In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
Convert like measurement units within a given measurement system.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Measurement System
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2 - Convert (Among different-sized standard measurement units within a given measurement system)
3 - Use (Unit conversions)
3 - Solve (Multi-step, real world problems involving unit conversions)
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2 - I can convert among different-sized standard measurement units within a given measurement system.
3 - I can use unit conversions to solve problems.
3 - I can solve multi-step, real world problems involving unit conversions.
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A. Within a given measurement system, like measurement units can be converted from one to the other to solve real world problems.
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A.1 What is a measurement system?
A.2 How can like measurement units be converted within a measurement system?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Operations
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3 - Make (Line plot, data set measurements in fractions of a unit 1/2, 1/4, 1/8)
3 - Use (Operations on fractions)
3 - Solve (Problems involving line plot information)
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3 - I can make line plots using data set measurements in fractions of a unit (1/2, 1/4, 1/8)
3 - I can use operations on fractions.
3 - I can solve problems involving information presented in line plots.
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A. Information can be displayed as fractional units on line plots.
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A.1 How can a line plot display fractional units?
A.2 How can the different volumes of identical beakers be displayed on a line plot?
A.3 How can operations on fractions and information from a line plot be used to solve problems?
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Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Unit cube [a,b]
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1 - Recognize (Volume attribute of solid figures)
2 - Understand (Volume measurement concepts)
2 - Understand (cube with side length 1 unit is called a unit cube [a])
2 - Understand (unit cube is used to measure volume [a])
2 - Understand (solid figure packed without gaps or overlap by n cubes has volume of n cubic units [b])
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1 - I can recognize volume as an attribute of solid figures.
2 - I can understand the concepts of volume measurement.
2 - I can understand that a cube with side length 1 unit is called a unit cube [a].
2 - I can understand that a unit cube is used to measure volume [a].
2 - I can understand that a solid figure packed without gaps or overlap by n cubes has a volume of n cubic units [b].
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A. Solid figures have the attribute of occupy space as measured by volume.
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A.1 How can the attribute of volume for a solid figure be described?
A.2 What is volume measurement?
A.3 How can the volume for a particular solid figure be measured?
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Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Measure (Volumes)
1 - Count (Cubic cm, in, ft, improvised unit)
3 - Use (Cubic cm, cubic in, cubic ft, improvised units)
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2 - I can calculate the volume of a cube.
1 - I can measure the dimensions of a cube.
2 - I can measure volumes by counting unit cubes.
1 - I can count cubic cm, cubic in, cubic ft, and improvised units.
3 - I can use cubic cm, cubic in, cubic ft, and improvised units.
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A. Volume is measured using three dimensions.
B. The volume of a solid figure can be determined by adding the sum of its unit cubes.
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A.1 What dimensions are involved with volume?
B.1 What is a unit cube? How can it be used to solve for the volume of a solid figure?
B.2 What units can be used for the measurement of a unit cube? Why?
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Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Rectangular prisms [b]
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3 - Relate (Volume and multiplication and addition operations)
3 - Solve (real world and mathematical problems)
2 - Find (volume of right rectangular prism with whole number side lengths by packing with unit cubes [a])
3 - Apply (formulas V=lxwxh and V=bxh for rectangular prisms [b])
2 - Find (volumes of right rectangular prisms with whole-number edge lengths [b])
2 - Solve (real world and mathematical problems [b])
2 - Recognize (volume as additive [c])
2 - Find (volumes of solid figures composed of 2 non-overlapping right rectangular prisms [c])
2 - Add (volumes of non-overlapping parts [c])
3 - Apply (technique of adding volumes [c])
2 - Solve (real world problems [c])
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3 - I can relate volume with multiplication and addition operations.
3 - I can solve real world and mathematical problems involving volume.
2 - I can find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes [a].
3 - I can apply the formulas V=lxwxh and V=bxh for rectangular prisms [b].
2 - I can find volumes of right rectangular prisms with whole-number edge lengths [b].
2 - I can solve real world and mathematical problems [b].
2 - I can recognize volume as additive [c].
2 - I can find volumes of solid figures composed of 2 non-overlapping right rectangular prisms [c].
2 - I can add volumes of non-overlapping parts [c].
3 - i can apply the technique of adding volumes [c].
2 - I can solve real world problems [c].
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A. Volume occupies space having length, width, and height.
B. Volume can be calculated using addition and multiplication.
C. There is more than one way to find the volume of a solid figure.
D. Formulas are useful tools when solving real world problems.
E. Volumes can be added together.
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A.1 How can volume be described?
B.1 How can volume be calculated to solve real world and mathematical problems?
C.1 How can I find the volume of a solid figure?
D.1 What are formulas used for?
E.1 When will I have to add volumes together?
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