Formative Instructional and Assessment Tasks
Coin Collection
4.NBT.1 - Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right.
Paper and pencil
Part 1:
You have a collection of 826 coins.
 If the coins are pennies, what would be the value of your collection?
 If the coins are dimes, what would be the value of your collection?
 If they were dollars instead of coins, what would be the value of your collection?
 If they were ten dollar bills what would be the value of your collection?
Part 2:
 Look at the four values that you wrote for Part 1.
 What do you notice about the value of your collections?
 What pattern do you notice about the value of your collections?
 Explain your thinking in words, pictures, or numbers.
Rubric
Level I
Level II
Limited Performance
Not Yet Proficient
 Part 1: Student correctly
 Part 1: Student correctly
identifies values for 0-2
identifies values for 3-4 coins.
coins.
 Part 2: Explanation shows a
developing understanding of
 Part 2: Explanation does not
show consistent
place value patterns.
understanding of place value
patterns.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 Part 1: Student correctly
identifies values for each coin.
Value in pennies: $8.26
Value in dimes: $82.60
Value in dollars: $826.00
Value in ten dollars: $8,260.00
 Part 2: Explanation
demonstrates conceptual
understanding of place value
patterns.
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
Coin Collection
Part 1:
You have a collection of 826 coins.
 If the coins are pennies, what would be the value of your collection?
 If the coins are dimes, what would be the value of your collection?
 If they were dollars instead of coins, what would be the value of your
collection?
 If they were ten dollar bills what would be the value of your collection?
Part 2:
Look at the four values that you wrote for Part 1.
 What do you notice about the value of your collections?
 What pattern do you notice about the value of your collections?
 Explain your thinking in words, pictures, or numbers.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Adding Zeros
4.NBT.1 Task 2
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right.
Paper and pencil
Give students the following writing prompt:
Gina said, “Forty-six multiplied by 10 is 460 because when you multiply a number by
ten, you add a zero on to the end of it.” Do you agree or disagree with Gina? Explain
your reasoning. Give at least one example to support your reason.
Level I
Limited Performance
 Students think that multiplying
by ten is like adding a zero on
to a number. They do not
understand the relationship
between multiplying by ten
and the place value shift that
digits make.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 The student may agree or
disagree, but cannot clearly
articulate that 46 x 10 = 460
because each digit is ten times
as much and shifts place value
one place to the left. The
student cannot generate an
example to support this idea.
Level III
Proficient in Performance
 The student may agree or
disagree, and can clearly
articulate that 46 x 10 = 460
because each digit is ten times
as much and shifts place value
one place to the left. The
student is able to generate an
example to support this idea.
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 Zeroes
Gina said, “Forty-six multiplied by 10 is 460 because when you multiply a number
by ten, you add a zero on to the end of it.”
Do you agree or disagree with Gina? Explain your reasoning. Give at least one
example to support your reason.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Packaging Soup Cans
4.NBT.1-Task 3
Domain
Cluster
Standard(s)
Materials
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right.
Paper and pencil, activity sheet, base 10 blocks (optional) , Virtual base ten blocks can be
found here: http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html
Task
Packaging Soup Cans
There are 202 soup cans are in the factory. A crate will hold 200 cans. A case will hold 20
cans. The rest of the cans go into individual boxes. The factory wants to use as few
packages as possible.
1.
2.
3.
4.
How many crates, cases, and individual boxes will you need to hold the 202 soup cans?
If you only had cases and individual boxes, how many of each would you need?
If you only had individual boxes, how many would you need?
What did you notice about the number of crates and cases in Part A compared to Part
B? Explain your reasoning.
Rubric
Level I
Limited Performance
 Students provide
correct answers
on two or fewer
of the parts
above.
1.
2.
3.
4.
5.
6.
7.
8.
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Students provide correct  Students provide correct answers to all problems.
answers on all but one
 Solutions: 1) 1 crate, 0 cases and 2 individual
of the parts above.
boxes, 2) 10 cases and 2 individual boxes, 3) 202
individual boxes,4) The explanation says something
about the trading of 1 crate for 10 cases. In Part A
we needed 1 crate and 0 cases. In Part B, there we
needed 10 cases.
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
Packaging Soup Cans
There are 202 soup cans are in the factory. A crate will hold 200 cans. A case will
hold 20 cans. The rest of the cans go into individual boxes. The factory wants to
use as few packages as possible.
1. How many crates, cases, and individual boxes will you need to hold the 202 soup
cans?
2. If you only had cases and individual boxes, how many of each would you need?
3. If you only had individual boxes, how many would you need?
4. What did you notice about the number of cases in Part A compared to Part B?
Explain your reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Value of the Bills
4.NBT.1-Task 4
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right.
Paper and pencil, Activity sheet
Part 1:
Gina said, “In my pocket I have 25 of the same amount of dollar bills. What is the value of
Gina’s money if she has:
a) 25 one dollar bills
b) 25 ten dollar bills
c) 25 hundred dollar bills
Part 2:
Gina reasoned, “The value of the 2 when I have ten dollar bills is 200, but the value of the
2 when I have one dollar bills is only 20.” Is Gina correct? Why or why not?
Part 3:
Consider Parts A, B, and C above if you had 260 of the same amount of dollar bills. What
would the value of the bills be? Explain how you found your answer.
Level I
Limited Performance
 Students get
incorrect answers
on all parts of the
task.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 The student is successful in  Answers: Part 1: 25; 250, 2,500; Part 2: Gina is
2 of the 3 parts of the task.
correct. The explanation should talk about the
idea that there are 25 groups of 1, 25 groups of
10, or 25 groups of 100.
 Part 3: 260; 2,600; 26,000. Explanation
discusses the idea that the value of each digit is
multiplied by 10 when the value of the dollar
bills increases 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
Value of the Bills
Part 1:
Gina said, “In my pocket I have 25 of the same amount of dollar bills. What is the
value of Gina’s money if she has:
a) 25 one dollar bills
b) 25 ten dollar bills
c) 25 hundred dollar bills
Part 2:
Gina reasoned, “The value of the 2 when I have ten dollar bills is 200, but the value
of the 2 when I have one dollar bills is only 20.” Is Gina correct? Why or why not?
Part 3:
Consider Parts A, B, and C above if you had 260 of the same amount of dollar bills.
What would the value of the bills be? Explain how you found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Arranging Students
4.NBT.2-Task 1
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2 Read and write multi-digit whole numbers using numerals, number names and
expanded form. Compare two multi-digit numbers based on meanings of the digits in each
place, using >, = and < symbols to record the results of comparisons.
Paper and pencil, Activity sheet, Base ten blocks, Virtual base ten blocks can be found
here: http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html
Arranging Students
For a field trip, 4th grade students will visit North Carolina State University’s Millennial
Campus. Students are in groups of 10. Each building can accommodate 10 groups at a
time. Based on this information:
1) How many students would be in 4 buildings?
2) All of the students in 2 buildings and 13 other groups on the field trip visit the electron
microscope before lunch. How many students saw the microscope?
3) There were 346 students from Hickory Elementary School. If they all were sent to the
same buildings how many buildings were completely full of students from Hickory
School? How many whole groups would go to another building? How many students
from that school would be leftover without a group?
4) Students from New Hanover Elementary School take up 2 whole buildings, 14 whole
groups in other buildings, and 9 students in different groups. Do they have more or less
students than Hickory Elementary? How do you know?
Level I
Limited Performance
 Students do not provide
correct answers to more than 2
parts.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students do not
provide correct
answers to 1 or 2
parts.
Level III
Proficient in Performance
 Students provide correct answers for
parts 1 through 4. Answers: 1) 400
students; 2) 330 students; 3) 3 whole
buildings, 4 whole groups in another
building, and 6 left over students; 4)
New Hanover- 349 students. New
Hanover has more students than
Hickory.
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
Arranging Students
For a field trip, 5th grade students will visit North Carolina State University’s
Millennial Campus. Students are in groups of 10. Each building can accommodate
10 groups at a time. Based on this information:
1) How many students would be in 4 buildings?
2) All of the students in 2 buildings and 13 other groups on the field trip visit the
electron microscope before lunch. How many students saw the microscope?
3) There were 346 students from Hickory Elementary School. If they all were sent
to the same buildings how many buildings were completely full of students from
Hickory School? How many whole groups would go to another building? How
many students from that school would be leftover without a group?
4) Students from New Hanover Elementary School take up 2 whole buildings, 14
whole groups in other buildings, and 9 students in different groups. Do they have
more or less students than Hickory Elementary? How do you know?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Juice Pouches
4.NBT.2-Task 2
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2 Read and write multi-digit whole numbers using numerals, number names and
expanded form. Compare two multi-digit numbers based on meanings of the digits in each
place, using >, = and < symbols to record the results of comparisons.
Paper and pencil, Activity sheet
Juice Pouches
Juice pouches are packaged in different ways. A box holds 10 pouches. A case holds 10
boxes. A crate holds 10 cases.
Some students bring in juice boxes for Field Day. The information is below.
Miguel- 1 crates, 12 cases, 3 boxes and 6 pouches.
Aaron- 1 crates, 13 cases, 17 boxes, and 2 pouches.
Sarah- 1 crates, 12 cases, 2 boxes and 17 pouches.
Vicky- 1 crates, 14 cases, 6 boxes, and 9 pouches.
1) If each person were going to reorganize their drink pouches to use as many of the
larger containers as possible, and so that there are no more than 10 of each type of
container, how many of each container would each of them need?
2) How many total drink pouches does each student have? Explain how you found
your answer.
3) List in order from the student who had the most juice pouches to the student with
the smallest number of juice pouches.
Extension (4.NBT.6)
If all of the boxes were going to be split evenly among the 6 grades at the school how
many boxes would each grade get? Would there be any leftovers?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students are unable to create
different representations of the
numbers and does not use
place value as a strategy to
compare them.
Rubric
Level II
Not Yet Proficient
 Students are able to
create different
representations of the
numbers, but does not
use place value as a
strategy to compare
them.
Level III
Proficient in Performance
 Students provide correct answers for
parts 1, 2, and 3. Solutions: Part 1:
Miguel- 2 crates, 2 cases, 3 boxes, and
6 pouches; Aaron- 2 crates, 4 cases, 7
boxes, and 2 pouches. Sarah- 2 crates, 2
cases, 3 boxes, and 7 pouches; Vicky- 2
crates, 4 cases, 6 boxes and 9 pouches;
 Part 2- Miguel- 2,236 pouches; Aaron2,472 pouches Sarah- 2,237 pouches;
Vicky- 2,469.Explanation discusses
adding up the number of pouches.
 Part 3- Aaron, Vicky, Sarah, Miguel.
*Extension- 1,569 pouches per grade with no left overs.
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
Juice Pouches
Juice pouches are packaged in different ways. A box holds 10 pouches. A case holds
10 boxes. A crate holds 10 cases.
Some students bring in juice boxes for Field Day. The information is below.
Miguel- 1 crates, 12 cases, 3 boxes and 6 pouches.
Aaron- 1 crates, 13 cases, 17 boxes, and 2 pouches.
Sarah- 1 crates, 12 cases, 2 boxes and 17 pouches.
Vicky- 1 crates, 14 cases, 6 boxes, and 9 pouches.
1) If each person were going to reorganize their drink pouches to use as many of the
larger containers as possible, how many of each container would each of them
need?
2) How many total drink pouches does each student have?
3) List in order from the student who had the most juice pouches to the student with
the smallest number of juice pouches.
Extension:
If all of the boxes were going to be split evenly among the 6 grades at the
school how many boxes would each grade get? Would there be any leftovers?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Open Number Lines
4.NBT.3-Task 1
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.3 Use place value understanding to round multi-digit numbers to any place.
Paper and pencil
Activity 1: Estimating sums and differences using an open number line.
Specified as a tool for estimating by the CCSSM, an open number line is simply a blank
number line. One way that it can be used as an estimation tool is by counting up from a
given number to reach benchmark numbers, and then totaling the 'jumps.' For example, to
find the difference between 46 and 100, you can jump 4 (from 46 to 50) and then 50 (from
50 to 100) to get a difference of 54. It is not necessary to draw ticks on the number line for
each unit.
Model using the open number line to find distances between numbers for each scenario.
 Molly needs to save $128 for a tablet. She received $47 for her birthday. About how
much more does she need to save?
I know that 47 is about 50. I'm trying to get to about 130. From 50 to 100 is 50. Then I
need to go 30 more to 130. So 50 plus 30 is 80. She needs to save about 80 more dollars.
 Mr. Smart's class read 362 books in the Read A Thon. Mrs. Walter's class read 275
books. About how many more books did Mr. Smart's class read?
I know that 362 is about 400 and 275 is about 300. That's a difference of about 100.
 Mrs. Collins' class read 446 books in the Read A Thon. That was about 100 more books
than Mrs. White's class. How many books could Mrs. White's class have read? What
are some exact numbers of books that would make sense?
Since 446 is closer to 400 than 500, we can round 446 to 400 and Mrs. White's class could
have read about 300 books. It would make sense to guess that Mrs. White's class could
have read exactly 326 books since that rounds to 300. If you round 446 to 450, Mrs.
White's class cold have read about 350 books.
Activity 2
Give students the following problems to practice using open number lines. Ask them to use
open number lines in at least two different ways for each problem.
 Find the difference between 429 and 216.
 Find the difference between 89 and 501.
 Find the difference between 350 and 1,050.
 Find the sum of 48 and 299.
 Find the sum of 12 and 372.
After students have had time to think about their solutions, allow time for them to share
their ideas, noticing similarities and differences in how they thought about the numbers
and how they used the open number lines to find the sums or differences.
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 do not understand
 Students understand how to
 Students understand how to
how to round a number to a
round a number to a given
round a number to a given
given place value. They are
place value. They are able to
place value. They are able to
unable to estimate sums and
estimate sums and differences
estimate sums and differences
differences using benchmark
using benchmark numbers
using benchmark numbers
numbers and/or open number
and/or open number lines as a
and/or open number lines as a
lines as a tool for computation.
tool for computation, but may
tool for computation, and can
They are unable to make
not be able to report more than
to report more than one
reasonable estimates of sums
one possible solution or way to
possible solution for finding
or differences and explain why
find an answer. They are
each sum or difference. They
an estimate can include a range
unable to explain why an
are able to explain why an
of exact numbers depending
estimate can include a range of
estimate can include a range of
on the place value to which a
exact numbers depending on
exact numbers, and can justify
number is rounded.
the place value to which a
their estimates using place
number is rounded.
value.
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
Planning a Pizza Party
4.NBT.3-Task 2
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.3 Use place value understanding to round multi-digit numbers to any place.
Pencil, paper, Activity sheet
Planning a Pizza Party
The following classes are having an end of the quarter pizza party for their good behavior.
Teacher
# of students participating
Mr. Thomas
23
Mrs. Little
24
Mrs. Jones
17
Mrs. Gordon
24
Part 1:
1) About how many students are participating in the pizza party?
2) How close was your estimate in question 1 to the actual answer?
3) Explain why your estimate was different from your actual answer.
Part 2:
4) One pizza will feed 4 students. How many pizzas are needed for all of the students?
5) If each pizza costs $12.75 about how much money will be spent on pizza?
6) About $324 is spent on the cost of pizza and drinks. Based on your estimate in question
4, about how much money will be spent on drinks? Explain how you found your
answer.
Rubric
Level I
Limited Performance
 Students cannot
provide correct
answers on more than
two questions.
Level II
Not Yet Proficient
 Students cannot
provide correct
answers on one or two
questions.
NC DEPARTMENT OF PUBLIC INSTRUCTION
Level III
Proficient in Performance
 Students provide correct answers on all
questions. Answers: 1) 20+20+20+20= 80. 2)
Actual: 88 students. 3) Possible answers could
include: “When we rounded to the tens place
and added the rounded numbers we got 80 for
the answer.” 4) 88 divided by 4 is 22 pizzas. 5)
We could round both numbers: 20x$13 = 260.
We could round only the pizza 22x13 = 286.
Either is acceptable. 6) 324 minus the answer to
number 5. Answers could be 64 or 38.
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
Planning a Pizza Party
The following classes are having an end of the quarter pizza party for their good
behavior:
Teacher
# of students participating
Mr. Thomas
23
Mrs. Little
25
Mrs. Jones
16
Mrs. Gordon
24
Part 1:
1) About how many students are participating in the pizza party?
2) How close was your estimate in question 1 to the actual answer?
3) Explain why your estimate was different from your actual answer.
Part 2:
4) One pizza will feed 4 students. How many pizzas are needed for all of the
students?
5) If each pizza costs $12.75 about how much money will be spent on pizza?
6) About $324 is spent on the cost of pizza and drinks. Based on your estimate in
question 4, about how much money will be spent on drinks? Explain how you
found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Filling the Auditorium
4.NBT.4 - Task 1
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard
algorithm.
Activity sheet
Filling the Auditorium
On a field trip, three different schools send their fourth graders across town to the high
school for a math competition. Each school sends between 120 and 170 students each.
There are 417 students total.
Part 1:
How many students could have come from each school? Show your thinking.
Part 2:
Find another possible solution to this task. Show your thinking.
Part 3:
If the number of students from each school was the same, how many students came from
each school? Explain how you found your solution.
Rubric
Level I
d) Level II
Limited Performance
Not Yet Proficient
 The student is unable to  The student has between
use strategies to find
two to four incorrect
correct answers to any
answers.
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 The answers are correct.
Part 1: All three numbers add up to 417.
Part 2: All three numbers add up to 417.
Part 3: Each school had 139 fourth
graders. 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
Filling the Auditorium
On a field trip, three different schools send their fourth graders across town to the
high school cafeteria. Each school sends between 120 and 170 students each. There
are 417 students total.
Part 1:
How many students could have come from each school? Show your thinking.
Part 2:
Find another possible solution to this task. Show your thinking.
Part 3:
If the number of students from each school was the same, how many students came
from each school? Explain how you found your solution.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
How Much Liquid?
4.NBT.4 - Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard
algorithm.
Task handout
How Much Liquid?
The following amounts of juice were in separate containers after the school’s parent
breakfast.
 Container 1: 750 ml
 Container 2: 1,450 ml
 Container 3: 2 L
 Container 4: 299 mL
 Container 5: 476 mL
Part 1:
If all of the liquid was put into one large container how much liquid would be in the large
container?
Part 2:
The large container can hold 5 Liters. How much room is left in the container? Write an
equation and an explanation about how you solved this problem.
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.
Rubric
Level II
Not Yet Proficient
 The student has between
1 and 2 errors.
Level III
Proficient in Performance
 The answers are correct.
Part 1: 4,975 ml. The equation is
correct.
Part 2: 5,000 ml – 4,975 ml = 25 ml.
 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
How Much Liquid?
The following amounts of juice were in separate containers after the school’s parent
breakfast.
 Container 1: 750 ml
 Container 2: 1,450 ml
 Container 3: 2 L
 Container 4: 299 mL
 Container 5: 476 mL
Part 1:
If all of the liquid was put into one large container how much liquid would be in the
large container?
Part 2:
The large container can hold 5 Liters. How much room is left in the container?
Write an equation and an explanation about how you solved this problem.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Multiplication Strategies
4.NBT.5-Task 1
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.5 Multiply a whole number of up to 4 digits by a one digit whole number, and
multiply two two-digit numbers, using strategies based on place value and the properties of
operations.
Paper and pencil
This standard calls for students to understand and use a variety of strategies for multiplying multidigit numbers. Strategies include the distributive property, doubling and halving, and drawing array
area models.
Part 1: Solve this word problem in at least three different ways. Show your thinking with
pictures, numbers, and words.
In the cafeteria, each row seats 22 students. There are 12 rows. How many students can be
seated?
As students work in pairs or groups, decide which strategies you would like them to share, and in
which order. You may start with students who drew array models, and then move to those who used
the distributive property in different ways.
Possible strategies:
Area array model:
20 x 10= 200
20 x 2 = 40
2 x 10 = 20
2x2=4
Distributive Property:
 I broke 22 into 20 and 2. I multiplied 20 x 12 and that is 200 + 40 or 240. Then I multiplied 2 x
12 to get 24. I added 240 + 24 to get 264.
 I broke 22 into 11 and 11. I multiplied 11 x 12 to get 132, and then doubled it to get 264.
 I broke 12 into 10 and 2. I multiplied 10 x 22 to get 220 and 2 x 22 to get 44. I added 220 + 44
to get 264.
 I broke 12 into 6 and 6. I multiplied 6 x 22 to get 132 and then doubled it to get 264.
Part 2: Connect the algorithm to student strategies
Model using the standard algorithm for multiplication to solve 22 x 12. Ask students to explain
how their strategies are the same as the algorithm.
Look at your numbers and pictures and look at the way we solved this problem with the
algorithm. What parts look the same? What parts look different?
How are they related?
Which strategy do you understand best, and why?
What questions do you still have about any of these strategies?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Students are unable to use a
strategy to solve the
multiplication problem. They
may be able to use the
algorithm to find an answer
but cannot explain why it
works.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Students can solve the multidigit multiplication problem
accurately in one way, but do
not provide a clear explanation
of why it works or how it is
related to the standard
algorithm for multiplication.
Level III
Proficient in Performance
 Students can solve the multidigit multiplication problem
accurately in at least two ways,
and can provide a clear
explanation of why each
strategy works and how it is
related to the standard
algorithm for multiplication.
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
Multiplication Strategies
Part 1: Solve this word problem in at least three different ways. Show your
thinking with pictures, numbers, and words.
In the cafeteria, each row seats 22 students. There are 12 rows. How many students
can be seated?
Part 2: Look at your numbers and pictures and look at the way we solved this
problem with the algorithm.
What parts look the same?
What parts look different?
How are they related?
Which strategy do you understand best, and why?
What questions do you still have about any of these strategies?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Who Has a Bigger Garden?
4.NBT.5- Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and
multiply two two-digit numbers, using strategies based on place value and the properties of
operations. Illustrate and explain the calculation by using equations, rectangular arrays,
and/or area models.
Task handout
Who Has a Bigger Garden?
In eastern North Carolina, three farmers are having a discussion about who has the largest
garden.
Mr. Sanchez: My garden is 87 yards long and its width is 1/3 of its length.
Mrs. Thompson: My garden’s width is 18 yards less than the width of Mr. Sanchez’
garden. Its length is 8 yards longer than the length of Mr. Sanchez’ garden.
Mr. Peterson: My garden is square and has a perimeter of 204 yards.
Part 1:
What are the dimensions of each garden?
Part 2:
List the gardens in order from smallest to largest area.
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.
e) Level II
Not Yet Proficient
 The student has
between 1 and 2
errors.
Level III
Proficient in Performance
 The answers are correct.
 Part 1: Mr. Sanchez: 87x29,
Mrs. Thompson: 95 x 11
Mr. Peterson: 51x51.
 Part 2: Mrs. Thompson: 1,045 square yards;
Mr. Sanchez: 2,523 square yards; Mr.
Peterson: 2,601 square yards.
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 a Bigger Garden?
In eastern North Carolina, three farmers are having a discussion about who has the
largest garden.
Mr. Sanchez: My garden is 87 yards long and its width is 1/3 of its length.
Mrs. Thompson: My garden’s width is 18 yards less than the width of Mr. Sanchez’
garden. Its length is 8 yards longer than the length of Mr. Sanchez’
garden.
Mr. Peterson: My garden is square and has a perimeter of 204 yards.
Part 1:
What are the dimensions of each garden?
Part 2:
List the gardens in order from smallest to largest area.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
College Basketball Attendance
4.NBT.5- Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and
multiply two two-digit numbers, using strategies based on place value and the properties of
operations. Illustrate and explain the calculation by using equations, rectangular arrays,
and/or area models.
Activity sheet
College Basketball Attendance
Part 1:
The college student sections at college basketball games vary UNC Chapel Hill has 1,197
seats reserve for their Carolina students. If students are only allowed to go to 1 game per
season, how many different students can go to 6 games?
Part 2:
Meanwhile, UNC Charlotte only has 874 seats reserved for college students. If students are
only allowed to go to 1 game per season, how many different students can go to 6 games?
Part 3:
How many more students can go to Caroline games than UNC Charlotte games? Explain
how you found your answer.
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.
Rubric
f) Level II
Not Yet Proficient
 The student has between 1
and 2 errors.
Level III
Proficient in Performance
 The answers are correct.
Part 1:1,197 x 6 = 7,182
Part 2: 874 x 6= 5,244
Part 3: 7,182- 5,244 = 1,938
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
College Basketball Attendance
Part 1:
The college student sections at college basketball games vary. UNC Chapel Hill has
1,197 seats reserved for their Carolina students. If students are only allowed to go to
1 game per season, how many different students can go to 6 games?
Part 2:
Meanwhile, UNC Charlotte only has 874 seats reserved for college students. If
students are only allowed to go to 1 game per season, how many different students
can go to 6 games?
Part 3:
How many more students can go to Carolina games than UNC Charlotte games?
Explain how you found your answer.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Dividing by Multiples of Ten
4.NBT.6 Task 1
Domain
Cluster
Standard(s)
Materials
Task
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.6 Find whole number quotients and remainders with up to four digit dividends and
one digit divisors, using strategies based on place value, the properties of operations,
and/or the relationship between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Paper and pencil
One component of understanding the relationship between multiplication and division is
understanding how multiples of 10, 100, or 1000 affect products and quotients. In these
explorations, students work with multiples of 10 as divisors to understand how they relate to the
quotient.
Part 1: Use pictures and numbers to explain how 27 divided by 3 is related to 270 divided by 3
and 2,700 divided by 3.
Part 2: Prove that 23 divided by 4 is the same as 230 divided by 40.
Level I
Limited Performance
 Students are unable to divide
multi-digit numbers using the
standard algorithm or invented
strategies.
Rubric
Level II
Level III
Not Yet Proficient
Proficient in Performance
 Students can divide multi-digit  Students use at least two
numbers using one or more
different ways to divide multistrategies, but they are not
digit numbers accurately. They
consistently accurate. They are
are able to explain how
multiples of 10, 100, or 1000
unable to explain how multiples
of 10, 100, or 1000 affect
products and quotients.
1.
2.
3.
4.
5.
6.
7.
8.
affect products and quotients.
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 by Multiples of Ten
Part 1: Use pictures and numbers to explain how 27 divided by 3 is related to 270
divided by 3 and 2,700 divided by 3.
Part 2: Prove that 23 divided by 4 is the same as 230 divided by 40.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Packaging Cupcakes
4.NBT.6- Task 2
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and
one-digit divisors, using strategies based on place value, the properties of operations,
and/or the relationship between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Activity sheet
Packaging Cupcakes
The cupcake factory packages cupcakes into packages of 3, 6, and 9 cupcakes each.
Part 1:
They have 1,782 cupcakes to package. The company’s leaders want to divide the cupcakes
so that an equal number of cupcakes will be put into the 3 different types of packages.
How many cupcakes will go into each type of package?
Part 2:
How many packs of cupcakes will have 3 cupcakes in each pack? How many packs of
cupcakes will have 6 cupcakes in each pack? How many packs of cupcakes will have 9
cupcakes in each pack?
Part 3:
Explain how you got your answer to Part 2 above.
Rubric
Level I
g) Level II
Limited Performance
Not Yet Proficient
 The student is unable to  The student has
use strategies to find
between 1 and 2
correct answers to any
errors.
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 The answers are correct.
 Part 1:1,782 divided by 3 = 594 cupcakes per
type of package.
 Part 2: 3 packs: 594 divided by 3 = 198 packs;
6 packs: 594 divided by 6: 99 packs; 594
divided by 9: 66 packs.
 Part 3: 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
Packaging Cupcakes
The cupcake factory packages cupcakes into packages of 3, 6, and 9 cupcakes each.
Part 1:
They have 1,782 cupcakes to package. The company’s leaders want to divide the
cupcakes so that an equal number of cupcakes will be put into the 3 different types
of packages. How many cupcakes will go into each type of package?
Part 2:
How many packs of cupcakes will have 3 cupcakes in each pack? How many packs
of cupcakes will have 6 cupcakes in each pack? How many packs of cupcakes will
have 9 cupcakes in each pack?
Part 3:
Explain how you got your answer to Part 2 above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE
Formative Instructional and Assessment Tasks
Dividing Resources
4.NBT.6- Task 3
Domain
Cluster
Standard(s)
Materials
Task
Number and Operations-Base Ten
Use place value understanding and properties of operations to perform multi-digit
arithmetic.
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and
one-digit divisors, using strategies based on place value, the properties of operations,
and/or the relationship between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Task handout
Dividing Resources
The school’s Parent Teacher Organization raised $7,326 through a fund raiser.
Part 1:
They divide the money evenly between the 6 grades at your school (Kindergarten through
5th Grade). How much will each grade receive?
Part 2:
With the amount of money that the fourth grade teachers received, they want to spend onethird of it on field trip fees. They will spend the rest on school supplies. How much money
was spent on field trip fees? How much was spent on school supplies?
Part 3:
Explain how you found your answer to Part 2 above.
Rubric
Level I
Level II
Limited Performance
Not Yet Proficient
 The student is unable to The student has between 1
use strategies to find
and 2 errors.
correct answers to any
aspect of the task.
1.
2.
3.
4.
5.
6.
7.
8.
Level III
Proficient in Performance
 The answers are correct.
 Part 1:7326 divided by 6 = $1,221
 Part 2: One-third of $1,221 is $1,221
divided by 3 = $407. $407 was spent on
field trip fees. The remaining $814 was
spent on school supplies.
 Part 3: 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
Dividing Resources
The school’s Parent Teacher Organization raised $7,326 through a fund raiser.
Part 1:
They divide the money evenly between the 6 grades at your school (Kindergarten
through 5th Grade). How much will each grade receive?
Part 2:
With the amount of money that the fourth grade teachers received, they want to
spend one-third of it on field trip fees. They will spend the rest on school supplies.
How much money was spent on field trip fees? How much was spent on school
supplies?
Part 3:
Explain how you found your answer to Part 2 above.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FOURTH GRADE