1. CCGPS Mathematics Grade 5 Update Webinar Unit 7: Volume and Measurement March 12, 2014
Update presentations are the result of collaboration between members of 2012 and 2013 Unit Review and Revision Teams and classroom teachers
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Turtle Toms-
Elementary Mathematics Specialist
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2. Webinar Guide Critical areas Content standards Related tasks Resources
Trudy

3. Today’s presenters Trudy Ives – Gwinnett County
Krista Bennett – Cobb County
Emily Heck – Gwinnett County
Each person introduces herself

4. Trudy

5. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data
MCC5.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.
MCC5. 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 evenly.
Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.
MCC5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. 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.
b. 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.
MCC5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
MCC5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. 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.
b. 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.
c. 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.
Trudy

6. Critical Areas in 5th Grade
Trudy – Understanding Volume is a critical area in 5th grade

7. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data MCC5.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.
Students will work within either the metric system OR the customary system to convert measurement units.
Students will use their ability to convert measurements within a measurement system to solve real world problems.
Students will use their prior knowledge of multiplying and dividing by powers of ten to convert measurements, as well as writing equivalent fractions and decimals.
Students will compare the metric system to our place value system and make connections between how the two systems are similar.
Emily

8. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data MCC5.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.
Strategies:
Have students discover the relationship between liquid units of measure in a science lab with containers.
Share prefixes for metric units to help deepen understanding.
Allow students to use tools to collect measurement data using two different units of measure. (Science Lab for weight and mass conversions; Leap Frog activity for linear measurement conversions)
Have students think of real world situations using various types of measurement. Students can think of another unit that they can convert the original measurement to and explain what operation was used to convert the measurement.
Have students make generalizations about why more or less units are needed when the conversion is made.
Emily

9. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data MCC5.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.
Misconceptions:
Mass vs. weight
Student confusion with fluid ounces and ounces – when to use, what the conversions are (16 ounces in a pound; 8 fluid ounces in a cup)
Applying multiplication and division patterns incorrectly because students forget to look at the size of the units being converted
Emily

10. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data
MCC5. 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 evenly.
Students will make line plots to represent data using measurements that are recorded to the nearest half, quarter and eighth of any measurement unit.
Students will add, subtract, multiply and divided fractions to solve problems about information given in the line plot.
Students are using their ability to collect measurements or use measurements that are provided to display liquid volume, length and mass data.
Emily

11. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data
MCC5. 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 evenly.
Strategies:
Collect data as a whole class and use the students or post it notes as data points on the line plot.
Do activities that will yield measurement data that contain fractions like Leap Frog (Ga.DOE), measuring length of pencils, finding shoe sizes, etc. so that students make line plots with fractions to the nearest half, quarter or eighth of an inch.
Emily

12. Unit 7 Content, Strategies and Misconceptions
Represent and interpret data
MCC5. 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 evenly.
Misconceptions:
Knowing the differences between line graphs and line plots
Helping students understand that even if a piece of data is missing from a data set that it still needs to appear on the line plot with no data points if it falls within the range of the data on the line plot
Emily

13. Suggested Task – MD.1 Estimate, Measure, Estimate
Trudy

14. New Task – MD.2 Survival Badge, Version 1
Trudy – new task; student WS missing from Frameworks but on wiki and will be pushed out with webinar; 2 versions – plot data on line plot & determine how much water there would be if it was evenly shared; example shown here; discuss how to balance points on line plot to share evenly

15. New Task – MD.2 Survival Badge, Version 2
Trudy – same task, different version

16. New Task – MD.2 A Little Mo Running
Trudy – give overview of task and discuss why this is not appropriate for a line plot

17. New Task – MD.2 A Little Mo Running
Trudy – discuss why this is not appropriate for a line plot

18. Unit 7 Content, Strategies and Misconceptions
Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.
Krista - C-R-A progression for intense concept building and addressing common misconceptions/problems:
Misconceptions and challenges
- Problems with spatial structuring (gaps, overlaps, visualization, etc.)
- Making connections between packing and filling
- Meaningless formula/procedural
- mistaking volume for surface area

19. Unit 7 Content, Strategies and Misconceptions
Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.
MCC5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. 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.
b. 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.
MCC5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
MCC5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. 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.
b. 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.
c. 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.
Krista - Collections of rectangular prisms (don’t forget cubes) and cubic units (primary teachers)

20. Unit 7 Content, Strategies and Misconceptions
Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.
MCC5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. 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.
b. 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.
MCC5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
MCC5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. 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.
b. 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.
c. 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.
Krista - CA 2,
Looking ahead for perspective: not a capstone standard – 6.G.2 (fractional side lengths), 7.G.6, 8.G.9, therefore super important to build conceptual understanding
Looking back for connections to build upon – 3.MD.5, 6, and 7 (next 4 slides)
4 ½ cm

21. Unit 7 Content, Strategies and Misconceptions
Grade 3 – Concepts of Area
Geometric Measurement: understand concepts of area and relate area to multiplication and to addition.
Grade 5 – Concepts of Volume
Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.
Krista - Move through these 4 slides quickly to show how area standards in grade 3 have a direct link and learning connection to volume standards in grade 5

22. Unit 7 Content, Strategies and Misconceptions
Grade 3 – Concepts of Area 5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Grade 5 – Concepts of Volume 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. 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. b. 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.
Krista - 3.a Learning experiences should include creating cubic units of varying sizes to build understanding of cubic units (mention u3)
3.b lots of packing or creating rectangular prisms with cubic units of varying sizes

23. Unit 7 Content, Strategies and Misconceptions
Grade 3 – Concepts of Area
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Grade 5 – Concepts of Volume
4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft,. and improvised units
Krista

24. Unit 7 Content, Strategies and Misconceptions
Grade 3 – Concepts of Area 7. Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Grade 5 – Concepts of Volume 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. 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. b. 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. c. 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.
Krista - Image is rectilinear
Discuss investing lots of time in 5.a (packing and layering)

25. Unit 7 Content, Strategies and Misconceptions
First nine lessons of EngageNY Module 5 focus on concepts of volume
Page 39
Page 26
Krista – From Engage NY, a resource that will be shared later in this webinar
Great strategy ideas include:
Building understanding by briefly spending time on finding volume of “structures” before focusing heavily on volumes of right rectangular prisms
Semi-abstract student representations of the layering concept and laying l to r is the same volume as layering top to bottom
Another resource for us to find ways to always be incorporating problem solving and real life scenarios
1. A storage shed is a rectangular prism and has dimensions of 6 meters by 5 meters by 12 meters. If Jean were to double these dimensions, she believes she would only double the volume. Is she correct? Explain why or why not. Include a drawing in your explanation. (page 102)

26. Task – Differentiating Area and Volume
Trudy – Good task for MD.3 – understanding what volume is, how it’s measured, how it’s different from area; could extend to how it’s different from perimeter

27. Task – Differentiating Area and Volume
Trudy – example of how to compare & contrast

28. Task – How Many Ways?
Trudy – good task for MD.4 – measuring volume by counting unit cubes

29. Task – Rolling a Rectangular Prism
Trudy – explain task and part 1; explain part 2 & how these conversions would be made; explain that this is beyond the scope of expectations for this 5th grade standards, but may be a good enrichment activity for students who need a challenge

30. Task – Toy Box Designs
Trudy – explain why 30 cu. meters is not a good measurement for this task; suggest 12 cu. ft. or 6,000 cu. in.

31. Resources
Quality resources for instruction and assessment: Progression document K-5 Geometric Measurement North Carolina Grade 5 wiki and unpacking document Howard County Grade 5 Wiki K- 5 Math Teaching Resources EngageNY illuminations.nctm.org
Krista – We hope that you’ve gotten some ideas for ways to teach Unit 7 using conceptual approaches and problem-based tasks.
Here are some additional resources that may help you.
Remind them of the important resources Turtle shared in the 2012 – 2013 webinar
Introduce EngageNY module 5
NCTM’s website – Illuminations with many interactive activities to explore volume and measurement

32. Turtle Toms Program Specialist (K-5) tgunn@doe.k12.ga.us
Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the K-5 Mathematics listserve. Follow on Twitter!
Turtle Toms Program Specialist (K-5)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.