EDUC 220
Quiz 4: Focus on Fraction Sense
Due: Friday December 12, 2008
Select any 5 of the following 8 fraction tasks. For each problem you select, identify the type of model being
used, then follow the directions to complete the task. Your work will be assessed on mathematical accuracy of
strategies and solutions as well as the clarity of your communication. Each is worth 5 points.
1. FRACTION WORD PUZZLE
Directions: Read each clue and follow the instructions to form words. You will end up with a
question that needs to be answered.
1. Write the first 2/3 of “who” and the first 2/9 of
“attention.”
2. Write the last ½ of “this.”
3. Write 3/3 of “the.”
4. Write the first ¼ of “tomorrow” and the second ¼ of
“open.”
5. Write the first 2/5 of “offer.”
6. Write the third 1/7 of “teacher.”
7. Write the first 3/8 of fragment, the fourth 1/7 of “discuss,”
and the last 4/10 of “population.”
8. Write the first 1/5 of “calculator,” the last 2/3 of “all,” and
the last ¼ of “compiled.”
2. FAIR SHARES “A”?
Here is a picture of a brownie cut into four pieces:
Some people think these are not fair shares. Write what you believe. “I believe
that the rectangle pieces and the triangle pieces (are/are not) the same size
because . . . .” Justify your response.
3. FAIR SHARES “B”?
One of your students discovered that sometimes ¼ really is bigger than ½. He
draws the following diagrams to show you what he found. What is your
response? Make sure to consider what you think is the student’s
misunderstanding and what you might do to help him to better understand this
concept.
4. CUISENAIRE COOKIE DOUGH RECIPES
Use each of the following recipes to find out the correct “rods” to use in the recipe. Note:
a pinch simply means a single rod.
Cuisenaire Snickerdoodle Cookie
Dough
Cuisenaire Oatmeal Raisin
Cookie Dough
In a small mixing bowl combine:
In a small mixing bowl combine:
7/10 orange rod
2/3 light green rod
5/7 black rod
2/4 purple rod
“pinch” of white rod
8/9 blue rod
3/5 yellow rod
3/6 dark green rod
“pinch” of white rod
7/10 orange rod
6/7 black rod
¼ purple rod
5. EQUIVALENT FRACTIONS
How do you know that ¾ = 9/12? Use a diagram to support your explanation.
6. FRACTION SENSE
Order the set of fractions using “fraction sense”—no common
denominators allowed. You may refer to the “rules” we created.
1/8, 2/5, 5/8, 5/6, 3/49, 3/56, 4/7, 3/10
7. ADDING FRACTIONS
A student tries to add 1/6 + 1/6 using the following model and says:
“These both represent 1/6 since one out of size parts is shaded. Now, if we put
these pictures together we have two out of twelve squares shaded, so 1/6 + 1/6
= 2/12.”
a. What is the student’s misconception and how do you help them to
understand?
b. Is there ever a time when the student would be correct in adding 1/6 +
1/6 and getting 2/12? Explain your thinking.
8. SHARING BROWNIES
Which group gets the larger share? Use diagrams to show your answer.
a. Group A: 3 people share 5 brownies.
b. Group B: 2 people share 3 brownies.