess of what you expect the y value will be. ​
  • Repeat with different numbers.​
  • Click the reset button and instead of entering an x-value, enter a y-value and predict what the x-value will be before pressing the enter key. 

What difficulties did you encounter in finding the corresponding x or y values?

Challenge #1

Fill in the input boxes with different proportional relationships that are equivalent to the one given. Then graph it afterwards. Try to include a ratio that fall within the limits of the axes. When you enter all the three points correctly, a “show grid” messahe appears. Click on it to assist you locate one of the points. Remember that the dollar amount is on the vertical scale, and the time is on the horizontal scale.

Challenge #2

Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2.

Challenge #3

A student argues that does not represent a proportional relationship between and because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student?

Quiz Time