Fraction Operations: Exploration into Connection Math Tasks, page 1 of 4
E Manipulatives:
BBN VMK (color tiles, fraction bars and geoboards)
Math Learning Center (geoboard app)
Math Task 1
Scenario 1: Suppose one of your students comes to you and says: “Look at these color
tiles; I think I have figured our fractions.
This shows that
1 1 2
 
2 3 5
a. Explain what your student did incorrectly in Scenario 1 (but don’t give the correct
model until part c)
Scenario 2: Suppose your student now comes to you and says: “OK, now I get the idea
of using the same model for one. I think I have figured our fractions now!
This shows that
1 1 4
 
2 3 6
b. Explain what your student did incorrectly in Scenario 2 (but don’t give the correct
model until part c)
1 1
c. Sketch a correct model, using a color tiles, showing  .
2 3
Connections questions for Math Task 1. Include in write up and post online using the
Connections forum.
1. Which CCSSM Practice Standards did you use in this math task? Please explain briefly.
2. Which CCSSM content standard(s) at which grade level(s) does this math task address?
3. What is the learning trajectory of this math task—what do children need to know to do
this task (relate to CCSSM content standards and grade) and what mathematics does this
task prepare the children for (relate to CCSSM content standards and grade)?
Fraction Operations: Exploration into Connection Math Tasks, page 2 of 4
Math Task 2abc
Please do not use dimensions (for example, “what is the area of a square that is 2/3 of a foot by 4
feet” would not be acceptable). For each of these, you should have a short story (three to five
sentences at most) and a simple, but clearly labeled model (briefly explain the model).
a. Create a simple story context suitable for an elementary school student that results in the
2

2
question:  4  of 4   ? Use a visual fraction model to show the product.
3
3


b. Create a simple story context suitable for an elementary school student that results in the
2
question: 4   ? Use a visual fraction model to show the quotient.
3
c. Create a simple story context suitable for an elementary school student that results in the
2 3
question:   ? Use a visual fraction model to show the quotient.
3 4
Connections questions for Math Task 2abc. Include in write up and post online using the
Connections forum.
1. Which CCSSM Practice Standards did you use in math task a, b, c? Please explain
briefly.
2. Which CCSSM content standard(s) at which grade level(s) do math tasks 2abc address?
3. What is the learning trajectory of math tasks 2abc—what do children need to know to do
this task (relate to CCSSM content standards and grade) and what mathematics does this
task prepare the children for (relate to CCSSM content standards and grade)?
Math Task 3
1
Use the relationship between multiplication and division to explain that 4   20 because
5
1
20   4.
5
Connections questions for Math Task 3. Include in write up and post online using the
Connections forum.
1. Which CCSSM Practice Standards did you use in this math task? Please explain briefly.
2. Which CCSSM content standard(s) at which grade level(s) does this math task address?
3. What is the learning trajectory of this math task—what do children need to know to do
this task (relate to CCSSM content standards and grade) and what mathematics does this
task prepare the children for (relate to CCSSM content standards and grade)?
Fraction Operations: Exploration into Connection Math Tasks, page 3 of 4
Math Task 4
 No associated Connections question post, math task and one CCSSM question write up only
If it is in a book, it must be true
This question is from a sixth grade math book
Tony works at a pizza shop. He cuts two pizzas into eight equal sections each.
7
7 7 14
14
Customers then eat of each pizza. Tony says that   , so
of all the pizza
8
8 8 16
16
was eaten. Is Tony's addition correct? Explain.
Here is what the teachers’ manual said:
14
of all the pizza was eaten, this would be less than one whole pizza. If there
16
are eight sections in each pizza, then people are eating eighths. And all together they at
14
6
, or 1 pizzas.
8
8
No. If
14
of all the pizza was eaten” correct?
16
7 7 14
b. Did Tony “do the math” correctly? That is, is   ?
8 8 16
c. Is everything said in the teachers’ manual correct? Pay close attention to the whole
answer, not just the conclusion. If you think the teachers’ manual is not fully correct,
rewrite the statement so it is fully correct.
a. Is Tony’s statement “
d. Which CCSSM content standard(s) at which grade level(s) does the student math task
described here address?
Math Task 5
 No associated Connections question post, math task and one CCSSM question write up only
 Please do not write an entire lesson plan, just give a simple explanation.
a c ac
 
works using “folding paper”
b d bd
examples as your model in a way that would makes sense to an inquisitive sixth grader.
a. Explain how the rule for multiplying fractions,
b. In which CCSSM content standard(s) at which grade level(s) is this rule mentioned?
Fraction Operations: Exploration into Connection Math Tasks, page 4 of 4
Math Task 6
 No associated Connections question post, math task and one CCSSM question write up only
 Please do not write an entire lesson plan, just give a simple explanation.
a c ad
 
, "invert and multiply" works in
b d bc
a way that would makes sense to an inquisitive sixth grader that asks you why this is the
rule.
a. Explain how the rule for dividing fractions,
b. In which CCSSM content standard(s) at which grade level(s) is this rule mentioned?