Different Objects, Same Ratios? – Equivalent Ratios
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
Explore Practice
Guided Preparing for Activity:
 NOTE: This activity is best before students have learned
strategies to determine if ratios are equivalent.
 Print card sets on card stock, cut out, and place each set in
an envelope
 Option: Read Activity 6.3 on p.161 of Teaching StudentCentered Mathematics Grades 5-8 by John A. Van de Walle
Assessment
Materials:
 Box/Truck Card sets for each
group
 Option: Dollars/Candy Card
sets for each group
 Different Objects, Same Ratio
Worksheet
Setting the Stage:

Have students grouped for discussion during activity

Use student-generated responses to discuss the
connection between ratios and the phrase “for every.”

Discuss the opening questions on the worksheet. Have
students discuss which rate makes more sense (boxes
per truck or trucks per box).
How will you introduce students to the
activity so as to provide access to all
students while maintaining the cognitive
demands of the task?
Explore the Concept:
What questions will be asked to focus
students’ thinking on the key
mathematics ideas?

How are these ratios different from fractions?
What questions will be asked to assess
student’s understanding of key
mathematics ideas?

Which set of cards did you start with? Why?
What questions will be asked to
encourage all students to share their
thinking with others or assess their
understanding of their peers?

What method did you use to compare your ratios? Is
there another method?
How will you extend the task to provide
additional challenge?

How could you use Card #6 to calculate how many trucks
you will need to move 48 boxes?

How could you use Card #5 to calculate how many trucks
you will need to move 48 boxes?

Distribute the Dollar/Candy card set and allow students to
repeat the activity with the new information where they
will need to use their understanding of decimals.
This can be used as an introduction into using ratios to
represent pricing
Reflection:
What specific questions will be asked so
that all students will:
 Make sense of the mathematical
ideas?

Expand on, debate and question
the solutions being shared?

Make connections between
different strategies that are
presented?

Look for patterns?

Begin to form generalizations?

Given a pair of cards, how can you tell if they are
equivalent?

How was card #4 different?
Source: Adapted from Van de Walle, J., Lovin, L. H. (2006). Teaching student-centered mathematics:
Grades 5-8 (Vol. 3). Boston, MA: Pearson Education, Inc. – p.161
Card #1
Card #2
Card #3
Card #4
Card #5
Card #6
Card #1
Card #2
Card #3
Card #4
Card #5
Card #6
Name_____________________________ Date ____________Period_____________
“Damian has 15 boxes and 3 trucks with
which to move them.”
Record 2 ratios that describe this situation:
Based on the two rate descriptions, which makes
more sense to use? Why?
_______________________________________
_______________________________________
Directions:
1. Use the space provided below to write down the key information from each card (and any other needed work).
2. Work with your teammates to decide which cards have ratios of trucks and boxes that are the same.
3. Answer the questions below.
Card #1
Card #2
Card #3
Card #4
Card #5
Card #6
Which cards show the same rate of boxes per truck?
Reflection:
Describe how you decided which cards had the same ratio of boxes to trucks.
______________________________________________________________________________________
______________________________________________________________________________________
What is special about card #6? If this card helped you with this task, describe how.
______________________________________________________________________________________
______________________________________________________________________________________
Challenge! Based on the ratios above, how many trucks will you need to move 48 boxes? (answer for each group of
same ratios) If each group of ratios represents a company that charges per truck, which will be cheaper to use?
Name_____________________________ Date ____________Period_____________
“Kyesha purchased 4 candy bars for $2.”
Based on the two rate descriptions, which makes
more sense to use? Why? Are they equally useful?
Record 2 ratios that describe this situation:
_______________________________________
_______________________________________
Directions:
1. Use the space provided below to write down the key information from each card (and any other needed work).
2. Work with your teammates to decide which cards have ratios of candy bars and dollars that are the same.
3. Answer the questions below.
Card #1
Card #2
Card #3
Card #4
Card #5
Card #6
Which cards show the same rate of candy bars per dollar?
Reflection:
Describe how this problem was more challenging than the boxes and trucks.
______________________________________________________________________________________
______________________________________________________________________________________
If a student told you that Card #2 and Card #6 are the same ratio because Card #2 has one more dollar
and one more candy bar, what could you explain to that student.
______________________________________________________________________________________
______________________________________________________________________________________
Challenge! Based on the ratios above, how much will it cost to buy 36 candy bars? (answer for each group of same
ratios) If each group of ratios represents a different store, which store is cheaper?