FIFTH GRADE
Third Marking Period
CCSS Extended Constructed Response Questions
2015-2016
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Elizabeth Public Schools
Intervention Block Framework
 Students
work independently to solve extended
constructed response question.
 Students
work in groups to either discuss responses and
compile 1 response or students work together to score
each response based on the rubric.
 Students
group.
share responses or discussion points as a whole
Scoring Guide for Mathematics
Extended Constructed Response Questions
(Generic Rubric)
3-Point Response
The response shows complete understanding of the problem’s essential mathematical concepts. The student executes procedures completely and
gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective
explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made.
2-Point Response
The response shows nearly complete understanding of the problem’s essential mathematical concepts. The student executes nearly all procedures and
gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may
not be clear, causing the reader to make some inferences.
1-Point Response
The response shows limited understanding of the problem’s essential mathematical concepts. The response
and procedures may be
incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to
how and why decisions were made.
0-Point Response
The response shows insufficient understanding of the problem’s essential mathematical concepts. The procedures,
if any, contain major errors.
There may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be
able to understand how and why decisions were made.
Marie was having a problem solving the following problem:
𝟓 ∗ 𝟗 + 𝟑 ∗ 𝟖 + (𝟒𝟓 − 𝟒𝟎) =
Marta kept getting an answer of 190.
• Explain Marta’s mistake.
• Show Marta step-by step how to correctly solve
the problem.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Ms. Johnson gives one-eighth of a pizza to each
of her 24 students.
Write a multiplication expression to represent
the total number of pizzas Ms. Johnson gives to
her students.
How many pizzas does Ms. Johnson give to her
students?
Represent the number of pizzas given to Ms.
Johnson’s class in a pictorial representation.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Ms. Webb is switching schools and needs to pack up her classroom. She has decided
to rent a moving truck so that she can move her boxes in one trip. All of the trucks
are 5 feet wide and 6 feet tall, but the trucks have different lengths. The choices of
lengths are 10 feet, 14 feet, 17 feet, 20 feet, 24 feet, and 26 feet. Find the volume
of each truck to determine how much it can hold.
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Shiloh wants to make 5 pitchers of tea. Each recipe calls
1
for cup of sugar for each pitcher. If she makes 5 pitchers
4
of tea will she need more or less than 1 whole cup of
sugar?
Explain your reasoning.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Tom makes a cake for a class party. The recipe
5
5
calls for cup of sugar and cup of flour. Can
8
12
Tom use a one-cup container to hold both the
sugar and flour at the same time?
Explain your mathematical thinking.
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Dan is saving money to buy a bicycle. The bicycle costs $165. Dan earns $15
in allowance each week. If he saves his whole allowance, how many weeks will
pass before Dan has enough money for this bicycle? Create a table to show
how long it will take and how much money Dan will have each week.
Dan decides that he wants to spend a little bit of his allowance each week
instead of saving it all. If he saves $10 a week, how long will it take him to
save up for the bicycle? Add a column to your table showing this data. What
if he only saves $5 a week? Add another column to your table showing how
long it will take Dan to save enough for his bicycle.
Use graph paper to draw a line graph displaying these three situations. Would
having this graph help Dan make a decision about how much he should save
each week? Why or why not?
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
George had ½ of a gallon of milk left.
He drank ¾ of what was left.
• How much of a whole gallon did he
drink?
• How much of the gallon is left?
Explain how you were able to solve this
problem.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Bennett and Seth are having an argument about the formula for finding
the volume of a rectangular prism. Bennett says that to find volume you
have to know the length, height, and width of the figure. Seth says that
you only need to know the base and height of the figure.
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Jackson claims that multiplication always makes a number bigger.
He gave the following examples:
• If I take 6, and I multiply it by 4, I get 24, which is bigger than 6.
1
2
1
• If I take , and I multiply it by 2 (whole number), I get or which is
4
1
4
4
2
bigger than .
Jackson’s reasoning is incorrect. Give an example that proves he is wrong,
and explain his mistake using pictures, words, or numbers.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Joe and Grace are baking cookies. They need a total
𝟏𝟏
of 2 cups of sugar for the recipe. Joe has cups of
𝟑
sugar and Grace has of a cup of sugar.
𝟒
𝟏𝟎
Without solving the problem, do they have enough
sugar? Explain your thinking. Solve the problem
using a model to justify your reasoning.
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Sarah has been able to save $20 before the summer has begun. She
finds a job that will pay her $8 for each hour she works over summer
break.
If Sara saves all of her money, how much will she have after working
3 hours? 5 hours? 10 hours?
Create a graph that shows the relationship between the hours Sara
worked and the amount of money she has saved. What other
information do you know from analyzing the graph?
Write an equation you can use to find out how much Sara would have
saved up after working 15 hours.
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
Evaluate the following numerical expressions. You cannot use a calculator.
a. 2 x 5 + 3 x 2 + 4 = _______
b. 2 x (5 + 3 x 2 + 4) = _______
c. 2 x 5 + 3 x (2 + 4) = _______
d. 2 x (5 + 3) x 2 + 4 = _______
e. (2 x 5) + (3 x 2) + 4 = _______
f. 2 x (5 + 3) x (2 + 4) = _______
Can the parentheses in any of these expressions be removed
without changing the value of the expression? Which expressions
would change? Explain your reasoning.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
𝟐
𝟑
𝟏
.
𝟒
Find the product of and
Represent your answer as
an area model and a
number line model.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Matthew is building a treasure box with a total volume
of 384 cubic inches. He wants the base of his treasure
box to be 12 inches by 4 inches. What is the height of
his treasure box?
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
1
3
1
3
When Angela solved the problem x she got an answer of
2
.
9
This confused Carissa. She thought the answer was incorrect because
she always thought multiplication results in a product larger than the
factors.
Use what you know about multiplying fractions to explain why Angela’s
answer is correct.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
𝟑
Claire took 𝟐 hours to read a book. Her brother, Dan,
𝟒
𝟐
took hour less to read his book. How much more time
𝟑
did Claire spend reading than Dan?
How much time did they spend altogether reading their
books?
Explain your mathematical thinking.
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Russell bought 3 movie tickets for a total of $21. Catherine
bought 5 movie tickets for a total of $35.
Create a table to show the pattern of the prices of movie
tickets.
How much is 1 ticket, 2 tickets, and 4 tickets? Graph the
corresponding terms as ordered pairs on a coordinate plane.
What pattern do you see? Explain why.
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
Monique went to the store to buy groceries for her party.
She bought 5 bananas for 50 cents each. She also
bought 4 cartons of ice cream for $3.00 each. At checkout, she was given 10 cents off the bananas.
• Write an expression that represents the problem.
• You may use models if you choose to do so.
• Then solve the problem to determine how much
Monique spent in all.
Explain your reasoning.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Find the area of a rectangle that has a
5
3
length of units and a width of of a
6
4
unit.
How many tiles that have an area of
1
of a unit squared, will cover the
24
rectangle described above?
Explain your reasoning?
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
cubes with
no
gaps and
no isoverlaps.
The inch
right rectangular
prism
represented
below
partially filled with 1-inch cubes
with no gaps and no overlaps.
What is filled
the volume
of the
t rectangular prism represented below is partially
with
1prism?
ch cubes with no gaps and no overlaps.
Show two different volume
formulas that can be used to
find the volume, and explain
how both formulas relate to
counting the cubes in bottom
layer and multiplying that
value by the height of the
prism.
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Kayla, Khalif, and Jose were collecting “Box Tops” as a fundraiser.
• Kayla collected 3 ¾ times as much as Khalif.
1
3
• Khalif collected as much as Jen.
Who collected the most? Who collected the least? Explain.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
𝟏
𝟏
Briana spent 𝟔 hours reading in May and 𝟗 hours
𝟒
𝟑
reading in June. How many more hours did she
spend reading in June?
If she wanted to read for a total of 10 hours in June,
how much longer would she need to read?
Explain your reasoning.
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Denise is working at the snack stand at a basketball game. Each
frozen yogurt costs $3, and each sandwich costs $6.
Create a table to show the costs for buying 0, 1, 2, 3, 4, 5, or 6
frozen yogurts. Create another table to show the costs for the same
number of sandwiches.
Use your tables to create a line graph with the information.
What patterns do you notice in your line graph?
How do the costs of frozen yogurts compare to the costs of an
equal number of sandwiches?
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Mr. Brown is building a flowerbed that is
𝟏
𝟔
𝟐
𝐟𝐞𝐞𝐭 by
𝟏
𝟒
𝟐
feet.
• Draw a model of the flowerbed, labeling all
dimensions.
• Find the total area of the flowerbed.
• Explain how finding area with whole number
measurements is different than finding area with
measurements that are fractions
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
PNC Plaza is the tallest and largest
skyscraper in Raleigh North Carolina. It is
538 feet high. Cassie’s Construction
Company wants to build a skyscraper that is
even taller. The spot they have to build the
building on is 200 square feet.
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Mrs. Bennett is planting two flower beds. The first flower
6
bed is 5 meters long and meters wide. The second
5
5
6
flower bed is 5 meters long and meters wide. How do
the areas of these two flower beds compare? Is the value
of the area larger or smaller than 5 square meters? Draw
pictures to prove your answer.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Jeremy measured the growth of his tomato plant every week.
1
One Monday, it was 7 inches tall. The following Monday, it
3
was 11 inches tall.
8
2
How much had it grown in one week?
If Jeremy’s tomato plant grows at the same
rate, how tall will the plant be on the next
Monday?
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Given the rule, 𝒕 = 𝒔 − 𝟔 create an input/output
table. Graph the resulting ordered pairs on a
coordinate plane.
Describe what you notice about your graph and table.
How does the graph help you analyze patterns?
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
Jack is trying to figure out the following problem:
[34 + 20- (10 * 40) /4]
List/show the steps needed to solve.
Explain your reasoning.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Draw a number line and mark the following labels:
1 2 3
, , ,1
4
4
4
Measure and cut a strip of paper that is as long as the
¾ mark. Fold the strip of paper in half.
Write an equation to determine the length of ½ of your
paper. Solve the equation.
Fold it again. Write an equation to find the length of
each new section. Solve.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
The base of the tower is a 75 x 75 meter square. If each floor is 4
meters tall, what is the volume of the Sears Tower?
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
The students in Raul’s class were growing grass seedlings in different
1
conditions for a science project. He noticed that Pablo’s seedlings were 1
2
3
Celina’s seedlings were
4
times a tall as his own seedlings. He also saw that
as tall as his own. Which of the seedlings shown below must belong to
which student? Explain your reasoning.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Sara and Harry are putting together a puzzle. Sara
7
put together of the puzzle pieces. Harry put
7
24
12
together of the puzzle pieces. What fraction of
the total number of puzzle pieces has NOT been
used?
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Draw a simple picture that can be formed with straight lines connecting
points on a coordinate grid. Use at least 8 points but no more than 15 points.
Record the ordered pairs you plotted in the order in which you connected
them.
Next, double each number of the original pair and plot the ordered number pairs
on the same grid in a different color. Connect the points in the same order
that you plot them.
What do you notice happened to your picture?
Think about what would happen if you only doubled one of the numbers in
your ordered pairs. Write down what you think would happen. Double
only one of the numbers in each of your ordered pairs and graph your
points. Were you correct? Explain what happened.
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
Analyze the following equation:
7 + 8 x 3 = 45
Where do the parentheses have to be placed for this equation to be
true?
Use the numbers 7, 8 and 3 in any order with any operation to
get an answer of 59. Be sure to use parenthesis, brackets, or
braces to make your answer true. Explain the steps you
used to determine the correct answer.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
What is the area of a rectangle
𝟐
that has a length of 𝟐 units and
a width of
𝟓
𝟏
𝟔
𝟑
units.
Draw an area model to represent
the problem.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
A fifth grade class has a fish tank that is 26
inches long, 1 foot wide, and 16 inches
deep. What volume of water can the tank hold
in inches?
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Mrs. Jones teaches in a room that is 60 feet wide
and 40 feet long. Mr. Thomas teaches in a room
that is half as wide, but has the same length. How
do the dimensions and area of Mr. Thomas’
classroom compare to Mrs. Jones’ room? Draw
a picture to prove your answer.
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
3
8
Jason painted of his house in August, and he painted
more of the house in September.
1
3
Did Jason paint more or less than ½ of his house in August and
September combined? Use estimation or draw pictures to explain
how you know.
What fraction of his house did Jason paint altogether in August and
September? Show your work.
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Farmer Brown has 12 animals in his barn. Some of them are cows,
and the rest are chickens. Altogether, his animals have 40 legs. How
many of them are cows, and how many are chickens?
Use a table to explore the different possibilities. Using the table you
created, graph a line.
Did your graph help you solve the problem? If so, how? If not, how
could you change your graph so it can help you understand the
problem?
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.
5.OA.1-Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
The 4th and 5th graders both have outdoor recess at the same time. The 4th
graders like to play basketball, the 5th graders like to play soccer, and some kids
from both grades like to sit and read. In order to keep everyone safe, the school
1
sets aside of the playground for kids to sit and read. Of the remaining
5
2
playground area, the school sets aside for students to play soccer. Use the
3
diagram above to show what fraction of the entire playground is set aside for
soccer. Defend your diagram using a mathematical equation and written
explanation.
5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
ylie
Trevor
the right
rectangular
Kylie and
and Trevor
made themade
right rectangular
prism model
shown below with prism model shown below
with 1-centimeter cubes.
1-centimeter cubes.
Kylie found the volume of the model by using
Trevor found the volume of the model by mul
of cubes in one layer by the number of layers
ylie found the volume of the model by using a volume formula.
evor found the volume of the model by multiplying the number
cubes in one layer by the number of layers, as shown below.
Kylie found the volume of the model by using a volume formula
Trevor found the volume of the model by multiplying the numbe
of cubes in one layer by the number of layers, as shown below.
5.MD.5- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Use the symbols <, >, or = to make each statement true without using any
calculations explain how you know your answers are correct.
66 x
5
5
329 x
100 x
1
6
9
4
66 x
8
5
329 x
6
6
100 x
1
4
5.NF.5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why
multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
3
Rene used 5 yards of fabric to make curtains.
8
1
She has 2 yards left. How much fabric did
4
she start with?
Explain your reasoning
5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
Joseph’s teacher said that beginning at age 2, children grow about 6
centimeters per year. Joseph is 125 centimeters tall and is 9 years old.
In the table below, Joseph used his current age and height to calculate his
possible height for each of the previous 3 years.
Complete a line graph of Joseph’s estimated
height from age 2 to age 13. How tall is
Joseph estimated to be at 13 years of age?
What is the difference in height from when
he was 2 years old to 13 years old?
Joseph’s Age and Height
Joseph’s Age
Joseph’s
(years)
Height
(centimeters)
9
125
8
119
7
113
6
107
5.OA.3- Analyze patterns and relationships 5.G.1 & 5.G.2 – Graph points on the coordinate plane to solve real-world and mathematical problems.