In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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System of Units
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1 - Know (units km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec)
1 - Know (relative measurement sizes, units within one system of units)
2 - Express (measurement, larger unit in smaller unit terms)
3 - Record (measurement equivalents, two-column table)
6 - Generate (conversion table, unit-based number pair list)
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1 - I can know (identify) the units km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.
1 - I can know the relative measured sizes of different units within one system of units.
2 - I can express the measurement of a larger unit in terms of a smaller unit.
3 - I can record the measurement equivalents within a two-column table.
6 - I can generate a conversion table displaying a unit-based number pair list.
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A. Within one system of units, a measured attribute can have equivalent, but different unit measures.
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A.1 What is a system of units?
A.2 How would you describe a system of units?
A.3 What are the relative sizes of measurement units within each system of units?
A.4 How can you express the measurement of a larger unit in terms of a smaller unit?
A.5 How can equivalent measures be displayed?
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Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Operations
Word Problems
Measurement quantities
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3 - Use (addition, subtraction, multiplication, division)
3 - Solve (word problems involving distances)
3 - Solve (word problems involving intervals of time)
3 - Solve (word problems involving liquid volumes)
3 - Solve (word problems involving masses of objects)
3 - Solve (word problems involving money)
3 - Solve (word problems involving simple fractions or decimals)
3 - Solve (word problems involving expressing measurements given in a larger unit in terms of a smaller unit)
3 - Use (diagrams, number line diagram with measurement scale)
2 - Represent (measurement quantities, diagram)
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3 - I can use addition, subtraction, multiplication, and division.
3 - I can solve word problems involving distances.
3 - I can solve word problems involving intervals of time.
3 - I can solve word problems involving liquid volumes.
3 - I can solve word problems involving masses of objects.
3 - I can solve word problems involving money.
3 - I can solve word problems involving simple fractions or decimals.
3 - I can solve word problems involving expressing measurements given in a larger unit in terms of a smaller unit.
3 - I can use diagrams such as number line diagrams that feature a measurement scale.
2 - I can represent measurement quantities on a diagram.
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A. Real-world problems can be solved combining a variety of mathematical skills.
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A.1 What real-world problems can be solved using mathematics?
A.2 How do the use of units help to solve these problems?
A.3 What mathematical skills can be used to solve real-world problems?
A.4 How can the skills be combined to solve them?
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Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Math Problems
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3 - Apply (rectangle area and perimeter formulas; real world, mathematical problems)
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3 - I can apply area and perimeter formulas for rectangles in real world and mathematical problems.
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A. Area and perimeter formulas can be viewed as equations with unknown factors to solve real world and mathematical problems.
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A.1 How can area and perimeter formulas be used as equations to solve problems?
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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). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Plot
Measurement data sets
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3 - Make (a line plot)
3 - Display (measurement data set in fractions of a unit - 1/2, 1/4, 1/8)
3 - Use (line plot information)
3 - Solve (problems involving addition and subtraction of fractions and information in line plots)
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3 - I can make a line plot.
3 - I can display within a line plot measurement data set in fractions of a unit (1/2, 1/4, 1/8).
3 - I can use information in a line plot.
3 - I can solve problems involving addition and subtraction of fractions by using information presented in line plots.
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A. Data can be plotted in fractions of a unit.
B. Problems can be solved using unit fractions displayed on a plot.
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A.1 How can data be plotted when the measured values fall between two whole numbers?
B.1 How does the addition or subtraction of fractions help to solve problems using information in a line plot?
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Geometric measurement: understand concepts of angle and measure angles.
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Angles
Angle measurement [a]
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1 - Recognize (angles as geometric shapes)
1 - Recognize (angles are formed from two rays sharing a common end point)
1 - Understand (an angle measure references a circle [a])
1 - Understand (circle center is at the common endpoint of the rays [a])
1 - Understand (circle arc [a])
1 - Understand (1/360 of a circle is a "one-degree angle" [a])
1 - Use (one-degree angles [a])
1 - 2: Understand (angle turning through n one-degree angles measures n degrees [b])
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1 - I can recognize angles as geometric shape.
1 - I can recognize angles are formed from two rays sharing a common end point.
1 - I can understand an angle measure references a circle [a].
1 - I can understand the circle center is at the common endpoint of the rays forming an angle[a].
1 - I can understand a circle arc [a].
1 - I can understand 1/360 of a circle is equal to a "one-degree" angle [a].
1 - I can use one-degree angles [a].
2 - I can understand thqt an angle that turns through n one-degree angles measures n degrees [b].
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A. Angles make up part of a circle.
B. 360 "one-degree" angles make up a complete circle.
C. Angle measure is additive.
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A.1 What is the relationship between an angle and a circle?
B.1 What is the relationship between the center of a circle and the common endpoint of rays?
B.2 How can angles be determined?
C.1 How do I measure an angle?
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Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Angle Measure
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2 - Measure (whole-number degree angles)
3 - Use (protractor)
3 - Sketch (angles with specific measures)
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2 - I can measure angles having whole-number degrees.
3 - I can use a protractor.
3 - I can sketch angles with specific measurements.
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A. A protractor simplifies the measurement and creation of angles.
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A.1 How can you use a protractor to measure an angle?
A.2 How can you use a protractor to create an angle with a specific angle measurement?
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Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Angle Measures
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2 - Recognize (angle measure as additive)
2 - Recognize (angle measure; the whole is the sum of its decomposed non-overlapping parts)
3 - Solve (real world and mathematical addition and subtraction problems, unknown angles)
2 - Find (unknown angles on a diagram)
3 - Use (equation with unknown angle measure symbol)
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2 - I can recognize angle measure as additive.
2 - I can recognize that when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measure of the parts.
3 - I can solve real world and mathematical addition and subtraction problems to find unknown angles on a diagram.
3 - I can use equations with a symbol for the unknown angle measure to solve for the angle.
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A. The measure of a whole angle is the sum of its parts.
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A.1 How is angle measure additive?
A.2 How can an unknown part of an angle be determined?
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