In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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1 - Tell (Time to the nearest minute)
1 - Write (Time to the nearest minute)
2 - Measure (Time intervals in minutes)
2 - Represent (solutions to time-based word problems on a number line diagram)
3 - Solve (word problems; addition, subtraction of time intervals in minutes)
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1 - I can tell time to the nearest minute.
1 - I can write time to the nearest minute.
2 - I can measure time intervals to the nearest minute.
3 - I can solve addition and subtraction word problems using time intervals in minutes.
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A. Time can be added or subtracted to find a new time.
B. Time intervals can be used to plan tasks and organize activities.
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A.1 Why do people measure time intervals?
A.2 How do people use time?
B.1 Why do people tell time?
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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Objects
Standard Units
Math Operation
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2 - Measure (grams, kilograms, liters)
2 - Estimate (grams, kilograms, liters)
3 - Use (standard units, grams, kilograms, liters)
3 - Solve (using drawings, one-step word problems, masses, liquid volumes, same units)
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2 - I can measure grams, kilograms, and liters.
2 - I can estimate grams, kilograms, and liters.
3 - I can use the standard units of grams, kilograms, and liters.
3 - I can use drawings to solve one-step word problems for liquid volumes and masses having the same units.
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A. Liquid volumes can be measured to solve problems.
B. Mass can be measured to solve problems.
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A.1 What is mass?
A.2 How do I measure mass?
A.3 What problems can I solve measuring mass?
B.1 What is liquid volume?
B.2 How do I measure liquid volume?
B.3 What problems can I solve measuring liquid volume?
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Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Graphs
Problems
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3 - Draw (scaled picture graph with several categories)
3 - Draw (scaled bar graph with several categories)
3 - Solve (one-part "how many more" and "how many less" problems)
3 - Solve (two-part "how many more" and "how many less" problems)
3 - Use (scaled bar graph information)
3 - Use (scaled picture graph information)
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3 - I can draw a scaled picture graph with several categories.
3 - I can draw a scaled bar graph with several categories.
3 - I can solve one-part problems involving "how many more" and "how many less."
3 - I can solve two-part problems involving "how many more" and "how many less."
3 - I can use information in a scaled bar graph.
3 - I can use information in a scaled picture graph.
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A. Scale graphs can be used to represent equal groups of objects in different categories.
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A.1 What is a scaled graph?
A.2 How can scaled graphs be used?
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Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Plot
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2 - Measure (lengths)
3 - Use (rulers, marked in inches, halves and fourths)
4 - Show (data, line plot)
6 - Make (line plot, horizontal scale, units — whole numbers, halves, quarters)
6 - Generate (measurable data)
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2 - I can measure lengths.
3 - I can use rulers marked in whole, halves, and quarter inch units.
4 - I can show data using a line plot.
6 - I can make a line plot with the horizontal scale in units of whole numbers, halves, and quarters.
6 - I can generate measurable data.
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A. Communicating measurable data involves both generating and plotting it.
B. The units for generating measurable data and then the graph for plotting it must be the same.
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A.1 How can we communicate information about measurable data?
B.1 What is the process for generating and plotting measurable data?
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Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Recognize area as an attribute of plane figures and understand concepts of area measurement.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Plane figures
Area measurement
Squares [a]
Plane figures [b]
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1 - Recognize (area attribute, plane figures)
2 - Understand (area measurement concepts)
2 - Understand (Square with side length 1 unit is called a unit square [a])
2 - Understand (Square with side length 1 unit has area of 1 square unit [a])
2 - Understand (Square with side length 1 can be used to measure area [a])
2 - Understand (Plane figure covered without gaps or overlaps by n unit squares has area of n square units [b])
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1 - I can recognize area as an attribute of plane figures.
2 - I can understand concepts of area measurement.
2 - I can understand square with side length 1 unit is called a unit square. [a]
2 - I can understand square with side length 1 unit has area of 1 square unit. [a]
2 - I can understand square with side length 1 can be used to measure area. [a]
2 - I can understand that a plane figure covered without gaps or overlaps by n unit squares has an area of n square units. [b]
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A. Plane figures have a measurable attribute of area.
B. Area is measured in terms of square units.
C. Area can be measured in terms of square units.
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A.1 What is area?
A.2 How can area be measured?
B.1 How do I measure area?
C.1 Why would I want to cover a figure in squares?
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Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Areas
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2 - Measure (areas)
2 - Counting (unit squares, square cm, square m, square in, square ft, improvised units)
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2 - I can measure areas.
2 - I can count unit squares such as square cm, square m, square in, square ft, and improvised units.
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A. Area is composed of square units.
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A.1 How can I calculate area using square units?
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Relate area to the operations of multiplication and addition.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Area operations
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3 - Relate (Area, multiplication, addition)
2 - Find (area of rectangle with whole number side lengths by tiling [a])
2 - Show (area is same as multiplying side lengths [a])
2 - Multiply (side lengths [b])
2 - Find (area of rectangles with whole number side lengths [b])
2 - Solve (real world and mathematical problems [b])
3 - Represent (whole number products as rectangular areas in mathematical reasoning [b])
3 - Use (tiling [c])
3 - Show (area of rectangle with whole number side lengths a and b+c equals axb plus axc [c])
3 - Use (area models [c])
3 - Represent (distributive property in mathematical reasoning [c])
2 - Recognize (areas as additive [d])
2 - Find (areas of rectilinear figures [d])
2 - Decompose (figures into non-overlapping rectangles [d])
2 - Add (areas of non-overlapping parts [d])
3 - Apply (technique of adding areas [d])
2 - Solve (real world problems [d])
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3 - I can relate area to the operations of multiplication and addition.
2 - I can find area of rectangle with whole number side lengths by tiling. [a]
2 - I can show area is same as multiplying side lengths. [a]
2 - I can multiply side lengths. [b]
2 - I can find the area of rectangles with whole number side lengths. [b]
2 - I can solve real world and mathematical problems. [b]
3 - I can represent whole number products as rectangular areas in mathematical reasoning. [b]
3 - Use (tiling) [c]
3 - I can show area of rectangle with whole number side lengths a and b+c equals axb plus axc. [c]
3 - I can use area models. [c]
3 - I can represent distributive property in mathematical reasoning. [c]
2 - I can recognize areas as additive. [d]
2 - I can find areas of rectilinear figures. [d]
2 - I can decompose figures into non-overlapping rectangles. [d]
2 - I can add areas of non-overlapping parts. [d]
3 - I can apply technique of adding areas. [d]
2 - I can solve real world problems. [d]
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A. Multiplication and addition can be used to solve for area.
B. There are multiple ways to find the area of a plane figure.
C. Real world problems sometimes involve finding areas of rectangles.
D. Arithmetic properties can be concretely modeled by using objects or tiles.
E. Areas can be added together.
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A.1 How can multiplication and addition be used to get the area of a plane figure?
B.1 How can I find the area of a rectangle?
C.1 How can I use the area of a rectangle?
D.1 How do properties relate to real world problems?
E.1 How does decomposing figures into smaller rectangles fit into solving real world problems?
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Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Polygon Problems
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3 - Solve (polygon perimeter problems, real world, mathematical)
2 - Find (perimeter given side lengths of polygon exhibiting rectangles, same perimeter, different areas)
2 - Find (perimeter given side lengths of polygon exhibiting rectangles, same area, different perimeters)
2 - Find (unknown side length of polygon exhibiting rectangles, same perimeter, different areas)
2 - Find (unknown side length of polygon exhibiting rectangles, same area, different perimeters)
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3 - I can solve real world and mathematical problems involving perimeters of polygons.
2 - I can find the perimeter given the side lengths of a polygon exhibiting rectangles with the same perimeter and different areas.
2 - I can find the perimeter given the side lengths of a polygon exhibiting rectangles with the same area and different perimeters.
2 - I can find the unknown side length of a polygon exhibiting rectangles with the same perimeter and different areas.
2 - I can find the unknown side length of a polygon exhibiting rectangles with the same area and different perimeters.
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A. Polygons and their area and perimeter attributes can be used to solve real world problems.
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A.1 How can the perimeter be found given the side lengths of a polygon rectangles with the same perimeter and different areas?
A.2 How can the perimeter be found given the side lengths of a polygon rectangles with the same area and different perimeters?
A.3 How can the unknown side length of a polygon be found exhibiting rectangles with the same perimeter and different areas.
A.4 How can the unknown side length of a polygon be found exhibiting rectangles with the same area and different perimeters?
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