Formative Instructional and Assessment Tasks
Measuring the Jump Ropes
4.MD.1-Task 1
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including
km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement,
express measurements in a larger unit in terms of a smaller unit. Record measurement
equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in.
Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches
listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil
Measuring the Jump Ropes
There are some jump ropes in a container in the gym. The students need to sort them by
length.
Sally picks all the ropes that are 40 inches or shorter
Mary picks all the ropes between 41 and 50 inches long.
Tanya picks all the ropes that are between 51 and 62 inches long.
Jose picks all the ropes that are between 63 and 74 inches long.
Lebron picks all the ropes that are 75 inches or longer.
Part 1:
Based on the data below, how many jump ropes does each person pick up?
3 ft
2 ft
5 ft
4 ft
4 ft
3 ft
7 ft
6 ft
6 ft
6 ft
3 ft
5 ft
5 ft
4 ft
Part 2:
Another bin is found. After students add the ropes below to their pile, how many do they
each have?
6 ft 2 in
4 ft 3 in
2 ft 11 in
3 ft 4 in
3 ft 5 in
3 ft 11 in
6 ft 8 in
5 ft 11 in
5 ft 2 in
5 ft 3 in
3 ft 1 in
2 ft 3 in
3 ft 6 in
4 ft 2 in
Part 3:
Describe how you solved the tasks in Part Two.
Level I
Limited Performance
 Students make
more than 2
errors.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Students make 1 or 2
 The student provides correct answers. Part 1:
errors OR their
Sally: 4 ropes, Mary: 3 ropes, Tanya: 3 ropes,
explanation in Part 3 is
Jose: 2 ropes, Lebron: 1 rope.
not accurate.
 Part 2: Sally: 4 ropes. Mary: 4 ropes, Tanya: 2
ropes, Jose: 3 ropes, Lebron: 1 rope.
 Part 3: Student discusses multiplying the number
of feet by 12 and adding the number of inches.
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
Measuring the Jump Rope
There are some jump ropes in a container in the gym. The students need to sort
them by length.
Sally picks all the ropes that are shorter than 40 inches.
Mary picks all the ropes between 41 and 50 inches long.
Tanya picks all the ropes that are between 51 and 62 inches long.
Jose picks all the ropes that are between 63 and 74 inches long.
Lebron picks all the ropes that are longer than 75 inches.
Part 1: Based on the data below, how many jump ropes does each person pick
up?
3 ft
7 ft
2 ft
6 ft
5 ft
6 ft
4 ft
6 ft
4 ft
3 ft
3 ft
5 ft
5 ft
4 ft
Part 2: Another bin is found. After students add the ropes below to their pile,
how many do they each have?
6 ft 2 in 4 ft 3 in
5 ft 11 in 5 ft 2 in
2 ft 11 in 3 ft 4 in
5 ft 3 in 3 ft 1 in
3 ft 5 in
2 ft 3 in
3 ft 11 in 6 ft 8 in
3 ft 6 in 4 ft 2 in
Part 3: Describe how you solved the tasks in Part Two.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
How Long Did I Jump?
4.MD.1-Task 2
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil
How Long Did I Jump?
At school three students are have a jumping competition to see who can jump the farthest.
Miguel, Nancy, and Sarah both jump between 3 and 4 feet.
Part 1:
A. If Nancy jumps farther than Miguel but shorter than Sarah, what are possible
distances that each person jumped in inches?
B. If all 3 people jumped farther than 3 feet 6 inches, what are the possible distances
that each person could have jumped in inches?
C. If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how long did
each person jump?
Part 2:
Write a sentence describing how you found the distances that each person jumped in
inches.
Rubric
Level I
Level II
Level III
Limited Performance Not Yet Proficient Proficient in Performance
 Students make
 Students make  The student provides correct answers. Part 1: A- Distances
more than 2
1 or 2 errors
must be between 37 and 47 inches. Miguel must have the
errors.
OR their
smallest distance, Nancy must have the 2nd longest, and
explanation in
Sarah must have the longest distance. B- Same as A, but the
Part 3 is not
distances must be between 43 and 47 inches. C- Miguel- 44
accurate.
inches, Nancy- 45 inches, Sarah- 46 inches.
 AND there is a clear and accurate explanation about how
they found the distances in inches.
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 Long Did I Jump?
At school three students are have a jumping competition to see who can jump
the farthest?
Miguel, Nancy, and Sarah both jump between 3 and 4 feet.
Part 1:
A. If Nancy jumps farther than Miguel but shorter than Sarah, what are
possible distances that each person jumped in inches?
B. If all 3 people jumped farther than 3 feet 6 inches, what are the possible
distances that each person could have jumped in inches?
C. If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how
long did each person jump?
Part 2: Write a sentence describing how you found the distances that each
person jumped in inches.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Baby Weights
4.MD.1-Task 3
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Baby Weights
Using the table below, answer the following questions:
Baby
Samuel
Nicole
TJ
Tyrette
Gender
Boy
Girl
Boy
Girl
Weight
7 and 2/4 pounds
7 and 7/8 pounds
1 and 3/4 pounds heavier than Samuel
1 and 4/8 of a pound heavier than Nicole
Part 1:
What is the weight of each baby in pounds?
What is the weight of each baby in ounces?
Part 2:
How many pounds do the boys weigh? How many ounces do the boys weigh?
How many pounds do the girls weigh? How many ounces do the girls weigh?
Part 3:
What was the total weight of all of the babies in pounds?
What was the total weight of all of the babies in ounces?
Part 4:
Write a sentence about a strategy that you used to convert the babies’ weights from pounds
to ounces.
Rubric
Level I
Limited
Performance
 Students make
more than 2
errors.
Level II
Not Yet Proficient
 Students make 1 or 2
errors OR their
explanation is not
accurate.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Part 1: Samuel- 7 and 2/4 pounds, 120 ounces;
Nicole- 7 and 7/8 pounds, 126 ounces; TJ- 9 and
1/4 pounds, 148 ounces; Tyrette- 9 and 3/8
pounds, 150 ounces
 Part 2: Boys- 16 and 3/4 pounds, 268 ounces;
Girls- 17 and 2/8 or 17 and 1/4 pounds; 276
ounces.
 Part 3: Ounces: 34 pounds; 544 ounces
 Part 4: The sentence includes a logical and
accurate approach of converting units.
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
Baby Weights
Using the table below, answer the following questions:
Baby
Gender
Weight
Samuel Boy
7 and 2/4 pounds
Nicole Girl
7 and 7/8 pounds
TJ
Boy
1 and 3/4 pounds heavier than Samuel
Tyrette Girl
1 and 4/8 of a pound heavier than Nicole
Part 1:
What is the weight of each baby in pounds?
What is the weight of each baby in ounces?
Part 2:
How many pounds do the boys weigh? How many ounces do the boys weigh?
How many pounds do the girls weigh? How many ounces do the girls weigh?
Part 3:
What was the total weight of all of the babies in pounds?
What was the total weight of all of the babies in ounces?
Part 4:
Write a sentence about a strategy that you used to convert the babies’ weights from
pounds to ounces.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Shipping Packages
4.MD.1-Task 4
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Shipping Packages
Four friends are each sending packages . Use the table below to answer the following
questions:
Package
Sarah’s box
Karen’s box
Tim’s box
Steve’s box
Weight
25 and 6/8 pounds
24 and 5/8 pounds
29 and 7/8 pounds
24 and 2/8 pounds
Part 1:
What is the weight of each person’s box in ounces?
Part 2:
What is the combined weight of each person’s box in pounds?
What is the combined weight of each person’s box in ounces?
Part 3:
Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if they are
between 400 and 500 ounces. How much does each package cost?
Part 4:
If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh the
same amount, how much do all of those boxes weigh in pounds? Write a sentence
explaining how you found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Sarah: 412 ounces; Karen: 394
than 2 errors.
OR their explanation is not
ounces; Tim: 478 ounces; Steve: 388 ounces.
accurate.
 Part 2: 104 and 4/8 pounds; 1,672 ounces
 Part 3: Karen and Steve will have to pay $10.
Sarah and Tim will have to pay $15.
 Part 4: Sarah’s 3 boxes would weigh 77 and
1/4 pounds. Tim’s 4 boxes would weigh 119
and 2/4 pounds. The combined weight would
be 196 and 3/4 pounds.
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
Shipping Packages
Four friends are each sending packages . Use the table below to answer the
following questions:
Package
Sarah’s box
Precious’ box
Tim’s box
Steve’s box
Weight
25 and 6/8 pounds
24 and 5/8 pounds
29 and 7/8 pounds
24 and 2/8 pounds
Part 1:
What is the weight of each person’s box in ounces?
Part 2:
What is the combined weight of each person’s box in pounds?
What is the combined weight of each person’s box in ounces?
Part 3:
Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if
they are between 400 and 500 ounces. How much does each package cost?
Part 4:
If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh
the same amount, how much do all of those boxes weigh in pounds? How much do
all of the boxes weigh in ounces? Write a sentence explaining how you found your
answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Relay Running
4.MD.1-Task 5
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Relay Running
The following runners are on the same relay team for the 4,000 meter race. Here are their
times:
Runner
Time
Alberto
2 minutes and 55 seconds
Kate
3 minutes and 8 seconds
Kelly
3 minutes and 17 seconds
Matt
2 minutes and 58 seconds
Part 1:
What was the time of each runner in terms of only seconds?
Part 2:
Write a sentence explaining how you solved the questions in Part 1.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Albert-175 seconds, Kate-188
than 2 errors.
OR their explanation is not
seconds, Kelly-197 seconds, Matt-178
accurate.
seconds
 Part 2: The sentence shows an appropriate
way of solving the problems in Part 1.
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
Relay Running
The following runners are on the same relay team for the 4,000 meter race. Here are
their times:
Runner
Alberto
Kate
Kelly
Matt
Time
2 minutes and 55 seconds
3 minutes and 8 seconds
3 minutes and 17 seconds
2 minutes and 58 seconds
Part 1:
What was the time of each runner in terms of only seconds?
Part 2:
Write a sentence explaining how you solved the questions in Part 1.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Off to the Races
4.MD.1-Task 6
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Off to the Races
The following runners just completed the Seaside Marathon race where they ran 26.2
miles.
Runner
Time
Angela
3 hours, 25 minutes, 15 seconds
Paul
3 hours, 26 minutes, 30 seconds
Sandy
3 hours, 41 minutes, 45 seconds
Jason
3 hours, 39 minutes, 15 seconds
Part 1:
What was the time of each runner in terms of only minutes and seconds (e.g., 185 minutes
and 15 seconds)?
Part 2:
Write a sentence explaining how you solved the questions in Part 1.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Angela: 205 min, 15 sec; Paul: 206
than 2 errors.
OR their explanation is not
min, 30 sec; Sandy: 221 min, 45 sec; Jason:
accurate.
219 min, 15 sec
 Part 2: The sentence shows an appropriate
way of solving the problems in Part 1.
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
Off to the Races
The following runners just completed the Seaside Marathon race where they ran
26.2 miles.
Runner
Angela
Paul
Sandy
Jason
Time
3 hours, 25 minutes, 15 seconds
3 hours, 26 minutes, 30 seconds
3 hours, 41 minutes, 45 seconds
3 hours, 39 minutes, 15 seconds
Part 1:
What was the time of each runner in terms of only minutes and seconds (e.g., 185
minutes and 15 seconds)?
Part 2:
Write a sentence explaining how you solved the questions in Part 1.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Mapping My Run
4.MD.1-Task 7
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Mapping A Run
On her iPhone Molly was able to track how far she ran each day this week. Here are her
distances.
Day
Monday
Tuesday
Wednesday
Thursday
Distance
5 km, 430 m, 0 cm
4 km, 789 m, 98 cm
6 km, 967 m, 56 cm
5 km, 5 m, 5 cm
Part 1:
How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters and 38
centimeters)?
Part 2:
Write a sentence explaining how you found out the distance that she ran.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Monday: 5,430 m and 0 cm; Tuesday:
than 2 errors.
OR their explanation is not
4,789 m and 98 cm; Wednesday: 6,967 m
accurate.
and 56 cm; Thursday: 5,005 m and 5 cm.
 Part 2: The sentence is logical and accurate.
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
Mapping A Run
On her iPhone Molly was able to track how far she ran each day this week. Here are
her distances.
Day
Monday
Tuesday
Wednesday
Thursday
Distance
5 km, 430 m, 0 cm
4 km, 789 m, 98 cm
6 km, 967 m, 56 cm
5 km, 5 m, 5 cm
Part 1:
How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters
and 38 centimeters)?
Part 2:
Write a sentence explaining how you found out the distance that she ran.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Filling the Jugs
4.MD.1-Task 8
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Filling the Jug
For a class project there was a large 10 Liter jug that had to be filled with water.
Unfortunately, the class only had a container marked in milliliters.
Part 1:
Complete the table below.
Amount in the jug
Amount in Milliliters
1 Liter
1 Liter and 250 mL
1 Liter and 750 mL
2 Liters
2 Liters and 400 mL
2 Liters and 756 mL
3 Liters
Part 2:
Write a sentence to explain how you found the answer to one of the rows of the table.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: 1 L = 1,000 mL; 1 L, 250 mL; 1,250
than 2 errors.
OR their explanation is not
mL; 1L, 750 mL= 1,750 mL; 2 L = 2,000
accurate.
mL; 2L, 400 mL = 2,400 mL; 2L, 756 mL;
2,756 mL; 3L = 3,000 mL
 Part 2: The sentence is logical and accurate.
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
Filling the Jug
For a class project there was a large 10 Liter jug that had to be filled with water.
Unfortunately, the class only had a container marked in milliliters.
Part 1:
Complete the table below.
Amount in the jug
Amount in Milliliters
1 Liter
1 Liter and 250 mL
1 Liter and 750 mL
2 Liters
2 Liters and 400 mL
2 Liters and 756 mL
3 Liters
Part 2:
Write a sentence to explain how you found the answer to one of the rows of the
table.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Making Punch
4.MD.1-Task 9
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;
kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in
a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Paper and pencil, activity sheet (attached)
Making Punch
For a party Mrs. Laney is making punch. She filled a few different large punch bowls.
Part 1:
Complete the table below.
Punch Bowl
Amount in Milliliters
2 Liters and 5 milliliters
2 Liters and 50 milliliters
2 Liters and 500 milliliters
3 Liters and 8 milliliters
3 Liters and 80 milliliters
3 Liters and 800 milliliters
Part 2:
Write a sentence to explain how you found the answer to one of the rows of the table.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: 2 L, 5 mL = 2,005 mL; 2L, 50 mL =
than 2 errors.
OR their explanation is not
2,050 mL; 2L, 500 mL = 2,500 mL; 3 L, 8
accurate.
mL = 3,008 mL; 3L, 80 mL = 3,080 mL; 3
L, 800 mL = 3,800 mL
 Part 2: The explanation contains an accurate
explanation.
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
Making Punch
For a party Mrs. Laney is making punch. She filled a few different large punch
bowls.
Part 1:
Complete the table below.
Punch Bowl
Amount in Milliliters
2 Liters and 5 milliliters
2 Liters and 50 milliliters
2 Liters and 500 milliliters
3 Liters and 8 milliliters
3 Liters and 80 milliliters
3 Liters and 800 milliliters
Part 2:
Write a sentence to explain how you found the answer to one of the rows of the
table.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Weighing the Books
4.MD.2-Task 1
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,
liquid volumes, masses of objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as number line diagrams that
feature a measurement scale.
Paper and pencil
Weighing the Books
Mrs. Floyd and her classmates want to know how heavy a few of the books in their
classroom are.
Part 1:
They want to know the masses of the objects in ounces; however the scale only gives the
mass in pounds. Using the table below, find out how many ounces each book is.
Math book
2 1/2 pounds
Science book
3 1/3 pounds
Dictionary
5 1/8 pounds
Part 2:
Two copies of one book and two copies of another book weigh a total of 6 pounds. Each
book weighs a whole number of ounces. How many ounces could each book weigh?
Explain how you solved this problem.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Math: 40 ounces, Science: 53 1/3
than 2 errors.
OR their explanation is not
ounces, Dictionary: 82 ounces.
accurate.
 Part 2: The books should have a combined
weight of 48 ounces, since 2 copies of both
books will be 6 pounds or 96 ounces.
 AND there is a clear and accurate
explanation about how they found the
distances in inches.
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
Weighing the Books
Mrs. Floyd and her classmates want to know how heavy a few of the books in
their classroom are.
Part 1:
They want to know the masses of the objects in ounces, however the scale only
gives the mass in pounds. Using the table below, find out how many ounces
each book is.
Math book
2 1/2 pounds
_______oz
Science book
3 1/3 pounds
_______oz
Dictionary
5 1/8 pounds
_______oz
Part 2:
Two copies of one book and two copies of another book weigh a total of 6
pounds. Each book weighs a whole number of ounces. How many ounces could
each book weigh? Explain how you solved this problem.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Getting Ready for School
4.MD.2-Task 2
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of
time, liquid volumes, masses of objects, and money, including problems involving simple
fractions or decimals, and problems that require expressing measurements given in a larger
unit in terms of a smaller unit. Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
Paper and pencil
Getting Ready for School
The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:
Eat breakfast: 15 minutes
Shower: 8 minutes
Get dressed: 7 minutes
Read a book: 12 minutes
Part 1:
What is the latest that Steve can get up and still be on time for the bus?
Part 2:
It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to eat
breakfast. What is the latest Rachel can get up and still be on time for the bus? Write a
sentence to explain how you found your answer.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Steve needs to be up by 7:33 a.m.
than 2 errors.
OR their explanation in
Part 2: Rachel needs to be up by 7:21 a.m.
Part 3 is not accurate.
 AND the explanation is clear and accurate.
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
Getting Ready for School
The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:
Eat breakfast: 15 minutes
Shower: 8 minutes
Get dressed: 7 minutes
Read a book: 12 minutes
Part 1:
What is the latest that Steve can get up and still be on time for the bus?
Part 2:
It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to
eat breakfast. What is the latest Rachel can get up and still be on time for the bus?
Write a sentence to explain how you found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Adding Up and Comparing Our Jumps
4.MD.2-Task 3
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,
liquid volumes, masses of objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as number line diagrams that
feature a measurement scale.
Paper and pencil
Adding Up and Comparing Our Jumps
At school three students are have a jumping competition to see who can jump the farthest.
Part 1:
Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy.
Sarah jumped 9 inches longer than Miguel.
How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?
How long did each person jump in only inches?
Part 2:
Write a sentence describing how you found the distances that each person jumped in
inches.
Part 3:
What was the combined length that all three students jumped in inches? What was their
distance in feet and inches?
Part 4:
Three other students jumped a combined distance of 15 feet. How much further did they
jump compared to the combined distance of Nancy, Miguel, and Sarah?
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Nancy: 3 ft, 11 in or 47 in; Miguel: 4
than 2 errors.
OR their explanation is not
ft, 4 in or 52 in; Sarah: 5 ft, 1 in or 61 in.
accurate.
 Part 2: The sentence contains a logical and
accurate description.
 Part 3: 160 inches or 13 ft 4 in.
 Part 4: The other students jumped 1 ft and 8
inches further.
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
Adding Up and Comparing Our Jumps
At school three students are have a jumping competition to see who can jump the farthest.
Part 1:
Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy.
Sarah jumped 9 inches longer than Miguel.
How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?
How long did each person jump in only inches?
Part 2:
Write a sentence describing how you found the distances that each person jumped in inches.
Part 3:
What was the combined length that all three students jumped in inches?
What was their distance in feet and inches?
Part 4:
Three other students jumped a combined distance of 15 feet. How much further did they jump
compared to the combined distance of Nancy, Miguel, and Sarah?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Adding Up and Comparing Our Jumps II
4.MD.2-Task 4
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit
to a smaller unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,
liquid volumes, masses of objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as number line diagrams that
feature a measurement scale.
Paper and pencil
Adding Up and Comparing Our Jumps II
At school three students are have a jumping competition to see who can jump the farthest.
Part 1:
Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy.
Mitch jumped 11 inches longer than Yani.
How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?
How long did each person jump in only inches?
Part 2:
Write a sentence describing how you found the distances that each person jumped in
inches.
Part 3:
What was the combined length that all three students jumped in inches? What was their
distance in feet and inches?
Part 4:
Three other students jumped a combined distance of 14 feet. How much further did they
jump compared to the combined distance of Timothy, Yani, and Mitch?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Rubric
Level I
Level II
Limited Performance Not Yet Proficient
 Students make
 Students make 1 or 2
more than 2
errors OR their
errors.
explanation is not
accurate.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 Part 1: Timothy- 3 feet 10 inches or 46 inches;
Yani- 4 ft and 2 inches or 50 inches; Mitch- 5 ft 1
inch or 61 inches
 Part 2: The sentence accurately describes an
appropriate process to find out each distance in
inches.
 Part 3: The combined distance was 157 inches or
13 feet 1 inch.
 Part 4: The three other students jumped 11 inches
farther than Timothy, Yani, and Mitch.
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
Adding Up and Comparing Our Jumps II
At school three students are have a jumping competition to see who can jump the farthest.
Part 1:
Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy.
Mitch jumped 11 inches longer than Yani.
How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?
How long did each person jump in only inches?
Part 2:
Write a sentence describing how you found the distances that each person jumped in inches.
Part 3:
What was the combined length that all three students jumped in inches? What was their distance
in feet and inches?
Part 4:
Three other students jumped a combined distance of 14 feet. How much further did they jump
compared to the combined distance of Timothy, Yani, and Mitch?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Area & Perimeter Exploration
4.MD.3-Task 1
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and
mathematical problems.
Paper and pencil, graph paper or square tiles
Examining the relationship between area and perimeter and using area and perimeter
formulas for quick calculation.
Activity 1:
Create all the possible arrays with an area of 36 square units.
Draw them on grid paper and label their dimensions.
How can you be sure that you found all the possible arrays with an area of 36 square units?
Find the perimeter for each figure.
What do you notice about the shapes and their perimeters?
What is the relationship between the perimeter and the shape of an array?
Activity 2:
Create all the possible arrays with a perimeter of 36 units.
Draw your arrays on grid paper and label their dimensions.
Use a chart to keep track of the area and dimensions for each rectangle.
How can you be sure that you found all the possible arrays with a perimeter of 36 units?
What do you notice about the shapes and their perimeters?
What is the relationship between the area and the shape of an array?
Activity 3:
What generalizations can be made about the relationship between the area and perimeter of
a figure?
How could this this information be used to solve a problem in real life? When might it be
useful to have this information?
Possible Solution:
Activity 1: All have area of 36 square units.
Perimeter
dimensions
74 units
1 x 36
40 units
2 x 18
30 units
3 x 12
26 units
4x9
24 units
6x6
Possible conclusions: The closer a shape gets to being a square, the smaller its perimeter.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Activity 2: All have a perimeter of 36 units.
Area
dimensions
17
1 x 17
32
2 x 16
45
3 x 15
56
4 x 14
65
5 x 13
72
6 x 12
77
7 x 11
80
8 x 10
81
9x9
Possible response: The closer a shape gets to being a square, the larger its area.
Squares have the largest possible area and the smallest possible perimeter.
Rubric
Level I
Level II
Limited Performance
Not Yet Proficient
 The student is unable to find
 The student is able to find all
all the possible figures with an
the possible arrays, areas, and
area of 36 and/or calculate the
perimeters for Activity 1 and
perimeter for each figure. The
Activity 2. They are unable to
student is unable to find all the
make generalizations about the
possible arrays with a
relationship between area and
perimeter of 36 and/or their
perimeters of squares and
areas. The student does not
rectangles. They are unable to
have an efficient strategy to
generate an example of how
check to make sure that s/he
this relationship might be
has found all the possible
useful in solving a real world
arrays that fit the requirements.
problem.
They are unable apply the
formula for area or perimeter
to perform the required
calculations.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 The student is able to find all
the possible arrays, areas, and
perimeters for Activity 1 and
Activity 2. They are able to
make generalizations about the
relationship between area and
perimeters of squares and
rectangles, and to generate at
least one example of how this
relationship might be useful in
solving a real world problem.
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
Area & Perimeter Exploration
Activity 1:
 Create all the possible arrays with an area of 36 square units.
 Draw them on grid paper and label their dimensions.
 How can you be sure that you found all the possible arrays with an area of 36
square units?
 Find the perimeter for each figure.
 What do you notice about the shapes and their perimeters?
 What is the relationship between the perimeter and the shape of an array?
Activity 2:
 Create all the possible arrays with a perimeter of 36 units.
 Draw your arrays on grid paper and label their dimensions.
 Use a chart to keep track of the area and dimensions for each rectangle.
 How can you be sure that you found all the possible arrays with a perimeter of
36 units? What do you notice about the shapes and their perimeters?
 What is the relationship between the area and the shape of an array?
Activity 3:
 What generalizations can be made about the relationship between the area and
perimeter of a figure?
 How could this this information be used to solve a problem in real life? When
might it be useful to have this information?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Putting Down Carpet
4.MD.3 - Task 2
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and
mathematical problems. For example, find the width of a rectangular room given the area
of the flooring and the length, by viewing the area formula as a multiplication equation
with an unknown factor.
Plastic square tiles, Paper, Pencil, Graph paper (optional)
Putting Down Carpet
Part 1:
You want to carpet 3 rooms of a house. Using the dimensions below, determine how much
carpet is needed.
Room 1: Perimeter is 38 yards and the width of the room is 12 yards.
Room 2: Perimeter is 50 yards and the width is 13 yards.
Room 3: Perimeter is 46 yards and the width is 10 yards.
For each room, determine how much carpet is needed.
Part 2:
Write a sentence and explain how you solved this task.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Room 1: Width is 12, Length is 7.
than 2 errors.
OR their explanation is not
Area is 84 square yards. Room 2: Width is
accurate.
13 yards, Length is 12 yards. Area is 156
square yards. Room 3: Width is 10, Length is
13. Area is 130 square yards.
 Part 2: The explanation is clear and accurate.
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
Putting Down Carpet
Part 1:
You want to carpet 3 rooms of a house. Using the dimensions below, determine
how much carpet is needed.
Room 1: Perimeter is 38 yards and the width of the room is 12 yards.
Room 2: Perimeter is 50 yards and the width is 13 yards.
Room 3: Perimeter is 46 yards and the width is 10 yards.
For each room, determine how much carpet is needed.
Part 2:
Write a sentence and explain how you solved this task.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Fencing Yards
4.MD.3 - Task 3
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and
mathematical problems. For example, find the width of a rectangular room given the area
of the flooring and the length, by viewing the area formula as a multiplication equation
with an unknown factor.
Plastic square tiles, Paper, Pencil, Graph paper (optional)
Fencing Yards
Part 1:
For a summer job, your older brother is working for a fencing company. Determine how
much fencing is needed for each of these rectangular yards.
Yard 1: Area is 500 square meters. Length is 25 meters.
Yard 2: Area is 567 square meters. Length is 9 meters.
Yard 3: Area is 736 square meters. Length is 4 meters.
Part 2:
Write a sentence and explain how you solved this task.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Yard 1: Width is 20 meters. Fencing:
than 2 errors.
OR their explanation is not
90 meters. Yard 2: Width is 63 meters.
accurate.
Fencing: 144 meters. Yard 3: Width is 184
meters. Fencing is 376 meters.
 Part 2: The explanation is clear and accurate.
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
Fencing Yards
Part 1:
For a summer job, your older brother is working for a fencing company. Determine
how much fencing is needed for each of these rectangular yards.
Yard 1: Area is 500 square meters. Length is 25 meters.
Yard 2: Area is 567 square meters. Length is 9 meters.
Yard 3: Area is 736 square meters. Length is 4 meters.
Part 2:
Write a sentence and explain how you solved this task.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Making a Dog Pen
4.MD.3 - Task 4
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Solve problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and
mathematical problems. For example, find the width of a rectangular room given the area
of the flooring and the length, by viewing the area formula as a multiplication equation
with an unknown factor.
Plastic square tiles, Paper, Pencil, Graph paper (optional)
Making a Dog Pen
Part 1:
You want to make a rectangular dog pen using 20 yards of fencing. The side lengths must
be in whole yards. Create as many different rectangular pens as you can.
Part 2:
Which dog pen gives your dog the most space to run around and play in? Write a sentence
explaining how you know.
Part 3:
You want to build the rectangular dog pen with 20 yards of fencing against your house
which is 20 yards wide. Which dimensions will give you the most space for your dog?
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2
 Part 1: The dimensions must add up to 10. 9x1,
than 2 errors.
errors OR their
8x2, 7x3, 6x4, 5x5.
explanation is not
 Part 2: The 5x5 pen gives the most space, 25
accurate.
square yards. AND the explanation is clear and
accurate.
 Part 3: The 10x5 rectangle gives the most
space. The 10 yard side runs parallel to the
house while the 5 yard sides connect the house
to the other side.
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
Making a Dog Pen
Part 1:
You want to make a rectangular dog pen using 20 yards of fencing. The side lengths
must be in whole yards. Create as many different rectangular pens as you can.
Part 2:
Which dog pen gives your dog the most space to run around and play in? Write a
sentence explaining how you know.
Part 3:
You want to build the rectangular dog pen with 20 yards of fencing against your
house which is 20 yards wide. Which dimensions will give you the most space for
your dog?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Reading Survey
4.MD.4 - Task 1
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Represent and interpret data.
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves
and fourths of an inch. Show the data by making a line plot, where the horizontal scale is
marked off in appropriate units— whole numbers, halves, or quarters.
Paper, pencils, white boards and dry-erase markers (optional)
Directions for students:
 As a class, have students survey 10 classmates and ask them “How long do you think
fourth graders should read each night at home?” They can choose ¼, ½, ¾ or 1 hour.
Students should record results on a piece of paper.
 Create a line plot to represent the data.
 Have students write a sentence about an observation that they notice from the line plot.
 If you were using this line plot to make a decision about how long students should read
each night, which time would you choose? Why?
Level I
Limited Performance
 Incorrect answer and work are
given.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Finds the correct answer, but
there may be inaccuracies or
incomplete justification of
solution OR
 Uses partially correct work
but does not have a correct
solution.
Level III
Proficient in Performance
 Accurately surveys and makes
a line plot, and analyses the
results.
 Uses an appropriate model to
represent and justify the
solution.
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 High Did it Bounce?
4.MD.4-Task 2
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Represent and interpret data.
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2,
1/4, 1/8). Solve problems involving addition and subtraction of fractions by using
information presented in line plots. For example, from a line plot find and interpret the
difference in length between the longest and shortest specimens in an insect collection.
Paper, pencil, Activity sheet
How High Did it Bounce?
A class measures how high a bouncy ball will bounce compared to the height of the wall.
Based on the data, make a line plot to display the data.
3/8
6/8
5/8
5/8
5/8
7/8
7/8
4/8
5/8
6/8
4/8
6/8
5/8
2/8
4/8
6/8
6/8
5/8
A) How many bouncy balls went halfway up the wall or higher?
B) How may bouncy balls went 3/4 of the wall or higher?
C) What is the combined height of all of the heights of the bouncy balls?
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  A) 16 balls, B) 7 balls, C) 11 and 3/8 of the
than 2 errors.
wall or 91 feet high.
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 High Did it Bounce?
A class measures how high a bouncy ball will bounce compared to the height of
the wall. Based on the data, make a line plot to display the data.
3/8
6/8
5/8
0
1/8
5/8
5/8
7/8
2/8
7/8
4/8
5/8
3/8
6/8
4/8
6/8
4/8
5/8
2/8
4/8
5/8
6/8
6/8
6/8
5/8
7/8
1
A) How many bouncy balls went halfway up the wall or higher?
B) How may bouncy balls went 3/4 of the wall or higher?
C) If the wall is 8 feet high, what is the combined height of all of the heights of
the bouncy balls?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Measuring Strings
4.MD.4-Task 3
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Represent and interpret data.
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2,
1/4, 1/8). Solve problems involving addition and subtraction of fractions by using
information presented in line plots. For example, from a line plot find and interpret the
difference in length between the longest and shortest specimens in an insect collection.
Paper, pencil, Activity sheet
Measuring Strings
A basket of strings is measured by the class and graphed. Based on the line plot:
1) How many strings are ½ of a foot or longer?
2) How many strings are shorter than 3/8 of a foot?
3) If students put the string together that is 1/8 or 2/8 of a foot long, how long would
that string be?
4) If students put all of the pieces of string together, how long would that string be?
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  1) 7. 2) 6, 3) 9/8 or 1 and 1/8, 4) 8 and 6/8
than 2 errors.
or 8 and 3/4
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
Measuring Strings
A basket of strings is measured by the class and graphed.
Lengths of string (feet)
0
x
x
x
1/8
x
x
x
2/8
x
x
3/8
x
x
x
4/8
x
x
5/8
x
x
6/8
x
X
X
7/8
1
Based on the line plot:
1) How many strings are more than ½ of a foot or longer?
2) How many strings are shorter than 3/8 of a foot?
3) If students put the string together that is 1/8 or 2/8 of a foot long, how long
would that string be?
4) If students put all of the pieces of string together, how long would that string be?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Intersecting Roads
4.MD.5 – Task 1
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a
common endpoint, and understand concepts of angle measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint
of the rays, by considering the fraction of the circular arc between the points where the two
rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n
degrees.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of
specified measure.
Task handout, Protractor (optional)
Intersecting Roads
Circle-town is shaped like a circle. All of the roads start in the center of the town and
extend from the center like rays.
Part 1:
On the map draw the following roads and label the measure of each angle.
a) Smith Street extends completely horizontal to the right of the center of town.
b) Smith Street and Main Street form a 45 degree angle.
c) Thompson Street forms a 30 degree angle with Main Street.
d) Young Avenue forms a 90 degree angle with Thompson Street.
e) Turnberry forms a 120 degree angle with Young Avenue.
Part 2:
Write an explanation about how you know your answers are correct in Part 1.
Rubric
Level I
Limited Performance
 The student is unable to
use strategies to find
correct answers to any
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
a) Level II
Not Yet Proficient
 The student has
between 1 and 2
errors.
Level III
Proficient in Performance
 The answers are correct.
 Part 1: Roads are drawn correctly and angles are
correctly labeled.
 Part 2: The explanation is 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
Intersecting Roads
Circle-town is shaped like a circle. All of the roads start in the center of the town
and extend from the center like rays.
Part 1:
On the map draw the following roads and label the measure of each angle.
a) Smith Street extends completely horizontal to the right of the center of town.
b) Smith Street and Main Street form a 45 degree angle.
c) Thompson Street forms a 30 degree angle with Main Street.
d) Young Avenue forms a 90 degree angle with Thompson Street.
e) Turnberry forms a 120 degree angle with Young Avenue.
Part 2:
Write an explanation about how you know your answers are correct in Part 1.
Extension: Create your own town and give direction as noted above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Going Different Directions
4.MD.6 – Task 1
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of
specified measure.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a
common endpoint, and understand concepts of angle measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint
of the rays, by considering the fraction of the circular arc between the points where the two
rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n
degrees.
Task handout, Protractor (optional)
Going Different Directions
Pairs of students worked together to explore the idea of creating an angle.
Part 1: Each student represents a point and each walk represents a ray. Draw the angle
each situation below creates.
a) Students stood back to back and walked away from each other;
b) One student faced forward while the other student turned 30 degrees and both
students walked forward;
c) One student faced forward while the other student turned 90 degrees and both
students walked forward;
d) One student faced forward while the other student turned 120 degrees and both
students walked forward.
Part 2: Explain how you solved the tasks above.
Rubric
Level I
Limited Performance
 The student is unable to
use strategies to find
correct answers to any
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
b) Level II
Not Yet Proficient
 The student has
between 1 and 2
errors.
Level III
Proficient in Performance
 The answers are correct.
 Part 1: Angles are drawn correctly. A is a 180
degree or straight angle.
 Part 2: The explanation is 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
Going Different Directions
Pairs of students worked together to explore the idea of creating an angle. Each
student represents a point and each walk represents a ray. Draw the angle each
situation below creates.
Part 1:
Draw each angle when:
c) Students stood back to back and walked away from each other.
d) One student faced forward while the other student turned 30 degrees and both
students walked forward.
e) One student faced forward while the other student turned 90 degrees and both
students walked forward.
f) One student faced forward while the other student turned 120 degrees and
both students walked forward.
Part 2:
Explain how you solved the tasks above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Making Shapes
4.MD.6 – Task 2
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of
specified measure.
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a
common endpoint, and understand concepts of angle measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint of
the rays, by considering the fraction of the circular arc between the points where the two
rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree
angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n
degrees.
Task handout, Geoboard, Protractor
Making Shapes
Part 1:
On the geoboard make the following shapes. Below, draw the shape and write the
measurement of each angle.
a) A rectangle
b) A trapezoid
c) A parallelogram that is not a rectangle
d) A right triangle
e) An isosceles triangle
f) An obtuse triangle
Part 2: Write an explanation describing how you measured each of the angles in the
isosceles triangle.
Rubric
Level I
Limited Performance
 The student is unable to
use strategies to find
correct answers to any
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
g) Level II
Not Yet Proficient
 The student has
between 1 and 2
errors.
Level III
Proficient in Performance
 The answers are correct.
 Part 1: The shapes are drawn correctly and angle
measures are correctly labeled.
 Part 2: The explanation is 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 Shapes
Part 1:
On the geoboard make the following shapes. Below, draw the shape and write the
measurement of each angle.
a) A rectangle
b) A trapezoid
c) A parallelogram that is not a rectangle
d) A right triangle
e) An isosceles triangle
f) An obtuse triangle
Part 2:
Write an explanation describing how you measured each of the angles in the
isosceles triangle.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Adding Up Angles
4.MD.7-Task 1
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.7 Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the
parts. Solve addition and subtraction problems to find unknown angles on a diagram in real
world and mathematical problems, e.g., by using an equation with a symbol for the
unknown angle measure.
Paper, pencil, Protractor
Adding Up Angles
A 90 degree angle is divided into two smaller angles.
Part 1:
What type of angles are both of the smaller angles? How do you know?
Part 2:
Give 3 possible combinations for the measurements of both angles. For each, draw the
angles and write the angle measure.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: Both angles have to be acute angles
than 2 errors.
OR the drawings are not
since the sum of both is 90 degrees.
close to the angle measure.  Part 2: The sum of both angles has to be 90
degrees for all 3 answers AND the drawings
are close to the angle measure.
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
Adding Up Angles
A 90 degree angle is divided into two smaller angles.
Part 1:
What type of angles are both of the smaller angles? How do you know?
Part 2:
Give 3 possible combinations for the measurements of both angles. For each, draw
the angles and write the angle measure.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
How Can We Split Angles?
4.MD.7-Task 2
Domain
Cluster
Standard(s)
Materials
Measurement and Data
Geometric measurement: understand concepts of angle and measure angles.
4.MD.7 Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the
parts. Solve addition and subtraction problems to find unknown angles on a diagram in real
world and mathematical problems, e.g., by using an equation with a symbol for the
unknown angle measure.
Paper, pencil, Protractor
How Can We Split Angles?
Part 1:
Use a protractor to split a 135 degree angle the following ways:
A) A right angle, a 35 degree angle and another acute angle. What is the measure of
the other angle?
B) A right angle and another angle. What is the measure of the other angle?
C) A 120 degree angle and another angle. What is the measure of the other angle?
D) 3 angles that are the same size.
E) A 15 degree angle and 2 angles that are the same size. What is the measure of the
other angles?
Part 2:
Describe how you solved one of the tasks above.
Rubric
Level I
Level II
Level III
Limited Performance
Not Yet Proficient
Proficient in Performance
 Students make more  Students make 1 or 2 errors  Part 1: A) The other angle is 10 degrees. B)
than 2 errors.
The other angle is 45 degrees. C) The other
angle is 15 degrees. D) Each angle is 45
degrees. E) The other angles are each 60
degrees.
 Part 2: Description is clear and accurate.
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 Can We Split Angles?
Part 1:
Use a protractor to split a 135 degree angle the following ways:
A) A right angle, a 35 degree angle and another acute angle. What is the measure
of the other angle?
B) A right angle and another angle. What is the measure of the other angle?
C) A 120 degree angle and another angle. What is the measure of the other
angle?
D) 3 angles that are the same size. What is the measure of each of the angles?
E) A 15 degree angle and 2 angles that are the same size. What is the measure of
the other angles?
Part 2:
Describe how you solved one of the tasks above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE