In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
Solve real-world and mathematical problems involving area, surface area, and volume.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Area e.g.
Problems
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2 - Find (Area)
6 - Compose (Shapes)
6 - Decompose (Shapes)
3 - Apply (Techniques)
3 - Solve (Real world problems)
3 - Solve (Mathematical problems)
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2 - I can find the area of right triangles, other triangles, special quadrilaterals and polygons.
6 - I can compose a variety of shapes into rectangles.
6 - I can decompose a variety of shapes into triangles and other shapes.
3 - I can apply the techniques of composing and decomposing shapes to solve problems.
3 - I can solve real world problems involving area by applying the techniques of composing and decomposing shapes.
3 - I can solve mathematical problems involving area by applying the techniques of composing and decomposing shapes.
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A. One can solve real world and mathematical problems involving area by applying the techniques of composing or decomposing shapes into other shapes.
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A.1 How do you find the area of triangles?
A.2 What are the special quadrilaterals?
A.3 How does one find the area of the special quadrilaterals?
A.4 What does it mean to compose a figure into other shapes?
A.5 What does it mean to decompose a figure into other shapes?
A.6 How does one find the area of a figure that has been composed into other shapes?
A.7 How does one find the area of a figure that has been decomposed into other shapes?
A.8 What are some real world problems that could be solved by using the techniques of composing or decomposing?
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Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Edge lengths
Cubes
Problems
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2 - Find (Volume by packing)
1 - Pack (Cubes)
4 - Show (Equal volume)
2 - Multiply (Edge lengths)
3 - Apply (Formulas)
2 - Find (Volume by formulas)
3 - Solve (Real world problems)
3 - Solve (mathematical problems)
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2 - I can find the volume or a right rectangular prism with fractional edge lengths by packing it with the appropriate unit cubes.
1 - I can pack a right rectangular prism with fractional edge lengths with unit cubes.
4 - I can show the volume is the same if you use unit cubes, or if you multiply edge lengths of the prism.
2 - I can multiply edge lengths to find the volume of a right rectangular prism.
3 - I can apply the formulas V=lwh and V=Bh to find the volume of a right rectangular prism.
2 - I can find the volume of a right rectangular prism by using the formulas.
3 - I can solve real world problems involving finding the area of a right rectangular prism.
3 - I can solve mathematical problems involving finding the area of a right rectangular prism.
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A. Real world and mathematical problems can be solved by finding the volume of a right rectangular prism.
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A.1 What is a right rectangular prism?
A.2 What are the formulas for finding the area or a right rectangular prism?
A.3 What do the variables V, l, w, h and B stand for in the formulas?
A.4 How does one use the formulas to find the area of a right rectangular prism in a real world problem?
A.5 How does one use the formulas to find the area of a right rectangular prism in a mathematical problem?
A.6 What is a unit cube?
A.7 What is the volume of a unit cube?
A.8 How does one find the volume of a right rectangular prism by packing it with unit cubes?
A.9 How does one solve a real world problem involving the area of a right rectangular prism by packing it with unit cubes?
A.10 How does one solve a mathematical problem involving the area of a right rectangular prism by packing it with unit cubes?
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Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Polygons
Techniques
Problems
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3 - Draw (Polygons)
3 - Use (Coordinates)
2 - Find (Length)
3 - Join (Points)
3 - Apply (Techniques)
3 - Solve (Real world problems)
3 - Solve (Mathematical problems)
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3 - I can draw polygons in the coordinate plane when given the coordinates for the vertices.
3 - I can use the coordinates of the vertices to find the side lengths.
2 - I can find the length of the sides by using the coordinates of the vertices.
3 - I can join the coordinates with the same first or second coordinates?
3 - I can apply the technique of joining the coordinates to solve problems.
3 - I can solve real world problems by drawing polygons in the coordinate plane.
3 - I can solve mathematical problems by drawing polygons in the coordinate plane.
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A. Drawing polygons in the coordinate plane is a technique that can be used to solve problems.
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A.1 What is a polygon.
A.2 How would one graph the coordinates for the vertices on the coordinate plane?
A.3 Which vertices should be connected when drawing the polygon in the coordinate plane?
A.4 How does one find the side lengths of the polygon once it is drawn in the coordinate plane?
A.5 How does one solve real world problems by graphing a polygon in the coordinate plane?
A.6 How does one solve mathematical problems by graphing a polygon in the coordinate plane?
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Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Figures
Techniques
Problem context
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2 - Represent (Three dimensional figure)
3 - Use (Nets)
2 - Find (Surface area)
3 - Apply (Techniques)
3 - Solve (Real world problems)
3 - Solve (Mathematical problems)
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2 - I can represent three dimensional figures using nets made up of rectangles and triangles.
3 - I can use nets made up of rectangles and triangles to find the surface area of a three dimensional figure.
2 - I can find the surface area of a three dimensional figure by using a net.
3 - I can apply the technique of using a net to solve problems.
3 - I can solve real world problems involving finding the surface area of a three dimensional figure by using nets.
3 - I can solve mathematical problems involving finding the surface area of a three dimensional figure by using nets.
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A. Nets of three dimensional figures can be used to solve real world problems involving surface area.
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A.1 What is a three dimensional figure?
A.2 What is a net?
A.3 How does one design a net for a three dimensional figure?
A.4 How does one find the surface area of a three dimensional figure by using the net made up of triangles and rectangles?
A.5 How does one use nets to solve real world problems involving finding the surface area of a three dimensional figure?
A.6 How does one use nets to solve mathematical problems involving finding the surface area of a three dimensional figure?
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