Forming Ratio Concepts and Using Ratio Language
Sources: http://nrich.maths.org/6870
Brief Summary of the Task:
The purpose of this task is for students to begin using ratio language and reasoning
to solve real-world mathematical problems. In this task, students begin to compare
ratios. Students can use a multitude of methods, including using tables of equivalent
ratios, tape diagrams, double number line diagrams, or equations, to solve authentic,
high cognitive demand ratio problems.
Level of Cognitive Demand:
This task is a Level 4 – Doing Mathematics task. It requires complex thinking, and
there is not a predictable, well-rehearsed approach outlined for students in the
instructions. Students are not told a method to use to solve the problem. This task
requires students to explore and understand the concepts of ratios and the
relationships between numbers in those ratios. In this tasks, students must monitor
their own thinking and work, checking to see if their solution method makes sense
along the way. Also, these problems require considerable cognitive effort, and they
may involve some level of anxiety for the student because they are not given a
formula to follow or a direct path to a solution.
Practice Standards Emphasized:
The Task:
1. I mixed up some lemonade in two glasses. The first glass had 200 ml of lemon
juice and 300 ml of water. The second glass had 100 ml of lemon juice and 200 ml of
water. Which mixture has the strongest tasting lemonade? How do you know?
Solutions/Commentary:
We can use manipulatives (such as blocks and chips) to visually see the relationship
between the amount of lemon juice and the amount of water in each mixture. In the
first glass, the ratio of lemon juice to water is 2:3. In the second glass, the ratio of
lemon juice to water is 1:2.
Therefore, in the first mixture, 2/5 of the mixture is lemon juice. In the second
mixture, only 1/3 of the mixture is lemon juice. We can use fraction strips to
compare the two fractions.
With these strips, we can see that 2/5 > 1/3. Therefore, the first mixture is the
stronger tasting lemonade.
Other solution methods:
We can use manipulatives (such as blocks for lemon juice and chips for water) to
visually see the relationship between the amount of lemon juice and the amount of
water in each mixture. In the first glass, the ratio of lemon juice to water is 2:3. In
the second glass, the ratio of lemon juice to water is 1:2. We can add one more block
to the second mixture to represent lemon juice. When we add one more part of
lemon juice to the second mixture, we also have to add 2 more parts of water.
Therefore, the first mixture would have 3 parts water for every 2 parts lemon, and
the second mixture would have 4 parts water for every 2 parts lemon. Thus, the first
mixture is the stronger tasking lemonade (because it is less watered down).
1 a.
A truck is carrying tomato juice, peach juice, and pear juice bottles in a ratio of 2 : 6 : 3. If there a
2 a.
A kennel has 105 dogs in total, some are puppies and some are adult dogs. The ratio of puppies t
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1 a.
Lucas has nickels, dimes, and quarters in the ratio of 2 : 4 : 2. If 40 of Lucas's coins are quarters, h
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=12pt&pad=10&border=1&color=teal&workspace=2&ptitle=&html_worksheet=1