CCGPS MathematicsGrade 5 Update WebinarUnit 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- tgunn@doe.k12.ga.us Elementary Mathematics Specialist

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Webinar Guide

Critical areasContent standards Related tasksResources

Today’s presenters

Trudy Ives – Gwinnett CountyKrista Bennett – Cobb CountyEmily Heck – Gwinnett County

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.

Critical Areas in 5th Grade

Unit 7 Content, Strategies and Misconceptions

Represent and interpret dataMCC5.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.

Unit 7 Content, Strategies and Misconceptions

Represent and interpret dataMCC5.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.

Unit 7 Content, Strategies and Misconceptions

Represent and interpret dataMCC5.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

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.

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.

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

Suggested Task – MD.1Estimate, Measure, Estimate

New Task – MD.2Survival Badge, Version 1

New Task – MD.2Survival Badge, Version 2

New Task – MD.2A Little Mo Running

New Task – MD.2A Little Mo Running

Unit 7 Content, Strategies and Misconceptions

Geometric Measurement: understand concepts of volume and relate volume to multiplication and addition.

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.

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.

4 ½ cm

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.

Unit 7 Content, Strategies and Misconceptions

Grade 3 – Concepts of Area5. Recognize area as an attribute of plane figures and understandconcepts 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 Volume3. 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.

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

Unit 7 Content, Strategies and Misconceptions

Grade 3 – Concepts of Area7. 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 Volume5. 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.

Unit 7 Content, Strategies and Misconceptions

First nine lessons of EngageNY Module 5 focus on concepts of volume

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)

Page 26

Page 39

Task – Differentiating Area and Volume

Task – Differentiating Area and Volume

Task – How Many Ways?

Task – Rolling a Rectangular Prism

Task – Toy Box Designs

Resources

Quality resources for instruction and assessment:Progression document K-5 Geometric MeasurementNorth Carolina Grade 5 wiki and unpacking documentHoward County Grade 5 WikiK- 5 Math Teaching Resources EngageNY illuminations.nctm.org

Thank You! Please visit http://ccgpsmathematicsk-5.wikispaces.com/ to share your feedback, ask

questions, and share your ideas and resources!Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx

to join the K-5 Mathematics email listserve.Follow on Twitter!

Follow @GaDOEMath

Turtle TomsProgram Specialist (K-5)tgunn@doe.k12.ga.us

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.