MATH 612 --RR Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
(Math task group tag order is C-D-A-B)
RR Math Task C: M & M Ratios
 The following task should help you think about how increasing basic ratios can be used to
think about large, still equivalent ratios
 Include all of your work, sketches, answers and written explanations for the math tasks (IIII) as well as your answers to the “Question for you” (IV) in your write up.
Ratio diagram, Ratio table and M & M models
1 5 10 15 20
3 6 9 12 15
M & M Ratio Questions
In a bag of M & M’s, the ratio of green M & M’s to yellow M & M’s is 2 to 5.
I. If there are only green and yellow M & M’s in the bag, what is the smallest number of M &
M’s possible? Illustrate and explain.
II. If there are 84 M & M’s in a bag of green and yellow M & M’s, how many are green?
a. Use a ratio diagram to solve this question, illustrate and explain.
b. Use an equivalent ratio table to solve this question, explain.
c. Use algebra to solve this question, explain.
III. If red M & M’s are added to the bag in part b to get a total of 100 M & M’s, what is the ratio
of green M & M’s to yellow M & M’s to red M & M’s? Illustrate and explain.
Question for you (please answer)
IV. Can you imagine an upper elementary or middle school student solving part b with (II) a
ratio diagram, (III) an equivalent ratio table or (IV) algebra? Which way would make the
most intuitive sense to them? Discuss each option as it would relate to student
understanding.
MATH 612 --RR Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
RR Math Task D: Jelly Bean Ratios
 The following task should help you think about the interaction of equivalent ratios (a
multiplicative relationship) and how addition and subtraction changes this equivalence
 Include all of your work, sketches, answers and written explanations for the math tasks (I)
as well as your answers to the “Question for you” (II) in your write up.
Ratio diagram, Ratio table and Jelly Bean models
1 5 10 15 20
3 6 9 12 15
Jelly Bean Ratio Questions
For the following question:
I. The ratio of red jelly beans to yellow jelly beans in a dish is 3 to 4. If Greg eats 3 red jelly
beans and 6 yellow jelly beans, the ratio of red jelly beans to yellow jelly beans is now 4 to
5. How many red and how many yellow jelly beans were originally in the dish?
a. Use a ratio diagram to solve this question, illustrate and explain.
b. Use an equivalent ratio table to solve this question, explain,
c. Use algebra to solve this question, explain.
Question for you (please answer)
II. Can you imagine an upper elementary or middle school student solving this question with (I)
a ratio diagram, (II) an equivalent ratio table or (III) algebra? Which way would make the
most intuitive sense to them? Discuss each option as it would relate to student
understanding?
MATH 612 --RR Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
RR Math Task A: The Bike Ride
 The following task should help you think about basic rates, how the relate to basic line
graphs and how the units involved with the rates are reflected in the graphs
 Include all of your work, sketches, answers and written explanations for the math tasks (IIV) as well as your answers to the “Question for you” (V) in your write up.
Ratio table and Bike models with a Graph
1 5 10 15 20
3 6 9 12 15
Bike Ride Questions
I.
Sally rode her bike from her house, at a constant rate, 7 ½ miles to her friend’s house. She
left at 10 a.m., roe straight to her friend’s house without stopping, and arrived at 10:40 a.m.
How far from home was Sally at 10 minutes, 20 minutes, and 30 minutes? How fast, in miles
per hour, did Sally ride on the way to her friend’s house?
II. The next day, Sally rode her bike to her friend’s house on the same path, at a constant rate
for the first 20 minutes, stopped at the 4 mile point for 5 minutes to see a nice view, then
continued on at a (possibly different) constant rate for the last 25 minutes until she arrived
at her friend’s house. How far from home was Sally at 10 minutes, 30 minutes, and 40
minutes? How fast, in miles per hour, did Sally ride on this second trip?
III. Graph both journeys on the same grid with the horizontal axis time in hours and the vertical
axis total distance, in miles, from Sally’s house. Be sure to label your graph and axes.
IV. Compare Sally’s speeds, when is she going fastest? How can you tell by looking at the
graphs? How can you tell using her speeds? Illustrate and explain.
Question for you (please answer)
V. How are these questions related to rates, and how do these rates relate to the graphs?
Discuss in detail.
MATH 612 --RR Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
RR Math Task B: Chickens and Eggs
 The following task should help you think about how ratios and rates work together, and the
importance of using units to help guide your thinking.
 Include all of your work, sketches, answers and written explanations for the math tasks (I)
as well as your answers to the “Questions for you” (II-III) in your write up.
Ratio diagram, Ratio table and Chicken models
1 5 10 15 20
3 6 9 12 15
Chicken and Egg Question
I.
If a dozen hens lay a dozen eggs in a dozen days, how many eggs do 108 hens lay in 108
days? Show and explain your solution fully, pay particular attention to units and correctly
showing rates. Hint – the answer is not 108 eggs!
Questions for you (please answer)
II. Now that you have an answer, can you use a different method to solve the question? Use a
different method from algebra, an equivalent ratio table, a ratio diagram or a different
method to show the solution path a different way.
III. How do your solution relate to ratios? Does increasing a triple ratio here (e.g., 1:2:3 is
equivalent to 2:4:6) work in this case? Why or why not? How does this relate to rates?