Fifth Grade
Fourth Marking Period
CCSS Extended Constructed Response Questions
2015-2016
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Elizabeth Public Schools
Intervention Block Framework
O Students work independently to solve extended constructed
response question.
O Students work in groups to either discuss responses and compile
1 response or students work together to score each response
based on the rubric.
O Students share responses or discussion points as a whole group.
Scoring Guide for Mathematics
Extended Constructed Response Questions
(Generic Rubric)
3-Point Response
O
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
O
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
O
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
O
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.
Part 1
The table below shows the amount of liquid in 8 glasses at a party. The
amount is in terms of cups. Based on the data, make a line plot to display the
data.
Part 2
•What is the difference between the amount of punch in the glass with the
most punch and the glass with the least amount of punch?
•What is the combined amount of punch in all 8 glasses?
•If all of the punch were to be poured into a container and then shared
equally among the 8 people how much punch would each person receive?
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
THE STRUCTURE ON THE LEFT IS PARTIALLY FILLED WITH UNIT CUBES. WHEN FULL, THE
STRUCTURE ON THE RIGHT APPEARS.
A. HOW MANY UNIT CUBES ARE IN THE STRUCTURE ON THE LEFT?
B. HOW MANY MORE UNIT CUBES WOULD BE NEEDED TO CONSTRUCT THE STRUCTURE ON THE
RIGHT?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
Mrs. Sullivan owns a bakery. One of her customers cancelled their
cake order after the cake was already made.
Mrs. Sullivan gave half of the cake to her employees to eat. She
brought the other half home for her family to eat.
If there are 5 members of the Sullivan family, and they share the
cake equally, how much of the original cake will each family
member get to eat?
Draw a model and write an equation
to show your work.
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
ISOSCELES. EQUILATERAL, AND ACUTE TRIANGLES HAVE SPECIAL CHARACTERISTICS.
EXPLAIN THE RELATIONSHIP BETWEEN ISOSCELES, EQUILATERAL, AND ACUTE
TRIANGLES.
BE SPECIFIC TO EXPLAIN YOUR REASONING.
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
The table below shows the length of strips of bubble gum that each
student has. Measurements are in feet.
2 and 5/8
2 and 5/8
1 and 3/8
2 and 1/4
2 and 1/4
2 and 5/8
2 and 1/4
2 and 1/2
1 and 3/4
1 and 7/8
2 and 1/2
2 and 3/8
Part 1
Based on the data, make a line plot to display the data. Write a sentence
explaining how you know that you plotted the data correctly.
Part 2
•What is the difference between the longest and shortest strips of gum?
•What is the total length of all of the strips of gum?
•If all of the strips were combined and equally distributed to the 10
students, how much gum would each student get?
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
Jeremy is building a wall out of bricks that are cubes. He builds the bottom row by
leaving some space between each brick. This is what his wall looks like:
ZZZZ
Jeremy continues building his wall until the bottom row has
8 bricks in it and it is 5 bricks high. He fills in the space
between the bricks with a special colorful plaster. Jeremy
then calculates that the volume of his wall is 38 cubic units.
Is Jeremy correct? Why or why not?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
Alysha really wants to ride her favorite ride
at the amusement park one more time
before her parents pick her up at 2:30 pm.
There is a very long line at this ride, which
Alysha joins at 1:50 pm (point A in the
diagram below).
Alysha is nervously checking the time as she
is moving forward in the line. By 2:03 she
has made it to point B in line.
What is your best estimate for how long it will take
Alysha to reach the front of the line? If the ride lasts 3
minutes, can she ride one more time before her parents
arrive?
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
Which polygon does not belong with the other 3?
Explain your reasoning.
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
Jim recorded the amount of lemonade mix, measured in cups, used at his lemonade stand over
the month of July, for the different sized pitchers. His data is marked on the line plot above.
• If Jim wanted to spread the amount of lemonade mix he used over 1 month equally over every pitcher no
matter it’s size, how much mix should he use (mean/average)?
• Jim is expecting to triple the amount of mix he needs for the month of August. How many cups of mixture
will he need in stock?
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
Jill’s teacher asked her to construct a rectangular prism from unit cubes. She has built the structure above. In order
for Jill to complete her assignment, how many unit cubes will Jill need to add to the above structure?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
Solve the four problems below. Which of the following problems
𝟏
can be solved by finding 𝟑 ÷ ?
𝟐
A. Shauna buys a three-foot-long sandwich for a party. She then cuts the sandwich
1
into pieces, with each piece being foot long. How many pieces does she get?
2
B. Phil makes 3 quarts of soup for dinner. His family eats half of the soup for dinner.
How many quarts of soup does Phil's family eat for dinner?
C. A pirate finds three pounds of gold. In order to protect his riches, he hides the
gold in two treasure chests, with an equal amount of gold in each chest. How many
pounds of gold are in each chest?
D. Leo used half of a bag of flour to make bread. If he used 3 cups of flour, how many
cups were in the bag to start?
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole
number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole
numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
Kites, rhombi, squares, rectangles, parallelograms, and
trapezoids are ALL inside the quadrilateral shape. Therefore,
ALL kites, rhombi, squares, rectangles, parallelograms, and
trapezoids are quadrilaterals.
Study the figure below carefully.
Quadrilaterals
Trapezoids
Parallelograms
Rectangles
Rhombi
Kites
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
Describe the difference between a piece of loose leaf paper and a stack of
loose leaf paper.
Dorothy suggested that they can be measured in square units and cubic
units. Henry wants to know which type of units he should use for each.
Explain to Henry which measurements are used for the loose leaf and
stack of paper.
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
Kulani is painting his room.
He
𝟏
𝟑
needs
of a gallon to paint the
whole room.
What fraction of a gallon will he need for each of
his 4 walls if he uses the same amount of paint on
each? Explain your work and draw a picture to
support your reasoning.
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole
number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole
numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
NICK AND CARLOS ARE STUDYING PARALLELOGRAMS AND TRAPEZOIDS. THEY AGREE THAT A PARALLELOGRAM IS A
QUADRILATERAL WITH 2 PAIRS OF PARALLEL SIDES.
NICK SAYS, “A TRAPEZOID HAS ONE PAIR OF PARALLEL SIDES AND A PARALLELOGRAM HAS TWO PAIRS OF
PARALLEL SIDES. SO A TRAPEZOID IS ALSO A PARALLELOGRAM.”
CARLOS SAYS, “NO. A TRAPEZOID CAN HAVE ONLY ONE PAIR OF PARALLEL SIDES.”
NICK SAYS, “THAT’S NOT TRUE. A TRAPEZOID HAS AT LEAST ONE PAIR OF PARALLEL SIDES, BUT IT CAN ALSO HAVE
ANOTHER.”
SOME PEOPLE USE NICK’S DEFINITION FOR A TRAPEZOID, AND SOME PEOPLE USE CARLOS’ DEFINITION. WHICH
STATEMENTS BELOW GO WITH NICK’S DEFINITION? WHICH STATEMENTS GO WITH CARLOS’ DEFINITION?
A. ALL PARALLELOGRAMS ARE TRAPEZOIDS.
B. SOME PARALLELOGRAMS ARE TRAPEZOIDS.
C. NO PARALLELOGRAMS ARE TRAPEZOIDS.
D. ALL TRAPEZOIDS ARE PARALLELOGRAMS.
E. SOME TRAPEZOIDS ARE PARALLELOGRAMS.
F. NO TRAPEZOIDS ARE PARALLELOGRAMS.
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
John had cut the following lengths of ribbon for wrapping gifts:
4 ½ feet, 3 ¼ feet, 5 ¾ feet, 3 ½ feet, 4 ¾ feet, 6 ¼ feet, 3 ¾ feet,
5 ¼ feet, 3 ¼ feet and 4 feet
A. Draw a line plot to display the amount of ribbon John cut.
B. How many feet of ribbon did John cut?
C. What is the difference between the longest and shortest piece of ribbon John
used?
D. If John wanted to cut an equal amount of ribbon for his next 10 gifts using the
total amount of ribbon he used displayed in your the line plot, how much should
he cut each ribbon?
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
USING CENTIMETER CUBES, BUILD FIVE DIFFERENT RECTANGULAR PRISMS.
ORDER YOUR RECTANGULAR PRISMS FROM LEAST TO GREATEST VOLUME.
DRAW EACH RECTANGULAR PRISM AND RECORD THE STEPS YOU TOOK TO
CALCULATE ITS VOLUME.
WHAT IS THE DIFFERENCE BETWEEN THE LEAST AND GREATEST VOLUME?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
Julius has 4 blue marbles. If one third of Julius'
marbles are blue, how many marbles does Julius
have?
Draw a diagram and explain.
If Julius gives ¼ of his marbles to his friend, how
many marbles will he have left?
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
JILL’S TEACHER PLACED THE STATEMENTS BELOW ON THE BOARD. THEY ARE INCORRECT
STATEMENTS. READ EACH STATEMENT AND EXPLAIN WHY EACH IS INCORRECT. BE
SPECIFIC IN YOUR REASONING.
1. All four-sided figures are not parallelograms because they do not
have two pairs of parallel sides.
2. Kites and trapezoids are parallelograms because they do not have
2 pairs of parallel sides.
3. Squares are not parallelograms because they have two pairs of
parallel sides.
4. Rectangles, rhombuses, and squares are not parallelograms because
they have two sets of parallel sides.
5. Squares are not rhombi because they have two sets of parallel
sides and all sides are the same length.
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
You have been asked to create the packaging for a new kind of
cereal. The manufacturer wants three different sized boxes:
1. A standard sized cereal box
2. A mini sized box that is half as tall, half as wide, and
half as deep as the standard size
3. A super sized box that is three times as tall, three
times as wide and three times as deep as the standard
size.
Using grid paper, draw a possible design for each box. Label the
dimensions and calculate the volume.
Which box do you think would be the best seller? Write your
answer on the lines
below and tell why you think so.
5.MD.4 –
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
Carolina’s banana pudding recipe calls for the following:
2 cups sour cream
5 cups whipped cream
3 cups vanilla pudding mix
4 cups milk
8 bananas
Carolina is making her special banana pudding recipe. She is looking for her cup measure, but can only
find her quarter cup measure.
A. How many quarter cups does she need for the sour cream? Draw a picture to
illustrate your solution, and write an equation that represents the situation.
B. How many quarter cups does she need for the milk? Draw a picture to illustrate your
solution, and write an equation that represents the situation.
C. Carolina does not remember in what order she added the ingredients but the last
ingredient added required 12 quarter cups. What was the last ingredient Carolina added to
the pudding? Draw a picture to illustrate your solution, and write an equation that
represents the situation.
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
Classify each shape. All shapes must be placed in at least one column.
If a shape meets the properties of more than one category, it must be placed into
the boxes of all the types of shapes it can be classified as.
Square
Rectangle Rhombus Parallelogram
Polygon
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
Quadrilateral
Trapezoid
You are designing a toy box for child’s bedroom. The
toy box needs to be able to hold 30 cubic meters of
toys. What might the dimensions be?
Draw and label two possible designs for the toy box.
Explain which design would work best in a child’s
bedroom and give reasons to support your choice.
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
The line plot above shows the amount of olive oil, in ounces,
used in 13 different pizza recipes. Isabella wants to make one
pizza from each of the recipes. Will she have enough olive oil
to make the pizzas if she buys a 16-ounce bottle of olive oil?
Explain or show your reasoning.
5.MD.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots
VIEW THE ABOVE STRUCTURE.
HOW MANY CUBES WOULD NEED TO BE ADDED IN ORDER TO HAVE A VOLUME OF 18 CUBIC
UNITS?
EXPLAIN YOUR REASONING
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
CARTER’S CANDY COMPANY IS SELLING A NEW TYPE OF CHOCOLATE. THEY
HAVE DECIDED TO SELL THE CANDY IN PACKAGES OF 24. YOU ARE LEADING A
TEAM IN CHARGE OF DEVELOPING A BOX FOR THE CANDY.
USE UNIT CUBES TO BUILD ALL OF THE POSSIBLE BOXES FOR THE PACKAGE OF CANDY.
HOW MANY POSSIBILITIES ARE THERE? RECORD THE DIMENSIONS AND VOLUME OF
EACH BOX. WHAT DO YOU NOTICE ABOUT ALL OF THE VOLUMES?
AFTER DETERMINING ALL OF THE POSSIBLE BOXES, YOU MUST MAKE A
RECOMMENDATION TO THE PRESIDENT OF THE COMPANY ABOUT WHICH BOX
SHOULD BE USED. WRITE A PARAGRAPH EXPLAINING WHICH BOX WOULD BE BEST.
MAKE SURE TO EXPLAIN YOUR REASONS FOR CHOOSING THIS BOX.
TWO OF YOUR TEAM MEMBERS GET IN AN ARGUMENT ABOUT THE BOXES. CATHY
SAYS THAT A 1X24 BOX IS THE SAME AS A 24X1 BOX. CURTIS SAYS THAT THESE
DIMENSIONS WOULD LEAD TO TWO DIFFERENT BOXES. WHO DO YOU AGREE WITH?
WHY?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
A recipe for chocolate chip cookies makes 4 dozen
cookies and calls for the following ingredients:
1
1 and 2 c margarine
3
1 and 4 c sugar
2 t vanilla
1
3 and 4 c flour
1 tsp baking powder
1
4
tsp salt
8 oz chocolate chips
A. How much of each ingredient is needed to make 3 recipes?
B. How much of each ingredient is needed to make three quarters of a recipe?
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
BOB SAYS THAT ALL SQUARES ARE RECTANGLES BUT ALL
RECTANGLES ARE NOT SQUARES. DO YOU AGREE WITH BOB’S
STATEMENT? WHY OR WHY NOT?
EXPLAIN YOUR REASONING BY PROVIDING CHARACTERISTICS OF
BOTH RECTANGLES AND SQUARES THAT SUPPORT YOUR ANSWER.
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
Your teacher wants to take three boxes of books home from school. She
needs to know if they will all fit in her truck, or if she needs to make two
trips to get all the boxes home. Here is some information you will need:
• Two of the boxes are the same size. (2 ft. long, 3ft. wide, and 2 ft. high)
• One box is larger than the others. (3 ft. long, 3 ft. wide, and 3 ft. high)
• Your teacher’s truck has 60 cu. ft. of space.
Can your teacher take all
three boxes in one load?
Show how you know with
pictures, words, and
numbers.
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.
JOHN SAYS THAT THE ABOVE STRUCTURE HAS A VOLUME OF 64 CUBIC UNITS. HENRY TELLS JOHN
THAT HE IS INCORRECT.
DO YOU AGREE WITH JOHN OR HENRY?
WHAT REASONING MAY HENRY GIVE JOHN TO EXPLAIN HIS OPINION?
5.MD.3 - Recognize volume as an attribute of solid figures & understand concepts of volume measurement
In class, Sarah and Tony are talking about the difference
𝟏
𝟏
between “ times 6” compared to “ divided by 6.”
𝟑
𝟑
Their teacher asks them to draw a picture and to write
a story problem for each expression.
What would Sarah and Tony’s work look like?
5.NF.7A-C -Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
Part 1: Create the following figures.
1. A shape with two sets of parallel sides and no right angles.
2. A shape with exactly one set of parallel sides and no right angles.
3. A shape with two sets of parallel sides and 2 or more right angles.
4. A shape with exactly one set of parallel sides and 2 or more right angles.
Part 2:
While doing Part 1 above, Kyle said, on problem 3 every time I make a
shape with 2 sets of parallel sides I create a shape with 4 right angles. It is
impossible to make a shape with 2 sets of parallel sides and only have two
right angles.
Is Kyle correct? Write a sentence explaining why or why not?
5.G.4 - Classify two-dimensional figures in a hierarchy based on its properties
Steve fills Box A and Box B with one
centimeter cubes.
How many cubes can Steve fit into
Box A?
How many cubes can Steve fit into
Box B?
Explain how you found the volume of
each box.
Which of the two boxes can hold
more cubes?
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.