Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58059
Party Punch - Compare Ratios
Students are asked to compare ratios given in two different tables.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, ratio, rate, ratio table, unit rate, compare
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PartyPunchCompareRatios_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Party Punch – Compare Ratios worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to recognize equivalent ratios.
Examples of Student Work at this Level
The student determines that the ratios within each table are not equivalent because:
There are different numbers in each row of the table.
There is less cranberry juice than ginger ale in each row of the table.
The same number cannot be added each time to the numbers in the left column to get the numbers in the right column.
All the ratios look different and [the numbers] keep getting farther apart.
page 1 of 5 The student uses a faulty strategy for comparing the ratios, e.g., by forming ratios within the same columns, saying
and
for Chris’s table and and
for Jenny’s table.
The student says the ratios in Chris’s table are proportional because you can multiply each amount of cranberry juice by four to get the related amount of ginger ale, but
the ratios in Jenny’s table are not proportional because there is no number to multiply to get all the numbers to equal.
Questions Eliciting Thinking
What is a ratio? Using Chris’s table, can you write an example of a ratio of cups of cranberry juice to cups of ginger ale?
What is the proportion of cranberry juice in Chris’s first recipe?
How can you tell if two ratios are equal?
Instructional Implications
Review the concept of a ratio and emphasize the meaning of specific ratios in context. For example, explain that if the ratio of cranberry juice to ginger ale is 1:4 then there
is one cup of cranberry juice for each four cups of ginger ale in a recipe. Guide the student to use ratio language, e.g., “for each”, “for every”, and “per,” when interpreting
ratios or describing their meaning. Use models or drawings to illustrate the ratio. Then review what it means for ratios to be equivalent. Assist the student in devising
strategies for determining when ratios are equivalent such as converting each ratio to a unit rate or writing each ratio as a fraction in lowest terms.
Be sure the student understands the multiplicative relationship between the parts of a ratio. Show the student that for each of Chris’s recipes, the amount of ginger ale is
always four times the amount of cranberry juice. Explain that this also indicates that the ratio of cranberry juice to ginger ale is the same for each of Chris’s recipes. Provide
an additional table entry such as nine cups of cranberry juice and ask the student to determine the amount of ginger ale needed to maintain the 1:4 ratio. Provide additional
tables of ratios and ask the student to determine which ratios, if any, are equivalent and to explain why.
Provide continued instruction on rates and ratios. Provide real-world context that is accessible to the student and ask comparative questions in context. Encourage the
student to use tape diagrams and double number lines to model and explore ratios.
Moving Forward
Misconception/Error
The student is unable to compare two different ratios.
Examples of Student Work at this Level
The student answers that the two ratios represented by each table are the same because:
They both have more ginger ale than cranberry juice.
When you add each row of cranberry juice and ginger ale in the two tables they are equal, e.g., 1 + 4 = 2 + 3 or 2 + 8 = 4 + 6.
If you add up all the numbers in each table they will both equal 55.
page 2 of 5 The student answers that Chris’s recipe is stronger because he uses more ginger ale.
Questions Eliciting Thinking
How can you compare two ratios?
What proportion of Chris’s punch is cranberry juice? What proportion of Jenny’s punch is cranberry juice?
Can you convert each ratio to a unit rate? How can that help you find the punch with a higher proportion of cranberry juice?
Instructional Implications
Review the meaning of ratios and strategies for comparing ratios. Guide the student to convert each ratio, i.e., 1:4 and 2:3, to a unit rate and interpret the meaning of
each unit rate in the context of the problem, e.g., “In Chris’s recipe there is cup of cranberry juice per cup of ginger ale.” Have the student compare the unit rates to
determine which punch is stronger.
Additionally, assist the student in using each ratio to express the fraction of the punch that is cranberry juice. For example, the ratio 1:4 indicates that Chris’s punch consists
of one part cranberry juice for each four parts of ginger ale so that the cranberry juice represents one of five total parts. Therefore Chris’s punch is cranberry juice. Use a
visual model to make this conversion clearer. Ask the student to calculate the fraction of Jenny’s punch that is cranberry juice and to compare the fractions to determine
which punch is stronger.
Provide additional opportunities to compare ratios that arise in real-world contexts.
Almost There
Misconception/Error
The student is unable to explain the comparison of the ratios using proportional reasoning.
Examples of Student Work at this Level
The student concludes that Jenny’s punch contains a higher proportion of cranberry juice but offers an incomplete explanation. The student says:
She uses more cranberry juice.
Chris didn’t add as much as Jenny.
Jenny’s recipe would be stronger because it’s 2:3 (without further explanation).
The student offers an incorrect explanation for Jenny’s punch having the stronger cranberry taste: Chris only started with one cup of cranberry juice compared to Jenny starting with two cups.
Chris has to add three cups but Jenny only has to add one cup of ginger ale.
All of Jenny’s numbers are higher.
Jenny’s amounts of cranberry juice are always double Chris’s cranberry juice amounts.
Questions Eliciting Thinking
How do you know that Jenny’s recipe is stronger? Can you explain how you determined this?
Suppose each recipe contained one cup of cranberry juice and Chris’s recipe also contained two cups of ginger ale. How much ginger ale could Jenny’s recipe contain so
that Jenny’s recipe is stronger? Weaker?
Instructional Implications
Model explaining the meaning of rates and ratios in the context of problems. Use ratio language, e.g., “for each”, “for every”, and “per,” when interpreting or describing the
meaning of ratios and unit rates. Model using and explaining unit rates to compare ratios. Expose the student to the explanations of his or her peers at the Got It level.
Provide more opportunities for the student to justify his or her reasoning in comparing ratios.
page 3 of 5 Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student concludes that:
Each of the ratios in Chris’s recipes is equivalent to 1:4 (or you can always multiply the amount of cranberry juice by four to get the amount of ginger ale).
Each of the ratios in Jenny’s recipes is equivalent to 2:3 (or you can always multiply the amount of cranberry juice by 1.5 to get the amount of ginger ale).
Jenny’s recipe is stronger because:
She has a greater proportion of cranberry juice to ginger ale, compared to Chris’s recipe.
For two cups of cranberry juice, Jenny will use three cups of ginger ale but Chris will use eight cups of ginger ale, so his will taste weaker.
When Chris uses one cup of cranberry juice he uses four cups of ginger ale, but when Jenny uses one cup of cranberry juice she will only use 1.5 cups of ginger ale.
Jenny’s is stronger because of it is cranberry juice but in Chris’s only is cranberry juice.
Questions Eliciting Thinking
What would the unit rate for each recipe be? If you want to make a recipe using only one cup of ginger ale, how much cranberry juice would you need for each recipe?
What amount of each ingredient would you need to use to result in a total of one cup (or a total of 20 cups) of each recipe?
Instructional Implications
Encourage the student to write an equation that shows the relationship between the amount of cranberry juice and the amount of ginger ale for each punch, e.g., g = 4c
describes the relationship between these quantities for Chris’s punch where c is the amount of cranberry juice and g is the amount of ginger ale. Ask the student to use
the equation to find the amount of one quantity given an amount of the other.
Provide the student with a fraction of a part of a two-component quantity, e.g., a quantity of chocolate milk is
chocolate syrup and the remainder is milk. Challenge the
student to determine the ratio of chocolate syrup to chocolate milk.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Party Punch - Compare Ratios worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the
tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to
mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being
mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve
page 4 of 5 MAFS.6.RP.1.3:
problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying
or dividing quantities.
e. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.
(1See Table 2 Common Multiplication and Division Situations)
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard, they use a range of reasoning and representations to analyze
proportional relationships.
page 5 of 5