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Formative Instructional and Assessment Tasks
Equivalent Pizzas
4.NF.1 - Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper and pencil, Graph paper (optional)
There is two-thirds of a pizza left.
How many pieces of pizza are left if the original pizza had a total of 3 slices? 6 slices?
12 slices?
Write a sentence to explain your thinking.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions: A 3 slice pizza
explanation is unclear OR
would have 2 slices left. A 6
work is logically shown but the
slice pizza would have 4 slices
student has made a calculation
left. A 9 slice pizza would
error.
have 6 slices left.
 The sentence includes a clear
explanation about finding
equivalent fractions.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Equivalent Pizzas
There is two-thirds of a pizza left.
How many pieces of pizza are left if the original pizza had a total of 3 slices?
How many pieces of pizza are left if the original pizza had a total of 6 slices?
How many pieces of pizza are left if the original pizza had a total of 12 slices?
Write a sentence to explain your thinking.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Comparing Ropes
4.NF.1- Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper and pencil, Graph paper (optional)
Sally has a piece of rope that is 3/4 of a foot long. Tomas has a piece of rope that is 1/2 of
a foot long. Mitch has a piece of a rope that is 1/3 of a foot long. How many inches is each
piece of rope? Write a sentence explaining your thinking.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions: Sally- 9 inches.
explanation is unclear OR
Tomas- 6 inches. Mitch- 4
work is logically shown but the
inches.
student has made a calculation  The sentence includes a clear
error.
explanation about finding
equivalent fractions.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Comparing Ropes
Sally has a piece of rope that is 3/4 of a foot long. Tomas has a piece of rope that is
1/2 of a foot long. Mitch has a piece of a rope that is 1/3 of a foot long.
How many inches is each piece of rope?
Write a sentence explaining your thinking.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Trading Blocks
4.NF.1 - Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Pattern blocks, Paper, Pencil, Activity sheet
*Computer-based pattern blocks can be found herehttp://illuminations.nctm.org/ActivityDetail.aspx?ID=27
Task sheet (below).
The 2 pattern blocks below have a value of 1 whole.
Part One:
 If the 2 pattern blocks above have a value of 1 whole, then what is the fractional
value of 3 trapezoids? What is the fractional value of 1 trapezoid?
 If you have 3 trapezoids, how many green triangles would it take to cover the same
area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all
the green triangles? What is the fractional value of one triangle?
 Since the number of trapezoids and the number of green triangles covers the same
space, they are equal. Write an equivalent fraction expressing the number of
trapezoids and the number of green triangles.
Part Two:
 If 2 hexagons have a value of 1 whole, what is the value of 4 blue rhombuses?
What is the value of 1 blue rhombus?
 If you have 4 rhombuses how many green triangles would it take to cover the same
area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all
the green triangles? What is the value of 1 green triangle?
 Write an equivalent fraction expressing the number of rhombuses and the number
of green triangles.
Conclusion:
Write a sentence explaining how you found equivalent fractions.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Accurate solutions: Part Oneexplanation is unclear OR
Trapezoids: 3/4, 1/4. Triangles
work is logically shown but the
9/12, 1/12. Fraction: 3/4 =
student has made a calculation
9/12. Part Two: Rhombuses:
error.
2/3, 1/3. Triangles: 8/12, 1/12.
Fraction: 2/3 = 8/12. AND
 Clearly and accurately explains
their strategy.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Trading Blocks
The 2 pattern blocks below have a value of 1 whole.
Part One:
If the 2 pattern blocks above has a value of 1 whole then what is the fractional value
of 3 trapezoids? What is the fractional value of 1 trapezoid?
If you have 3 trapezoids, how many green triangles would it take to cover the same
area? If the 2 hexagons has a value of 1 whole, what is the fractional value of all the
green triangles? What is the fractional value of one triangle?
Since the number of trapezoids and the number of green triangles covers the same
space, they are equal. Write an equivalent fraction expressing the number of
trapezoids and the number of green triangles.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Part Two:
If 2 hexagons have a value of 1 whole, what is the value of 4 blue rhombuses? What
is the value of 1 blue rhombus?
If you have 4 rhombuses how many green triangles would it take to cover the same
area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all
the green triangles? What is the value of 1 green triangle?
Write an equivalent fraction expressing the number of rhombuses and the number
of green triangles.
Conclusion:
Write a sentence explaining how you found equivalent fractions.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Splitting to Make Equivalent Fractions
4.NF.1-Task 4
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper and pencil
This standard addresses the idea that equivalent fractions can be made by multiplying the
numerator and the denominator by the same number. It also introduces the idea that dividing or
splitting the numerator and denominator by the same number results in an equivalent fraction.
Students will make models to show that splitting the number in the whole also splits the number in
a part of the whole. The resulting fraction is the same.
Task 1:
Jenna ate 1/3 of a cake and had 2/3 leftover for her friends. She split each of the remaining thirds
into four pieces. How many pieces of cake did she have? What fraction of the whole was each
piece?
Each of her friends ate the same amount of cake as Jenna. How many pieces would each friend get
to eat 1/3 of the whole cake? Write or draw this fraction in two different ways.
Solution: There are 8 pieces of cake leftover, each piece is 1/12 of the whole, so 8/12 is leftover.
Each friend will need to eat 4/12 to eat the same amount as Jenna (1/3). 1/3 = 4/12.
Task 2:
Ronoldo ate ¼ of a pizza for dinner and had ¾ of the pizza leftover. He cut the leftover pizza into 6
equal slices for his friends. What fraction of the whole pizza was each piece?
Each of his friends ate the same amount of pizza as Ronoldo. How many pieces would each friend
get in order to eat ¼ of the whole pizza? Represent (write or draw) the solution (fraction) in two
different ways.
Solution: There are 6 pieces leftover, each piece is 1/8 of the whole. If each friend ate ¼ of the
whole, that would be 2 pieces that are eighths, or 2/8, so 2/8 = ¼.
Task 3:
4/12 = 1/3
2/8 = ¼
Look at the equivalent fractions from the story problems. What relationships do you notice between
the numerators and denominators in each equation? What is happening to the numbers? We see the
numbers being split. How can we see this idea happening in the models that you drew?
Can you think of additional examples that show the numerator and denominator of fractions being
split by the same number? What is the result?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students are unable to show
with numbers or models that
a/b = (𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), or to explain
why dividing the numerator and
denominator of a fraction by the
same number yields an equivalent
fraction.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students can show with
numbers or models that a/b =
(𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), but are unable
to explain why dividing the
numerator and denominator of
a fraction by the same number
yields an equivalent fraction.
Level III
Proficient in Performance
 Students can show with
numbers or models that a/b =
(𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), and are able to
explain why dividing the
numerator and denominator of
a fraction by the same number
yields an equivalent fraction.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Splitting to Make Equivalent Fractions
Task 1:
Jenna ate 1/3 of a cake and had 2/3 leftover for her friends. She split each of the
remaining thirds into four pieces. How many pieces of cake did she have? What
fraction of the whole was each piece?
Each of her friends ate the same amount of cake as Jenna. How many pieces would
each friend get to eat 1/3 of the whole cake? Write or draw this fraction in two
different ways.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Splitting to Make Equivalent Fractions
Task 2:
Ronoldo ate ¼ of a pizza for dinner and had ¾ of the pizza leftover. He cut the
leftover pizza into 6 equal slices for his friends. What fraction of the whole pizza
was each piece?
Each of his friends ate the same amount of pizza as Ronoldo. How many pieces
would each friend get in order to eat ¼ of the whole pizza? Represent (write or
draw) the solution (fraction) in two different ways.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Splitting to Make Equivalent Fractions
Task 3:
4/12 = 1/3
2/8 = 1/4
Look at the equivalent fractions from the story problems. What relationships do you
notice between the numerators and denominators in each equation? What is
happening to the numbers? We see the numbers being split. How can we see this
idea happening in the models that you drew?
Can you think of additional examples that show the numerator and denominator of
fractions being split by the same number? What is the result?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Fraction Rectangles
4.NF.1-Task 5
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper and pencil, color tiles
This standard addresses the idea that equivalent fractions can be made by multiplying the
numerator and the denominator by the same number. Students will make models to show that
doubling the number in the whole also doubles the number in a part of the whole. The resulting
fraction is the same.
Task 1: Use color tiles to make a rectangle or square that is one half red and one half blue.
Students will make several different representations of one half. By looking at them in order, they
can see that the denominator and numerator are being multiplied by the same number. Write the
equations so that they can see the proper notation.
Task 2: Use color tiles to make a rectangle or square that is one third red. Find at least three
different ways to represent one third. Using pictures, numbers, and/or words, prove that the
three models that you made are all equal to one third.
Repeat the task with ¼ and 1/6 for additional practice.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students are unable to show
with numbers or models that
a/b = (n x a)/(n x b), or to
explain why multiplying the
numerator and denominator of
a fraction yields an equivalent
fraction.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students can show with
numbers or models that a/b =
(n x a)/(n x b), but are unable
to explain why multiplying the
numerator and denominator of
a fraction yields an equivalent
fraction.
Level III
Proficient in Performance
 Students can show with
numbers or models that a/b =
(n x a)/(n x b), and can explain
why multiplying the numerator
and denominator of a fraction
yields an equivalent fraction.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Fraction Rectangles
Task 1: Use color tiles to make a rectangle or square that is one half red and one
half blue.
Task 2: Use color tiles to make a rectangle or square that is one third red. Find at
least three different ways to represent one third. Using pictures, numbers, and/or
words, prove that the three models that you made are all equal to one third.
Repeat the task with ¼ and 1/6 for additional practice.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Tiling the Patio
4.NF.1 - Task 6
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper, Pencil
Covering the Patio
Part 1:
Cover the patio below with the same kind of tile.
Part 2:
Now cover half of the patio. Complete the table below for how many tiles it would take to
cover half of the tile.
Part 3: For one of the fractions above explain how multiplication can help you find
equivalent fractions.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Accurate solutions: Part 1:
explanation is unclear OR
Each region is accurately
work is logically shown but the
partitioned into equal sections.
student has made a calculation
Part 2: Tile A: 12, 6, 6/12. Tile
error.
B: 6, 3, 3/6. Tile C: 4, 2, 2/4.
Tile D: 8, 4, 4/8.
 Part 3: The student writes
something about, “Multiplying
both the numerator and the
denominator by the same
number will result in an
equivalent fraction.”.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Covering the Patio
Cover the patio below with the same kind of tile.
Part 1:
Tile A: It takes 12 tiles
Tile B: It takes 6 tiles
Tile C: It takes 4 tiles
Tile D: It takes 8 tiles
Part 2:
Cover half of the patio. Complete the table below for how many tiles it would take
to cover half of the tile.
Tile Tiles needed to
cover the whole
patio.
Tile
A
Tile
B
Tiles needed to Fraction showing how much of the patio
cover half the
is covered.
patio.
1
= 6 . 6 of the patio is covered by tiles.
Tile
C
Tile
D
2
12
12
1

2
1

2
1

2
Part 3: For one of the fractions above explain how multiplication can help you find
equivalent fractions.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Weird Pieces of Cake
4.NF.1 - Task 7
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though
the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions.
Paper, Pencil
Weird Pieces of Cake
Part 1:
A baker makes square cakes and decides to cut the pieces different each day of the week.
If she wants to make 8 dollars for the whole cake, how much money will each individual
piece sell for?
Part 2: While shopping on Wednesday, Martina says to the baker, “Buying 2 pieces of
cake today will cost the same as one piece of cake on Monday. Is Martina correct? Explain
why or why not.
(Modified from the Unusual Baker, NCTM, 2012)
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Accurate solutions: Part 1:
explanation is unclear OR
Monday- $4 each. Tuesday- $4
work is logically shown but the
for large piece. Small pieces
student has made a calculation
are $2 each. Wednesday- $2
error.
each. Part 2: The explanation
says something about,
“Monday’s slices are ½ of the
whole cake. Wednesday’s
slices are 2/4 of the whole
cake. ½ = 2/4.”
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Weird Pieces of Cake
Part 1:
A baker makes square cakes and decides to cut the pieces different each day
of the week. If she wants to make 8 dollars for the whole cake, how much
money will each individual piece sell for?
Part 2: While shopping on Wednesday, Martina says to the baker, “Buying 2
pieces of cake today will cost the same as one piece of cake on Monday. Is
Martina correct? Explain why or why not.
(Modified from the Unusual Baker, NCTM, 2012)
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
The Whole Matters
4.NF.2-Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g.
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as ½. Recognize that comparisons are valid only when the two fractions refer
to the same size whole. Record the results of comparisons with symbols >, =, or <, and
justify conclusions, e.g., by using a visual fraction model.
Paper and pencil
Task 1:
Two friends each ate ½ of a pizza. Joselin says they must have eaten the same amount, but Donnie
says they could have eaten different amounts. Who do you think is correct, and why? Explain your
thinking in words, pictures, and numbers.
Possible solution: The two friends could have each eaten half of two different size pizzas. Half of
a large pizza is more than half of a medium pizza because the wholes are not the same size.
Task 2:
Mrs. Johnson and Mrs. Black each gave ½ of their students a pencil. Mrs. Johnson handed out 5
more pencils than Mrs. Black. What can we say about the number of students in each class?
If Mrs. Johnson handed out 16 pencils and that was 5 more than Mrs. Black, how many students
are in each class?
Possible solution: Mrs. Black must have 22 students in her class. Mrs. Johnson must have 32
students in her class.
Task 3:
Jerry made one gallon of sweetened tea and one half gallon of lemonade for a picnic. If he drank ¼
of each container, how many cups of tea did he drink? How many cups of lemonade?
*1 gallon = 16 cups
If Jerry drank 2 cups of lemonade and 2 cups of tea, what fraction of the tea did he drink? What
fraction of the lemonade did he drink?
Possible solution:
Question 1: Jerry drank 4 cups of tea and 2 cups of lemonade.
Question 2: Jerry drank 1/8 of the gallon of tea and ¼ of the half gallon of lemonade.
Connect the tasks by discussing with students how the size of the wholes matters in each context.
Level I
Limited Performance
 Students are unable to solve
Task 1, 2, or 3.
Rubric
Level II
Not Yet Proficient
 Students can solve 1 or 2 of
the 3 tasks correctly with a
complete explanation.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Students can solve and explain
their answers to all three tasks.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
The Whole Matters
Task 1:
Two friends each ate ½ of a pizza. Joselin says they must have eaten the same
amount, but Donnie says they could have eaten different amounts. Who do you
think is correct, and why? Explain your thinking in words, pictures, and numbers.
Task 2:
Mrs. Johnson and Mrs. Black each gave ½ of their students a pencil. Mrs. Johnson
handed out 5 more pencils than Mrs. Black. What can we say about the number of
students in each class?
If Mrs. Johnson handed out 16 pencils and that was 5 more than Mrs. Black, how
many students are in each class?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
The Whole Matters
Task 3:
Jerry made one gallon of sweetened tea and one half gallon of lemonade for a
picnic. If he drank ¼ of each container, how many cups of tea did he drink? How
many cups of lemonade?
*1 gallon = 16 cups
If Jerry drank 2 cups of lemonade and 2 cups of tea, what fraction of the tea did he
drink? What fraction of the lemonade did he drink?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Enough Soda
4.NF.2 - Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.
Paper and pencil, Graph paper (optional)
You need 3/4 of a Liter of soda to make punch for a party. Which containers have enough
soda in them to make punch? Write a sentence explaining your thinking.
Container A- 2/4 of a Liter
Container B- 2/3 of a Liter
Container C- 5/6 of a Liter
Container D- 11/12 of a Liter
Container E- 7/12 of a Liter
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions: Containers C and D.
explanation is unclear OR
 The sentence shows a clear and
work is logically shown but the
logical explanation of their
student has made a calculation
strategy.
error.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Enough Soda
You need 3/4 of a Liter of soda to make punch for a party. Which containers have
enough soda in them to make punch? Write a sentence explaining your thinking.
Container A- 2/4 of a Liter
Container B- 2/3 of a Liter
Container C- 5/6 of a Liter
Container D- 11/12 of a Liter
Container E- 7/12 of a Liter
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Which is Bigger?
4.NF.2- Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2. Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.
Pattern blocks, Paper and pencil
Optional: Graph paper
*Computer-based pattern blocks can be found herehttp://illuminations.nctm.org/ActivityDetail.aspx?ID=27
Which is Bigger?
Two joint hexagons have a value of 1 whole. Based on that, draw each fraction in terms of
pattern blocks and determine which is bigger:
 3/4 or 4/6
 1/2 or 5/12
 2/4 or 3/6
 5/6 or 3/4
Write your own comparison question using fourths, sixths, or twelfths. Draw a picture to
prove which is easier.
Pick one of the questions above and write a sentence explaining how you know that you
are correct.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions: 4/6, 1/2, they are
explanation is unclear OR
equal, 5/6. AND
work is logically shown but the  The sentence shows a clear and
student has made a calculation
logical explanation of their
error.
strategy.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Which is Bigger?
If two hexagons have a value of 1 whole, think about the value of other pattern block. Draw
each fraction below in terms of pattern blocks and determine which is bigger:
 3/4 or 4/6
 1/2 or 5/12
 2/4 or 3/6
 5/6 or 3/4
Write your own comparison question using fourths, sixths, or twelfths. Draw a picture to prove
which is easier.
Pick one of the questions above and write a sentence explaining how you know that you are
correct.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pattern Blocks
4.NF.2-Task 4
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g.
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as ½. Recognize that comparisons are valid only when the two fractions refer
to the same size whole. Record the results of comparisons with symbols >, =, or <, and
justify conclusions, e.g., by using a visual fraction model.
Paper and pencil, pattern blocks, grid paper
Task 1: Use pattern blocks.
 If a hexagon is one whole, which block represents ½? Which block represents 1/3? Which
blocks represents 2/3?
 If a trapezoid if one whole, which block represents 1/3? Which block represents 2/3?
 If a blue rhombus is one whole, which block represents ½?
 If a blue rhombus is ½ of a whole, what would one whole look like?
 Find one half of a hexagon and one half of a blue rhombus. Why don't they make one whole
altogether?
 If a green triangle is 1/3 of a whole, what would one whole look like? How many these wholes
could you make with 3 hexagons?
Task 2: Use grid paper.
1. Justin planted tomatoes in 1/3 of his 6' x 6' garden. Gina planted tomatoes in 1/3 of her 8' x 7'
garden. How many square feet of the garden did each person use for tomatoes? If each person
planted 1/3 of their garden with tomatoes, why did they use a different amount of square feet?
2. Deon used a 9 x 9 grid to represent 1 whole and Shawn used a 12 x 12 grid to represent 1. Each
boy shaded in squares to show 1/3 of the whole. How many squares did Deon shade? How
many squares did Shawn shade? Why did they shade different numbers of squares if they each
shaded in 1/3?
Level I
Limited Performance
 Students are unable to solve
Task 1 or 2.
Rubric
Level II
Not Yet Proficient
 Students can solve 1 of the 2
tasks correctly with a complete
explanation.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Students can solve and explain
their answers to both tasks.
Responses indicate that they
understand that the size of the
whole determines the amount
in a fraction of that whole.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pattern Blocks
Task 1: Use pattern blocks.
If a hexagon is one whole, which block represents ½?
Which block represents 1/3?
Which blocks represents 2/3?
If a trapezoid if one whole, which block represents 1/3?
Which block represents 2/3?
If a blue rhombus is one whole,which block represents ½?
If a blue rhombus is ½ of a whole, what would one whole look like?
Find one half of a hexagon and one half of a blue rhombus. Why don't they make
one whole altogether?
If a green triangle is 1/3 of a whole, what would one whole look like?
How many these wholes could you make with 3 hexagons?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Task 2: Use grid paper.
1. Justin planted tomatoes in 1/3 of his 6' x 6' garden. Gina planted tomatoes in 1/3
of her 8' x 7' garden. How many square feet of the garden did each person use for
tomatoes? If each person planted 1/3 of their garden with tomatoes, why did they
use a different amount of square feet?
2. Deon used a 9 x 9 grid to represent 1 whole and Shawn used a 12 x 12 grid to
represent 1. Each boy shaded in squares to show 1/3 of the whole. How many
squares did Deon shade? How many squares did Shawn shade? Why did they
shade different numbers of squares if they each shaded in 1/3?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who’s on the Bus?
4.NF.2 - Task 5
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.
Paper and pencil, Graph paper (optional)
There are some children on the bus.
2/6 of the children are wearing tan pants.
6/10 of the children are wearing tennis shoes.
5/12 of the children are wearing a red shirt.
2/3 of the children are wearing a hat.
For each item of clothing, are more than half or less than half of the children wearing that
item?
Write a sentence explaining how you know that you are correct.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions: Less than half- tan
explanation is unclear OR
pants, red shirt. More than
work is logically shown but the
half- tennis shoes, hat.
student has made a calculation  The sentence demonstrates a
error.
clear understanding of
comparing fractions to the
benchmark of 1/2.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who’s On The Bus?
There are some children on the bus.
 2/6 of the children are wearing tan pants.
 6/10 of the children are wearing tennis shoes.
 5/12 of the children are wearing a red shirt.
 2/3 of the children are wearing a hat.
For each item of clothing, are more than half or less than half of the children
wearing that item?
Write a sentence explaining how you know that you are correct.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who Has More Gum?
4.NF.2- Task 6
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Extend understanding of fraction equivalence and ordering.
4.NF.2. Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.
Paper, pencil, sentence strips or paper to fold (optional)
Who has more gum?
A group of friends buys a big long strip of gum and tear it into pieces. Sally has 2/3 of a
foot of gum. Josey has 3/4 of a foot of gum. Mitch has 4/6 of a foot of gum. Gary has 3/6
of a foot of gum.
Part 1:
Draw pictures and write an expression using the >, <, or = signs to show who has more
gum between:
Gary or Sally?
Mitch or Sally?
Josey or Mitch?
Part 2:
Taylor comes in and gets ½ of a foot of gum. Gary says, “We have the same amount.” Is
Gary correct? Why or why not?
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to find equivalent fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Answer is correct, but the
 Solutions:
explanation is unclear OR
Part 1: Sally. 3/6 < 2/3. The
work is logically shown but the
same. 4/6 = 2/3. Mitch. ¾ <
student has made a calculation
4/6.
error.
Part 2: Gary is correct. 3/6 = ½.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who Has More Gum?
A group of friends buys a big long strip of gum and tear it into pieces. Sally has
2/3 of a foot of gum. Josey has 3/4 of a foot of gum. Mitch has 4/6 of a foot of
gum. Gary has 3/6 of a foot of gum.
Part 1:
Draw pictures and write an expression using the >, <, or = signs to show who
has more gum between:
Gary or Sally?
Mitch or Sally?
Josey or Mitch?
Part 2:
Taylor comes in and gets ½ of a foot of gum. Gary says, “We have the same
amount.” Is Gary correct? Why or why not?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Sharing Cake
4.NF.3- Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Build fractions from unit fractions.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify decompositions, e.g.,
by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8
= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Other Standard:
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Paper, pencil
At a party you are giving out 8 pieces of cake. People will get different amounts of cake.
Tom and Hal will both get 1 piece of cake. Mary will get 2 pieces of cake. Nancy and Bob
share equally the remaining pieces of cake. What fraction of the cake will each person eat?
Write an equation to match the situation. Write a sentence explaining the strategy used to
solve the problem.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to represent the pieces of cake
as fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Answer is correct, but the
equation or explanation is
incorrect OR work is logically
shown but the student has
made a calculation error.
Level III
Proficient in Performance
 Solutions: Tom and Hal: 1/8,
Mary, Nancy and Bob: 2/8
 Equation: 1/8 + 1/8 + 2/8 + 2/8
+ 2/8 = 8/8 AND The sentence
clearly describes an accurate
strategy.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Sharing Cake
At a party you are giving out 8 pieces of cake. People will get different amounts of
cake.
 Tom and Hal will both get 1 piece of cake.
 Mary will get 2 pieces of cake.
 Nancy and Bob share equally the remaining pieces of cake.
What fraction of the cake will each person eat? Write an equation to match the
situation.
Write a sentence explaining the strategy used to solve the problem.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Candy Bucket
4.NF.3 - Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Build fractions from unit fractions.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify decompositions, e.g.,
by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8
= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Other Standard:
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Paper, pencil
There are 12 pieces of candy in the bucket. Maria and Sam each get 2 pieces of candy.
Tom gets 5 pieces of candy. Vinny gets the rest of the candy. What fraction does each
student get? Write an equation to match this story. Write a sentence to explain the strategy
used to solve the problem.
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to represent the pieces of cake
as fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Answer is correct, but the
equation or explanation is
incorrect OR work is logically
shown but the student has
made a calculation error.
Level III
Proficient in Performance
 Solutions: Maria and Sam:
2/12 or 1/6. Tom: 5/12. Vinny
3/12.
 Equation: 2/12 + 2/12 + 5/12 +
3/12 AND The sentence
clearly describes an accurate
strategy.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Candy Bucket
There are 12 pieces of candy in the bucket.
 Maria and Sam each get 2 pieces of candy.
 Tom gets 5 pieces of candy.
 Vinny gets the rest of the candy.
What fraction does each student get? Write an equation to match this story.
Write a sentence to explain the strategy used to solve the problem.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Square Tiles
4.NF.3-Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each
mixed number with an equivalent fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
Pencil, paper, square tiles
Task 1: Use square tiles to build mixed numbers.
Place 3 color tiles together as a whole on the table or draw on board or display however works best
for your classroom.
One way to understand mixed numbers is to look at them as groups of unit fractions. Model how to
use square tiles to build the number 2 1/3.
 If this rectangle is a whole what does one tile represent? (thirds)
 How many square tiles does it take to make one whole? (three thirds)
 How many thirds will we need to build 2 whole? (six thirds)
 Build arrangement below, how many thirds in all did we use? (seven thirds or 1/3 + 1/3 + 1/3 +
1/3 + 1/3 + 1/3 + 1/3)
Continue to use the square tiles to connect unit fractions and mixed numbers. Now the square tiles
represent ¼.
 If we wanted to build the number 3 ¼, how many tiles would we need? How do you know?
 Build 2 3/8. How many tiles do you need? How many unit fractions make one whole?
 If you have 17 square tiles and each one is an unit of a whole, how many fourths can you
build? Students should make four groups of four fourths with one fourth left over. What mixed
number does this make? 4 ¼
Task 2: Use mixed number fractions to compute.
In Task 2, some students may be able to transition to drawing the mixed number models while
others may continue to need the square tiles to count the unit fractions. Some may draw or build
the models and cross out or combine pieces to find answers. One strategy of efficiently adding and
subtracting mixed number is to convert them to improper fractions, and some students may be able
to do this using models. Allow students to complete the problems and then share their strategies.
Addition:
Maria needs 6 1/3 feet of string for a solar system mobile. She has 2 2/3 feet of yellow string and 3
2/3 feet of green string. How much string does she have altogether? Will it be enough to complete
the project? Explain why or why not.
Subtraction:
Leland has 5 1/8 pizzas left over from his birthday party. After giving some pizza to his friend, he
has 3 3/8 pizzas left. How much pizza did Leland give away to his friend?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students are unable to convert
mixed numbers to improper
fractions, use models to build
mixed numbers, or add or
subtract mixed numbers with
like denominators.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students can build and draw
mixed numbers, and can use
models to show the
equivalence of improper
fractions and mixed numbers.
Students are unable to solve
mixed number word problems
by breaking up mixed numbers
to facilitate addition and
subtraction.
Level III
Proficient in Performance
 Students can build and use
models and equations with unit
fractions to solve the problems.
Students are able to use the
idea of mixed numbers as
groups of unit fractions, or as
an improper fraction to solve
addition and subtraction
problems with like
denominators.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Square Tiles
Addition:
Maria needs 6 1/3 feet of string for a solar system mobile. She has 2 2/3 feet of
yellow string and 3 2/3 feet of green string. How much string does she have
altogether? Will it be enough to complete the project? Explain why or why not.
Subtraction:
Leland has 5 1/8 pizzas left over from his birthday party. After giving some pizza to
his friend, he has 3 3/8 pizzas left. How much pizza did Leland give away to his
friend?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pattern Blocks & Unit Fractions
4.NF.3-Task 4
Domain
Cluster
Standard(s)
Materials
Task
Number and Operation- Fractions
Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
4.NF.3 Understand a fraction a/b with a> 1 as a sum of fractions 1/b.
4.NF.3a. Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Pattern blocks, Pencil, Paper
Use unit fractions in the equations to show that a fraction can be thought of as the sum of several
unit fractions.
Task 1: Use pattern blocks.
Establish equivalencies with students. If the yellow hexagon is one whole, what fraction of the
whole is each block? If the green triangle is 1/6 of the whole, how many green triangles would we
need to build 4/6?
Use the pattern blocks to model and solve these problems. Write an equation to represent each
situation. Use unit fraction to represent each pattern block in the equation.
 Scott and Zachary shared a sub. Scott ate 2/6 of the sub. Zachary ate 1/6 of the sub. How much
of the sub did they eat together? 1/6 + 1/6 + 1/6 = 3/6
 Three students were sharing 2 pies. Each student ate ½ of a pie. How much of the total amount
of pie did they eat together? ½ + ½ + ½ = 3/2 or 1 ½
 Trevor had 1 1/3 pizzas. His dad ate 2/3 of a pizza. How much pizza was left? 1 1/3 = 3/3 +
1/3 or 4/3. 4/3 = 1/3 + 1/3 + 1/3 + 1/3. If you subtract 2/3 from that there will be 2/3 leftover.
 Madeline had 7/6 yards of fabric. She cut off one yard to make curtains. How much fabric was
left? 7/6 = 6/6 + 1/6 so she had 1/6 of one yard of fabric left.
 Lauren had 7/3 pans of brownies leftover after a party. Her brother ate 2/3 of a pan of
brownies. What part of the total amount of brownies was left? 7/3 = 3/3 + 3/3 + 1/3 or 2 1/3.
2 1/3 = 1 + 1/3 + 1/3 + 1/3 +1/3 and if we subtract 2/3 there will be 1 2/3 pans of brownies
leftover.
Task 2: Use unit fractions to solve.
Use what you know about unit fractions to solve the problems. Write an equation that includes unit
fractions to show the answer for each problem.
2/3 + 2/3 =
1¼–¾=
½x5=
4/3 = 1/3 + x
2 1/5 – 3/5 =
1 3/5 + 4/5 =
Rubric
Level I
Level II
Limited Performance
Not Yet Proficient
 Students are unable to use
 Students can use models to solve
models or unit fractions to
the problems in Task 1 but have
solve the problems in Tasks 1
difficulty writing equations with
and 2.
unit fractions in Task 1 and/or 2.
NC DEPARTMENT OF PUBLIC INSTRUCTION
5/7 + y = 12/7
8/9 – 3/9 =
2/3 x 4 =
Level III
Proficient in Performance
 Students can use models and
equations with unit fractions
to solve the problems in Tasks
1 & 2.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pattern Blocks & Unit Fractions
Use the pattern blocks to model and solve these problems. Write an equation to
represent each situation. Use unit fraction to represent each pattern block in the
equation.
 Scott and Zachary shared a sub. Scott ate 2/6 of the sub. Zachary ate 1/6 of the
sub. How much of the sub did they eat together?
 Three students were sharing 2 pies. Each student ate ½ of a pie. How much of
the total amount of pie did they eat together?
 Trevor had 1 1/3 pizzas. His dad ate 2/3 of a pizza. How much pizza was left?
 Madeline had 7/6 yards of fabric. She cut off one yard to make curtains. How
much fabric was left?
 Lauren had 7/3 pans of brownies leftover after a party. Her brother ate 2/3 of a
pan of brownies. What part of the total amount of brownies was left?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Task 2: Use unit fractions to solve.
Use what you know about unit fractions to solve the problems. Write an equation
that includes unit fractions to show the answer for each problem.
2/3 + 2/3 =
4/3 = 1/3 + x
5/7 + y = 12/7
1¼–¾=
2 1/5 – 3/5 =
8/9 – 3/9 =
½x5=
1 3/5 + 4/5 =
2/3 x 4 =
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Dividing Up the Land
4.NF.3- Task 5
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Build fractions from unit fractions.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify decompositions, e.g.,
by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8
= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Other Standard:
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Paper, pencil
Pattern blocks
Virtual pattern blocks can be found herehttp://www.mathplayground.com/patternblocks.html
There is a plot of land shaped like the figure below. Each hexagon has a value of 1 whole
unit. The plot of land, therefore, has a value of 3 whole units.
Determine how to use pattern blocks to divide the shape up into the following ways. For
each way, make a picture and write an equation.
Part 1: The land owner will only sell the land in sections that are one-third of a unit. The
following people buy land: Taylor: 2 sections
Bill: 1 section
Nick: 4 sections
Use your pattern blocks to make a picture of how the land was divided up.
Is there any land left? If so, how much?
Write an equation to show how the land was split up by the land owner
Part 2: The land owner will only sell the land in sections that are one-sixth of a unit. The
following people buy land: Tom: 3 sections
Susan: 2 sections
Bob: 4 sections
Mallory: 1 section
Wes: 6 sections
Use your pattern blocks to make a picture of how the land was divided up.
Is there any land left? If so, how much?
Write an equation to show how the land was split up by the land owner.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to represent the pieces of cake
as fractions.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Answer is correct, but the
equation or explanation is
incorrect OR work is logically
shown but the student has
made a calculation error.
Level III
Proficient in Performance
 Solutions: Part 1: There are 2
sections left or 2/3 of a unit
left. 2/3 + 1/3 + 4/3 + 2/3 = 3.
Part 2: There are 2 sections left
or 2/6 of a unit. 3/6 + 2/6 + 4/6
+ 1/6 + 6/6 + 2/6.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Dividing Up the Land
There is a plot of land shaped like the figure below. Each hexagon has a value of 1
whole unit. The plot of land, therefore, has a value of 3 whole units.
Determine how to use pattern blocks to divide the shape up into the following ways.
For each way, make a picture and write an equation.
Part 1
The land owner will only sell the land in sections that are one-third of a unit.
The following people buy land:
Taylor: 2 sections
Bill: 1 section
Nick: 4 sections
Use your pattern blocks to make a picture of how the land was divided up.
Is there any land left? If so, how much?
Write an equation to show how the land was split up by the land owner. Include any
unsold land.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Part 2
The land owner will only sell the land in sections that are one-sixth of a unit.
The following people buy land:
Tom: 3 sections
Susan: 2 sections
Bob: 4 sections
Mallory: 1 section
Wes: 6 sections
Use your pattern blocks to make a picture of how the land was divided up.
Is there any land left? If so, how much?
Write an equation to show how the land was split up by the land owner. Include any
unsold land.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
How Much Punch is Left?
4.NF.3- Task 6
Domain
Cluster
Standard(s)
Materials
Task
Number & Operations- Fractions
Build fractions from unit fractions.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify decompositions, e.g.,
by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8
= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Other Standard:
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
Paper, pencil
Part 1
There are 2 gallons of punch left in the punch bowl. It gets divided between 8 students,
with each getting a different amount.
a) Micah takes 1/12 of a gallon of punch.
b) Roberta takes three times as much Micah.
c) Steve takes twice as much as Roberta.
d) Yanni takes 2/12 of a gallon of punch less than Steve.
e) Amy takes 1/12 of a gallon of punch less than Yanni.
f) The remaining punch is divided between Tom, Jackie, and Henry.
g) Tom and Jackie had the same amount of punch.
h) Henry had less punch than both Tom and Jackie.
How much punch did each person take?
Draw a picture and write an equation to match this context.
Part 2
At the next party, the amount of punch doubled to 4 gallons. Each person took the same
fraction of the punch. How much would each person get?
Level I
Limited Performance
 The student has not shown a
clear understanding about how
to represent the pieces of cake
as fractions.
Rubric
Level II
Not Yet Proficient
 Answer is correct, but the
equation or explanation is
incorrect OR work is logically
shown but the student has
made a calculation error.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Solutions: Part 1: Micah: 1/12;
Roberta, 3/12 or ¼; Steve: 6/12
or ½; Yanni: 4/12 or 1/3; Amy:
3/12 or ¼: Henry 1/12 while
Tom and Jackie each get 3/12.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
How Much Punch is Left?
Part 1
There are 2 gallons of punch left in the punch bowl. It gets divided between 8
students, with each getting a different amount.
a) Micah takes 1/12 of a gallon of punch.
b) Roberta takes three times as much Micah.
c) Steve takes twice as much as Roberta.
d) Yanni takes 2/12 of a gallon of punch less than Steve.
e) Amy takes 1/12 of a gallon of punch less than Yanni.
f) The remaining punch is divided between Tom, Jackie, and Henry.
g) Tom and Jackie had the same amount of punch.
h) Henry had less punch than both Tom and Jackie.
How much punch did each person take?
Draw a picture and write an equation to match this context.
Part 2
At the next party, the amount of punch doubled to 4 gallons. Each person took the
same fraction of the punch. How much would each person get?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Boxing Up Leftover Brownies
4.NF.3 Task 7
Domain
Cluster
Standard(s)
Number and Operations - Fractions
Build fractions from unit fractions.
4.NF3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each
mixed number with an equivalent fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to
the same whole and having like denominators, e.g., by using visual fraction models and
equations to represent the problem.
Materials
Task
Activity sheet
Boxing Up Leftover Brownies
Amaria has brownies at her birthday party. At the end of the party there are the following
brownies left over:




5 brownies with cream cheese frosting
4 plain chocolate brownies
3 chocolate brownies with nuts
7 brownies with caramel frosting
Part 1:
After the party the brownies are put into boxes. A box can hold 8 brownies. If each type of
brownie were packed into their own box, what fraction of a box does each type of brownie
take up? Draw pictures below to show your work.
Part 2:
Amaria and her Mom want to use fewer boxes and put different types of brownies into the
same box. How many whole boxes do they fill? Will there be a box partially filled? If so
what fraction of the box is partially filled? Draw pictures to show your work.
Part 3:
Write an equation to match the picture that you drew in Part 2.
Part 4:
Is there space for any more brownies? If so how many more brownies do you have room
for? Write an equation that shows your work.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Solutions include many
errors and show limited
understanding.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Solutions will include between
1 to 3 errors in various parts of
the task.
Level III
Proficient in Performance
 Solutions include correct answers
and show a deep understanding of
concepts.
 Answers: Part 1: Pictures are
correctly drawn and fractions are
correctly labeled. Cream cheese:
5/8. Plain: 4/8. Nuts: 3/8. Caramel:
7/8.
 Part 2: Picture is correctly drawn.
Answer is 2 and 3/8.
 Part 3: 5/8 + 4/8 + 3/8 + 7/8 = 2
and 3/8.
 Part 4: There is space for 5 more
brownies or there is 5/8 of a box
empty. Equation: 3 – 2 and 3/8 =
5/8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Boxing Up Leftover Brownies
Amaria has brownies at her birthday party. At the end of the party there are the following
brownies left over:
 5 brownies with cream cheese frosting
 4 plain chocolate brownies
 3 chocolate brownies with nuts
 7 brownies with caramel frosting
Part 1:
After the party the brownies are put into boxes. A box can hold 8 brownies. If each type of
brownie were packed into their own box, what fraction of a box does each type of brownie take
up? Draw pictures below to show your work.
Part 2:
Amaria and her Mom want to use fewer boxes and put different types of brownies into the same
box. How many whole boxes do they fill? Will there be a box partially filled? If so what
fraction of the box is partially filled? Draw pictures to show your work.
Part 3:
Write an equation to match the picture that you drew in Part 2.
Part 4:
Is there space for any more brownies? If so how many more brownies do you have room for?
Write an equation that shows your work.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Going the Distance
4.NF.3 Task 8
Domain
Cluster
Standard(s)
Number and Operations - Fractions
Build fractions from unit fractions.
4.NF3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each
mixed number with an equivalent fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to
the same whole and having like denominators, e.g., by using visual fraction models and
equations to represent the problem.
Materials
Task
Activity sheet
Going the Distance
In order to train for the Girls on the Run 5K Race, the girls’ running team at Lincoln
Elementary School runs the following distances:
Week
Week 1
Week 2
Week 3
Week 4
Distance
1 and 1/6 miles
1 and 3/6 miles
2 and 4/6 miles
2 and 5/6 miles
Part 1: Draw a number line to show the distance that the girls ran each week.
Part 2: How far did the girls run in all? Write an equation that matches the story.
Part 3: The girls at Jefferson Elementary School ran 10 miles total during the same time.
How much farther did they run than the girls at Lincoln Elementary School? Use a picture
and an equation to find your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Solutions include many
errors and show limited
understanding.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Solutions will include between
1 to 3 errors in various parts of
the task.
Level III
Proficient in Performance
 Solutions include correct answers
and show a deep understanding of
concepts.
 Answers: Part 1: The number line
matches the distance that the girls
ran.
 Part 2: The girls ran 8 and 1/6
miles. Equation: 1 1/6 + 1 3/6 + 2
4/6 + 2 5/6 = 8 1/6.
 Part 3: Picture is correct. Equation:
10 – 8 1/6 = 1 5/6 miles.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Going the Distance
In order to train for the Girls on the Run 5K Race, the girls’ running team at Lincoln
Elementary School runs the following distances:
Week
Week 1
Week 2
Week 3
Week 4
Distance
1 and 1/6 miles
1 and 3/6 miles
2 and 4/6 miles
2 and 5/6 miles
Part 1: Draw a number line to show the distance that the girls ran each week.
Part 2: How far did the girls run in all? Write an equation that matches the story.
Part 3: The girls at Jefferson Elementary School ran 10 miles total during the same time. How
much farther did they run than the girls at Lincoln Elementary School? Use a picture and an
equation to find your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pasta Party
4.NF.4 - Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication to multiply a fraction by
a whole number.
4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ +
¼ ); be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a
whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b;
Solve word problems involving multiplication of a fraction by a whole number.
Paper and pencil
Part 1:
Katie makes 1/4 pound of pasta for each person at her dinner party. If seven people attend
the party, how many pounds of pasta will be needed for her guests?
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Extension:
Students can write their own word problem using ¼ x 7.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Part 1: Student is unable
to write an addition
equation or draw a
model.
 Part 2: Student is unable
to write a multiplication
equation or draw a
model.
Rubric
Level II
Not Yet Proficient



1.
2.
3.
4.
5.
6.
7.
8.
Part 1: Student writes a correct
addition equation that totals 7/4 (i.e.,
¼ + ¼ + ¼ + ¼ + ¼ + ¼ + ¼ = 7/4),
but is unable to show the sum on a
number line as seven ‘jumps’ of ¼,
or as an area model, and does not
clearly explain how the model
matches their addition equation.
Part 2: Student writes a correct
multiplication equation (¼ x 7= 7/4),
but is unable to show the total 7/4 on
a number line or area model, and
does not clearly explain how the
model matches their multiplication
equation.
Part 3: Students have some idea how
they are alike and different.
Level III
Proficient in Performance



Part 1: Student writes a correct
addition equation that totals 7/4 (i.e.,
¼+¼+¼+¼+¼+¼+¼=
7/4).They show the sum on a
number line as seven ‘jumps’ of ¼,
or as an area model, and clearly
explain how the model matches their
addition equation.
Part 2: Student writes a correct
multiplication equation (¼ x 7=
7/4). They show the total 7/4 on a
number line or area model, and
clearly explain how the model
matches their multiplication
equation.
Part 3: Students understand how
they are alike and different and
clearly states.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Pasta Party
Part 1:
Katie makes 1/4 pound of pasta for each person at her dinner party. If seven people
attend the party, how many pounds of pasta will be needed for her guests?
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Extension:
Write your own word problem using ¼ x 7.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Drawing a Model
4.NF.4 Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication to multiply a fraction by a
whole number.
4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ + ¼ );
be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a whole
number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b; Solve word
problems involving multiplication of a fraction by a whole number.
Paper and pencil
Part 1:
Kelly was making curtains for her living room. She bought four pieces of fabric that were
each 2/3 yard long. How many yards of fabric did Kelly buy in all?
Draw a picture and write an equation to show the total amount of fabric if each piece is 2/3
yard long.
Part 2:
With the fabric that she bought in part 1, Kelly cut each piece of fabric into a 1/3 yard long
piece. Draw a picture and write an equation to show the total amount of fabric if each piece is
1/3 yard long.
Part 3:
Is the amount of fabric in Part 1 and Part 2 the same? Use pictures to prove it. Write a sentence
to explain how you know that you are correct.
Rubric
Level I
Level II
Level III
Limited Performance
 Part 1
Student is unable to
create a correct
equation and/or
picture.
Not Yet Proficient
 Part 1
addition equation
2/3 + 2/3 + 2/3 + 2/3 = 8/3
multiplication equation
4 x 2/3 = 8/3
Picture should show four groups of 2/3.
 Part 2
Addition equation
1/3 + 1/3 + 1/3 + 1/3 + 1/3 +1/3 + 1/3
+ 1/3= 8/3
Multiplication equation
8 x 1/3 = 8/3
Picture should show eight groups of
1/3
 Part 3
It is unclear from the student’s picture
that they understand the relationship
8/3 = 4 x 2/3.
Proficient in Performance
 Part 1
addition equation
2/3 + 2/3 + 2/3 + 2/3 = 8/3
multiplication equation
4 x 2/3 = 8/3
Picture should show four groups of 2/3.
 Part 2
Addition equation
1/3 + 1/3 + 1/3 + 1/3 + 1/3 +1/3 + 1/3 +
1/3= 8/3
Multiplication equation
8 x 1/3 = 8/3
Picture should show eight groups of 1/3
 Part 3
Picture and explanation should show that
eight individual copies of one third can
be grouped as four groups of two-thirds.
Equations: 8 x 1/3 = 4 x 2/3

Part 2
Student is unable to
create a correct
equation and/or
picture.

Part 3
The student cannot
draw a model to
show this
relationship or
explain it in words
or numbers.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Drawing a Model
Part 1:
Kelly was making curtains for her living room. She bought four pieces of fabric
that were each 2/3 yard long. How many yards of fabric did Kelly buy in all?
Draw a picture and write an equation to show the total amount of fabric if each
piece is 2/3 yard long.
Part 2:
With the fabric that she bought in part 1, Kelly cut each piece of fabric into a 1/3
yard long piece. Draw a picture and write an equation to show the total amount of
fabric if each piece is 1/3 yard long.
Part 3:
Is the amount of fabric in Part 1 and Part 2 the same? Use pictures to prove it. Write
a sentence to explain how you know that you are correct.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Chris’s Cookies
4.NF.4-Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication to multiply a fraction by
a whole number.
4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ +
¼ ); be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a
whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b;
Solve word problems involving multiplication of a fraction by a whole number.
Paper and pencil
Students will work together or independently to show their solutions to the fraction word
problems.
Chris’s Cookies
Chris is making cookies for his friend’s birthday party using the following recipe.
Chocolate Chip Cookies:
Makes 2 dozen cookies
2 cups flour
1/2 teaspoon baking soda
1 teaspoon salt
3/5 cups butter, softened
3/4 cups sugar
1/2 cup light brown sugar
1 egg
1 teaspoon vanilla extract
1 package (6 ounces) chocolate chips
1/2 cup chopped walnuts
From http://www.mccormick.com/
1.
How much butter will he need to make 3 batches of cookies? Write an equation to show your
answer.
2.
How much butter will Chris need to make 6 batches of cookies? Write an equation to show your
answer.
3.
How much butter will Chris need to make 9 batches of cookies? Write an equation to show your
answer.
4.
What patterns do you notice in the amounts of butter needed for 3 batches, 6 batches, and 9 batches
of cookies?
5.
How can we use these patterns to predict the amount of butter needed for 18 batches? 36 batches?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students may or may not be
able to correctly compute
answers to 1-3. They may still
be relying on addition to
compute.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 1. 3 x 3/5 = 9/5
 2. 6 x 3/5 = 18/5
 3. 9 x 3/5 = 27/5
 4. Students may notice
patterns but they have
difficulty using them to
predict answers.
Level III
Proficient in Performance
1.
3 x 3/5 = 9/5
2.
6 x 3/5 = 18/5
3.
9 x 3/5 = 27/5
4.
Students may notice
patterns such as:
Alternating odd and even totals
(9/5, 18/5, 27/5)
n x a/b = (n x a)/b Multiplying
the numerator times the whole
number always yields the answer.
As the multiplier (3) grows by 3,
the amount of butter increases by
9. Students may notice that this is
because the numerator is 3.
To predict the amount of butter
for 18 batches, students may
notice that they can double 3/5 x
9 since 9 doubled is 18 so that
they have (3/5 x 9) x 2 = 27/5 x 2
= 54/2.
To predict the amount of butter
needed for 36 batches, students
may double the amount for 18
batches, multiply the amount
needed for 9 batches by 4, etc.
(3/5 x 3) x 12 = 9/5 x 12 = 108/5
(3/5 x 6) x 6 = 18/5 x 6 = 108/5
(3/5 x 9) x 4 = 27/5 x 4 = 108/5
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Chris’s Cookies
Chris is making cookies for his friend’s birthday party using the following recipe.
Chocolate Chip Cookies:
Makes 2 dozen cookies
2 cups flour
1/2 teaspoon baking soda
1 teaspoon salt
3/5 cups butter, softened
3/4 cups sugar
1/2 cup light brown sugar
1 egg
1 teaspoon vanilla extract
1 package (6 ounces) chocolate chips
1/2 cup chopped walnuts
From http://www.mccormick.com/
1. How much butter will he need to make 3 batches of cookies? Write an equation to show
your answer.
2. How much butter will Chris need to make 6 batches of cookies? Write an equation to show
your answer.
3. How much butter will Chris need to make 9 batches of cookies? Write an equation to show
your answer.
4. What patterns do you notice in the amounts of butter needed for 3 batches, 6 batches, and 9
batches of cookies?
5. How can we use these patterns to predict the amount of butter needed for 18 batches? 36
batches?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Going the Distance
4.NF.4 - Task 4
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication to multiply a fraction by
a whole number.
4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ +
¼ ); be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a
whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b;
Solve word problems involving multiplication of a fraction by a whole number.
Paper and pencil
During her first week of training for the Girls on the Run 5K, Molly runs ¾ of a mile each
day for 6 days.
Part 1:
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Part 4
Molly’s friend Tonya ran 1 and 2/4 miles each day for 3 days. Who ran more? Explain
your reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Part 1: Student is
unable to write an
addition equation or
draw a model.
 Part 2: Student is
unable to write a
multiplication equation
or draw a model.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Part 1: Student writes a correct
addition equation, but is unable to
show the sum on a number line as
seven ‘jumps’ of ¼, or as an area
model, and does not clearly
explain how the model matches
their addition equation.
 Part 2: Student writes a correct
multiplication equation, but is
unable to show the total on a
number line or area model, and
does not clearly explain how the
model matches their multiplication
equation.
 Part 3: Students communicate
unclearly how they are alike and
different.
 Part 4: Student does not clearly
communicate that they need 4
containers that are 1 cup each.
Level III
Proficient in Performance
 Part 1: Student writes a correct
addition equation that totals 18/4
(3/4+3/4+3/4+3/4+3/4+3/4=
18/4). They show the sum on a
number line as five ‘jumps’ of
3/4 or as an area model, and
clearly explain how the model
matches their addition equation.
 Part 2: Student writes a correct
multiplication equation ¾ x 6 =
18/4). They show the total 18/4
on a number line or area model,
and clearly explain how the
model matches their
multiplication equation.
 Part 3: Student understands how
they are alike and different and
clearly states.
 Part 4: Student communicates
that Molly and Tanya have run
the same amount.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Going the Distance
During her first week of training for the Girls on the Run 5K, Molly runs ¾ of
a mile each day for 6 days.
Part 1:
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Part 4
Molly’s friend Tonya ran 1 and 2/4 miles each day for 3 days. Who ran more?
Explain your reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Serving Ice Cream
4.NF.4 - Task 5
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Apply and extend previous understandings of multiplication to multiply a fraction by
a whole number.
4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ +
¼ ); be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a
whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b;
Solve word problems involving multiplication of a fraction by a whole number.
Paper and pencil
Katie uses 2/3 of a cup of ice cream for each ice cream sundae that she makes. For a party
she makes 5 sundaes.
Part 1:
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Part 4
If ice cream were sold in 1 cup containers how many containers does she need to buy for
her party?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Part 1: Student is
unable to write an
addition equation or
draw a model.
 Part 2: Student is
unable to write a
multiplication equation
or draw a model.
Rubric
Level II
Not Yet Proficient




1.
2.
3.
4.
5.
6.
7.
8.
Part 1: Student writes a correct
addition equation, but is unable to
show the sum on a number line as
seven ‘jumps’ of ¼, or as an area
model, and does not clearly explain
how the model matches their addition
equation.
Part 2: Student writes a correct
multiplication equation, but is unable
to show the total on a number line or
area model, and does not clearly
explain how the model matches their
multiplication equation.
Part 3: Students communicate
unclearly how they are alike and
different.
Part 4: Student does not clearly
communicate that they need 4
containers that are 1 cup each.
Level III
Proficient in Performance




Part 1: Student writes a correct
addition equation that totals 10/3
(2/3 + 2/3+2/3+2/3+2/3).They show
the sum on a number line as five
‘jumps’ of 2/3 or as an area model,
and clearly explain how the model
matches their addition equation.
Part 2: Student writes a correct
multiplication equation 2/3 x 5 =
10/3). They show the total 10/3 on a
number line or area model, and
clearly explain how the model
matches their multiplication
equation.
Part 3: Student understand how
they are alike and different and
clearly states.
Part 4: Student communicates that
in order to buy 10/3 cups of ice
cream they must buy 4 containers
that are 1 cup each.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Serving Ice Cream
Katie uses 2/3 of a cup of ice cream for each ice cream sundae that she makes.
For a party she makes 5 sundaes.
Part 1:
Write an addition equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows addition.
Part 2:
Write a multiplication equation to show this situation.
Show your answer with a number line or an area model.
Use numbers or words to explain how your model shows multiplication.
Part 3
How are your addition and multiplication equations alike? Different?
Would you use one over the other? Why or why not?
Part 4
If ice cream were sold in 1 cup containers how many containers does she need
to buy for her party? Write a sentence explaining your reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Karen’s Garden
4.NF.5 Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a
denominator of 100, and use this technique to add two fractions with respective
denominators 10 and 100. Express 3/10 as 30/100 and add 3/10 + 4/100 =34/100.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
In this task, students will be using decimal grids (hundredths) to shade in tenths and
hundredths as decimals and fractions, and find totals and differences.
Introduce the manipulatives and task with the following practice problem.
Karen is planting vegetables in her 10’ x 10’ garden. She wants 3/10 of the garden to be
tomatoes. If Karen has already planted peas in 0.25 of the garden, how much space will
she have left for other vegetables?
Some students may be comfortable using hundredths grids while others may need the
additional support of using base ten blocks (flat = 1 whole, ten stick = 1/10, unit cube =
1/100).
Students may work on the Karen’s Garden sheet independently or in pairs if they need
support. As they work, they should shade in hundredths grids or use base ten blocks to
solve the addition or subtraction.
Rubric
Level I
Limited Performance
 Solutions will
include many errors
in conversions and
equivalencies, as
well as addition and
subtraction errors.
Students may
struggle to choose
appropriate
numbers from the
problems for
computation.
Level II
Not Yet Proficient
 Students should be able to
convert decimals (tenths
and hundredths) to
fractions with 10 or 100 as
a denominator. Their
solutions should show that
they can work flexibly with
fractions and decimals.
 At this level, their solutions
will include errors in
several conversions and
equivalencies.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 At this level, their solutions will include few
or no errors in conversions and
equivalencies.
Possible solutions:
1. 76/100 + 24/100 = 100/100
2. 0.6 + 0.23 = 0.83
6/10 + 23/100 = 83/100
60/100 + 23/100 = 83/100
3. 0.5 – 0.14 = 0.36
0.14 + 0.36 = 0.50
14/100 + 36/100 = 5/10 or 50/100
4. 2/10 + 0.2 + 20/100 = 0.6 or 6/10 or 60/100
5. Students should figure out that 0.6 + 0.36 =
0.96 of the original grid, so 0.04 would be
leftover for radishes. If radishes are now
taking up 22/100 of the garden, 0.22 – 0.04
= 0.18. The deer ate peas in 0.18 of the
garden.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Karen’s Garden
Use 10 x 10 grids to shade in your solutions to these problems.
1. Karen planted squash and watermelon in her 10’ x 10’ garden. She planted
squash in 0.4 of her garden, but it grew so much that it took up 76/100 of the
garden. How much space is left for watermelon?
2. Six tenths of the garden is planted with green beans. Twenty-three hundredths
is planted with radishes. How much of the garden is planted?
3. Karen wants half of her garden to be planted with tomatoes. She has planted
0.14 of the garden with tomatoes so far. How much of the garden does she
still need to plant with tomatoes?
4. Karen planted lettuce in 2/10 of her garden, peas in 0.2 of her garden, and
peppers in 20/100 of the garden. How much of the garden is planted?
5. Six tenths of the garden was planted with peppers. Thirty six hundredths of
the garden was planted with peas, but some of them were eaten by deer. Karen
planted radishes in the leftover space and the empty space where the peas
were eaten by deer. If radishes now take up 22/100 of the garden, how much
of the garden did the deer eat?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Filling the Jar
4.NF.5 Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a
denominator of 100, and use this technique to add two fractions with respective
denominators 10 and 100. Express 3/10 as 30/100 and add 3/10 + 4/100 =34/100.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
In this task, students will be using decimal grids (hundredths) to shade in tenths and
hundredths as decimals and fractions, and find totals and differences.
Part 1:
A jar can hold 100 marbles. For each of the situations below, find the amount for the
various colors of marbles.
3
2
19
Jar A: The jar contains
blue,
white, and
red marbles. The rest are yellow.
10
10
100
What fraction represents the number of yellow marbles? _____
7
1
4
green,
purple, and
brown. The rest are white. What fraction represents
10
10
100
the number of white marbles? ______
Jar B:
3
51
gray and
black. The rest are pink or yellow. There are more pink than
10
100
yellow marbles. What fraction represents the number of pink and yellow marbles? ____
pink, ____ yellow.
Jar C:
2
18
clear and
orange. The rest are red and blue. There are 2 more red marbles
10
100
than blue marbles.
Jar D:
What fraction represents the number of red and blue marbles? ___ red, ____ blue.
Part 2: Pick one of the tasks above. Explain how you worked with the different
denominators to find your answer.
Some students may be comfortable using hundredths grids while others may need the
additional support of using base ten blocks (flat = 1 whole, ten stick = 1/10, unit cube =
1/100).
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Solutions will include many
errors in conversions and
equivalencies, as well as
addition and subtraction
errors. Students may struggle
to choose appropriate numbers
from the problems for
computation.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students should be able to
convert decimals (tenths and
hundredths) to fractions with
10 or 100 as a denominator.
Their solutions should show
that they can work flexibly
with fractions and decimals.
 At this level, their solutions
will include errors in several
conversions and equivalencies.
Level III
Proficient in Performance
 Students correctly find the
answer to each problem. Jar
A: 31/100 yellow. Jar B:
16/100 white. Jar C: Multiple
possible answers. Both
fractions must add up to
19/100 and the fraction for
pink must be greater than
yellow. Jar D: Red: 32/100,
Blue: 30/100.
 Part 2: The answer discusses
that tenths can also be written
as hundredths by multiplying
the numerator and
denominator both by 10.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Filling the Jar
A jar can hold 100 marbles. For each of the situations below, find the amount for the
various colors of marbles.
Jar A: The jar contains
3
2
19
blue,
white, and
red marbles. The rest are yellow.
10
10
100
What fraction represents the number of yellow marbles? _____
Jar B:
7
1
4
green,
purple, and
brown. The rest are white. What fraction represents
10
10
100
the number of white marbles? ______
Jar C:
3
51
gray and
black. The rest are pink or yellow. There are more pink than
10
100
yellow marbles. What fraction represents the number of pink and yellow marbles? ____
pink, ____ yellow.
Jar D:
2
18
clear and
orange. The rest are red and blue. There are 2 more red marbles
10
100
than blue marbles.
What fraction represents the number of red and blue marbles? ___ red, ____ blue.
Part 2: Pick one of the tasks above. Explain how you worked with the different
denominators to find your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Children’s Shirts
4.NF.5 Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a
denominator of 100, and use this technique to add two fractions with respective
denominators 10 and 100. Express 3/10 as 30/100 and add 3/10 + 4/100 =34/100.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
Part 1:
2
A group of 100 fourth graders are on the playground.
of the group are wearing black
10
11
3
shirts.
of the group are wearing blue shirts.
of the group are wearing white shirts.
100
10
The rest of the class is wearing green or yellow shirts. There are more children wearing
yellow shirts than green shirts. What fraction of the group is wearing yellow shirts? Green
shirts? Find at least three different correct solutions.
Part 2:
Describe your process for solving the task above.
Rubric
Level I
Level II
Limited Performance
Not Yet Proficient
 Solutions will include  Students should be able to
many errors in
convert decimals (tenths and
conversions and
hundredths) to fractions with
equivalencies, as well
10 or 100 as a denominator.
as addition and
Their solutions should show
subtraction errors.
that they can work flexibly
Students may struggle
with fractions and decimals.
to choose appropriate  At this level, their solutions
numbers from the
will include errors in several
problems for
conversions and
computation.
equivalencies.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 There are 39 students wearing a green
or yellow shirt. Students should be able
to find three correct solutions that show
a that there are more yellow than green
shirts and that add up to 39 of the 100
students.
 Students should be able to explain the
process for finding solutions.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Children’s Shirts
A group of 100 fourth graders are on the playground.
wearing black shirts.
11
100
2
10
of the group are
of the group are wearing blue shirts.
3
10
of the group
are wearing white shirts. The rest of the class is wearing green or yellow shirts.
There are more children wearing yellow shirts than green shirts.
What fraction of the group is wearing yellow shirts?
What fraction of the group is wearing green shirts?
Find at least three different correct solutions.
Part 2:
Describe how you used equivalent fractions to solve the task above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Where am I now? How much farther?
4.NF.6 Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example,
rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line
diagram.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
Where am I now? How much farther?
Part 1:
You have walked 0.32 of the way from your house to the school.
A) What is that distance as a fraction?
B) If you walk another 17/100 of the way to the school how far have you gone now in
terms of both a fraction and a decimal?
C) If you walk another 3/10 of the way to the school how far have you gone now in terms
of both of a fraction and a decimal?
D) Draw a number line from 0 to 1 and label each tenth on the number line. Plot the three
distances above as both fractions and decimals.
Part 2:
Write an explanation explaining how you worked with equivalent fractions and decimals
to solve this task.
Level I
Limited Performance
 Solutions will include
many errors in
conversions and
equivalencies, as well
as addition and
subtraction errors.
Students may struggle
to choose appropriate
numbers from the
problems for
computation.
Rubric
Level II
Not Yet Proficient
 Students should be able to
convert decimals (tenths and
hundredths) to fractions with
10 or 100 as a denominator.
Their solutions should show
that they can work flexibly
with fractions and decimals.
 At this level, their solutions
will include errors in several
conversions and
equivalencies.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Students correctly find the answer to
each problem. A) 32/100. B) 49/100,
C) 79/100, D) all 3 fractions and
decimals are correctly plotted on a
number line.
 Part 2: The answer discusses that
tenths can also be written as
hundredths by multiplying the
numerator and denominator both by
10, and that decimals are equivalent to
fractions that have either a 10 or 100
in the denominator.
FOURTH GRADE
Formative Instructional and Assessment Tasks
1.
2.
3.
4.
5.
6.
7.
8.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Where Am I Now? How Much Farther?
Part 1:
You have walked 0.32 of the way from your house to the school.
A) What is that distance as a fraction?
B) If you walk another 17/100 of the way to the school how far have you gone
now in terms of both a fraction and a decimal?
C) If you walk another 3/10 of the way to the school how far have you gone now
in terms of both of a fraction and a decimal?
D) Draw a number line from 0 to 1 and label each tenth on the number line. Plot
the three distances above as both fractions and decimals.
Part 2:
Write an explanation explaining how you worked with equivalent fractions and
decimals to solve this task.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Is the Tire Full Yet?
4.NF.6 Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations - Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example,
rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line
diagram.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
Is the tire full?
Part 1:
You are about to go on vacation with your family. Your tire is 78/100 full of air. If you add
air so that it 0.93 full, what fraction of the tire did you just fill with air? What fraction (and
decimal) of the tire still needs to be filled with air?
Part 2:
Write an explanation explaining how you worked with equivalent fractions and decimals
to solve this task.
Level I
Limited Performance
 Solutions will include
many errors in
conversions and
equivalencies, as well as
addition and subtraction
errors. Students may
struggle to choose
appropriate numbers
from the problems for
computation.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students should be able to
convert decimals (tenths and
hundredths) to fractions with
10 or 100 as a denominator.
Their solutions should show
that they can work flexibly
with fractions and decimals.
 At this level, their solutions
will include errors in several
conversions and equivalencies.
Level III
Proficient in Performance
 Students correctly find the answer
to each problem. A) 15/100 or
0.15. B) 7/100 or 0.07.
 Part 2: The answer discusses that
tenths can also be written as
hundredths by multiplying the
numerator and denominator both
by 10, and that decimals are
equivalent to fractions that have
either a 10 or 100 in the
denominator.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Is the Tire Full?
Part 1:
You are about to go on vacation with your family. Your tire is 78/100 full of
air. If you add air so that it 0.93 full, what fraction of the tire did you just fill
with air? What fraction (and decimal) of the tire still needs to be filled with
air?
Part 2:
Write an explanation explaining how you worked with equivalent fractions and
decimals to solve this task.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who Jumped Farther?
4.NF.7-Task 1
Domain
Cluster
Standard(s)
Materials
Number and Operations – Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that
comparisons are valid only when the two decimals refer to the same whole. Record the
results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by
using a visual model.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
Who Jumped Farther?
Part 1:
Tom, Steve, and Peter each jump in a jumping contest. They measure their jumps and then
discuss who jumped farther.
Tom said, “I jumped 1 and 34 hundredths of a meter.”
Steve said, “I jumped 1 and 43 hundredths of a meter.”
Peter said, “I jumped 1 and 4 tenths of a meter.”
For each ingredient, shade in the decimal grid and write a comparison statement using >,
<, or =.
Which boy jumped farther between Tom and Steve? How do you know?
Which boy jumped farther between Tom and Peter? How do you know?
Which boy jumped farther between Steve and Peter? How do you know?
Part 2:
Mitch jumped a distance between Steve and Peter. How far could he have jumped?
Alex jumped a distance between Tom and Peter. How far could he have jumped?
Level I
Limited Performance
 Students are unable to
accurately compare
decimals.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students make 1 or 2 errors
comparing decimals. OR
students get correct answers
but do not provide clear and
accurate explanations.
Level III
Proficient in Performance
 The student provides correct answers.
Part 1: 1.2 > 1.02, 1.2<1.23,
1.02<1.23. Part 2: You need either
1.21 or 1.22 Liters of fruit juice.
 All explanations are clear and
accurate.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who Jumped Farther?
Part 1:
Tom, Steve, and Peter each jump in a jumping contest. They measure
their jumps and then discuss who jumped farther.
Tom said, “I jumped 1 and 34 hundredths of a meter.”
Steve said, “I jumped 1 and 43 hundredths of a meter.”
Peter said, “I jumped 1 and 4 tenths of a meter.”
Shade in the decimal grids for each of the boys’ distances.
Which boy jumped farther between Tom and Steve? How do you know?
Which boy jumped farther between Tom and Peter? How do you know?
Which boy jumped farther between Steve and Peter? How do you know?
Part 2:
Mitch jumped a distance between Steve and Peter. How far could he have
jumped?
Alex jumped a distance between Tom and Peter. How far could he have
jumped?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Making Punch
4.NF.7-Task 2
Domain
Cluster
Standard(s)
Materials
Number and Operations – Fractions
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that
comparisons are valid only when the two decimals refer to the same whole. Record the
results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by
using a visual model.
Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil
Making Punch
Part 1:
While making punch for a party the following ingredients are needed:
1.2 Liters of Ginger Ale
1.02 Liters of Sprite
1.23 Liters of Fruit Juice
For each ingredient, shade in the decimal grid and write a comparison statement using >,
<, or =.
Do you need more Ginger Ale or Sprite? Explain your reasoning.
Do you need more Ginger Ale or Fruit Juice? Explain your reasoning.
Do you need more Sprite or Fruit Juice? Explain your reasoning.
Part 2:
For a different recipe, frozen yogurt can be added. The amount of frozen yogurt is between
the amount of Ginger Ale and Fruit Juice. How much frozen yogurt is needed? Explain
how you found your answer.
Rubric
Level I
Limited Performance
 Students are unable
to accurately
compare decimals.
1.
2.
3.
4.
5.
6.
7.
8.
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Students make 1 or 2 errors
 The student provides correct answers.
comparing decimals. OR
Part 1: 1.2 > 1.02, 1.2<1.23, 1.02<1.23.
students get correct answers but
Part 2: You need either 1.21 or 1.22
do not provide clear and accurate
Liters of fruit juice.
explanations.
 All explanations are clear and accurate.
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Making Punch
Part 1:
While making punch for a party the following ingredients are needed:
1.2 Liters of Ginger Ale
1.02 Liters of Sprite
1.23 Liters of Fruit Juice
For each ingredient, shade in the decimal grid.
Do you need more Ginger Ale or Sprite? Explain your reasoning.
Do you need more Ginger Ale or Fruit Juice? Explain your reasoning.
Do you need more Sprite or Fruit Juice? Explain your reasoning.
Part 2:
For a different recipe, frozen yogurt can be added. The amount of frozen
yogurt is between the amount of Ginger Ale and Fruit Juice. How much frozen
yogurt is needed? Explain how you found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE