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Common Core Learning StandardsGRADE 5 Mathematics
MEASUREMENT & DATA
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Convert like measurement units within a given measurement system.
conversion of measurements
Convert measurements within a given measurement system.
measurement systems
convert
5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Solve multi-step measurement conversion word problems.
SAMPLE TASKSI. Compare the difference in height between Billy and Johnny. Billy is 5 ‘ 3” and Johnny is 49 inches tall. Who is taller in inches and
demonstrate how you know.
II. Prove who is correct. Sally has 2,938 milliliters of water and Bobby has 2.938 liters of water. Sally said she has more water, but Bobby claims they have the same amount. Who is right? How do you know?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III. Show which amount is not the same capacity as the others. a. 96 fluid ouncesb. 18 cupsc. 6 pintsd. 3 quarts
IV. Find the total distance in meters that Jack ran in three days. He ran 1.3 kilometers on day one, walked 645 meters day two and jogged 47,550 centimeters.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Represent and interpret data. line plots Create and label a line plot to display a data set containing fractions.
line plot data average
(mean) fractions lowest terms
Calculate the average of a data set containing fractions with unlike denominators.
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. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Solve problems using data (fractions) represented in a line plot.Add, subtract, multiply, and divide fractions.
Simplify/reduce fractions to lowest terms.
SAMPLE TASKSI. Complete the line plot below based on the data. There are four packs of gum that weigh of a pound, three packs weigh ,
and two packs weigh . Find the total weight of gum packs in pounds being sold at the candy story.
0 1
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
unit cubeExplain a unit cube as having side length of one.
unit cube volume side lengthsDescribe volume in terms of cubic units.
5.MD.3a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
Explain volume as multiplying side lengths.
SAMPLE TASKS
I How many cubic units are in the following figure?
a. 5b. 20c. 10d. 1
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II Which figure has more cubic units?
a.
b.
c.
d.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III How many cubic units are in the following figure?
Answer ___________________________________
Explain how you found your answer.
___________________________________________________________________________________________________
___________________________________________________________________________________________________
___________________________________________________________________________________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
packing solid figures
Explain/show the volume of a solid figure through repeated addition of unit cubes.
repeated addition
volume solid figure 2D figures 3D figures
Explain the difference between 2D and 3D figures.
5.MD.3b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
SAMPLE TASKSI Calculate the volume of the following figure.
Answer ___________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II What is the volume of the following rectangular prism?
III Find the volume of the following figure.
Answer _________________________________________________
Explain how you calculated the volume.
________________________________________________________________________________________________
________________________________________________________________________________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
volume Calculate the volume of a solid figure by counting the unit cubes.
unit cube solid figure volume convert
Select the appropriate unit of measure for calculating the volume of a figure.
5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Convert between units of measure when calculating volume.
SAMPLE TASKSI Calculate the number of cubic units contained in the rectangular prism below.
a. 15b. 20c. 60d. 40
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II Which rectangular prism does not have a volume of (X number) of cubic units?
a.
b.
c.
d.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III Part a - How many cubic units are in the rectangular prism shown?
Answer: ________________________
PartB – Explain how you found your answer.
_______________________________________________________________________________________________________
_______________________________________________________________________________________________________
_______________________________________________________________________________________________________
_______________________________________________________________________________________________________
_______________________________________________________________________________________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
volume with unit cubes
Define right rectangular prism. right rectangular prism
unit cubes volume
Calculate the volume of a right rectangular prism by packing it with unit cubes.
5.MD.5a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Calculate the volume of a right rectangular prism by using the formulas V = l x w x h and V = B x h (Area of the Base times the height.)Explain how finding the volume using the methods above result in the same solution.
SAMPLE TASKSI Explain two ways to calculate volume for the rectangular prism below.
A. __________________________________________________________________________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
_________________________________________________________________________________________________
B. ________________________________________________________________________________________________________________________________________________________________________________________
II Calculate the total volume of the storage unit.
Answer ___________________________________________
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III What is the volume of the storage unit below?
a. 28 ft.b. 30 ft.c. 148 ft.d. 160 ft.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
IV A jewelry box shaped like a cube has sides that are 10 centimeters long. What is the volume of the jewelry box?
A. 25 cmB. 100 cmC. 125 cmD. 525 cm
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
volume formulas
Calculate the volume of a rectangular prism using the formulas: V=l x w x h and V=B x h
volume right
rectangular prism
base length width height Area of the
base (B)
Describe/show how l x w = B (length times width equals area of the base (B).
5.MD.5b. Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Calculate the volume of a right rectangular prism in the context of a word problem.
SAMPLE TASKSI For the rectangular prism shown below, use the two formulas shown to tell the number of cubic units in it.
A. V = L x W x H
_______________________________________________________________________________________________________________
B. V = B x H
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II What is the volume of the storage unit below?
a. 168 ft.b. 13.6 ft.c. 128 ft.d. 30 ft.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III What is the volume of the juice box?
Height = 8 inchesWidth = 2 inchesLength = 6 inches
a. 48 inchesb. 12 inchesc. 96 inchesd. 90 inches
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards Concepts Embedded Skills Vocabulary
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
volume as additive
Calculate the volumes of non-overlapping right rectangular prisms and add them together.
Volume right
rectangular prism
non-overlapping parts
Solve word problems requiring the calculations of multiple volumes and adding them together.
5.MD.5c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
SAMPLE TASKS
I What is the total volume of the figure below?
a. 12,000mmb. 24,000mmc. 4,800mmd. 120,000mm
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
