In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
Draw, construct, and describe geometrical figures and describe the relationships between them.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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3 - Solve (problems involving scale drawings of geometric figures)
3 - Compute (actual lengths and areas from a scale drawing)
3 - Reproduce (scale drawing at a different scale)
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3 - I can solve problems involving scale drawings of geometric figures.
3 - I can compute actual lengths and areas from a scale drawing.
3 - I can reproduce a scale drawing at a different scale.
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A. Actual lengths and areas can be computed from scale drawings.
B. Scaled drawings can be scaled up or down into larger or smaller drawings.
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A.1 What information can be found from a scale drawing? How can this information be computed?
B.1 How can a scaled drawing be increased or decreased in size using mathematics?
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Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Drawings
Geometric shapes
Triangles
Conditions of Constructed Figure
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3 - Draw (Geometric shapes by freehand)
3 - Draw (Geometric shapes by ruler)
3 - Draw (Geometric shapes by technology)
3 - Construct (Triangles)
1 - Notice (Conditions)
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3 - I can draw geometric shapes by freehand if given enough information about the sides and angles.
3 - I can draw geometric shapes with a ruler if given enough information about the sides and angles.
3 - I can draw geometric shapes with technology if given enough information about the sides and angles.
3 - I can construct triangles is given three measures of sides or angles.
1 - I can notice when the conditions given determine a unique triangle, more than one triangle or no triangle.
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A .One can draw a geometric shape when given conditions either by freehand, ruler and protractor, or with technology.
B. One should notice when the conditions given for a triangle determine a unique triangle, more than one triangle or no triangle.
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A.1 How does one freehand geometric shapes when given conditions for the measures of the angles and sides?
A.2 How does one use a ruler and a protractor to draw a geometric shape when given conditions for the measures of the angles and sides?
A.3 How does one use technology to draw a geometric shape when given conditions for the measures of the angles and sides?
B.1 What conditions for the angles and side lengths of a triangle indicate a unique triangle?
B.2 What conditions for the angles and side lengths of a triangle indicate more than one triangle?
B.3 What conditions for the angles and side lengths of a triangle indicate that no triangle could be drawn.
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Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Describe (Two dimensional figure)
2 - Slice (Two dimensional figure)
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2 - I can describe the two dimensional figure that results from slicing a three dimensional figure.
2 - I can mentally picture the results of slicing a three dimensional figure.
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A. One can mentally picture the two dimensional figure that results from slicing a three dimensional figure and then can describe those results.
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A.1 What is a two dimensional figure?
A.2 What are the names of the two dimensional figures?
A.3 What is a three dimensional figure?
A.4 What are the names of the three dimensional figures?
A.5 How does one mentally slice a three dimensional figure?
A.6 How does one describe a three dimensional figure?
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Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problems
Relationship between:
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1 - Know (Formula for area of a circle)
1 - Know (Formula for circumference of a circle)
3 - Use (Formula of a circle)
3 - Use (Formula of the area of a circle)
3 - Solve (Problems)
2 - Give (Derivation of relationship between area and circumference of a circle)
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1 - I can state the formula for the area of a circle.
1 - I can state the formula for the circumference of a circle.
3 - I can use the formula for circumference of a circle.
3 - I can use the formula for the area of a circle.
3 - I can solve problems about area and circumference of circles.
3 - I can give the derivation of the relationship between area and circumference of a circle.
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A. One can memorize and then use the formulas for the area and circumference of a circle to solve problems.
B. One can also give an informal derivation of the relationship between the circumference and area of a circle.
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A.1 What is the formula for the area of a circle?
A.2 What is the formula for the circumference of a circle?
A.3 How does one use the formula for area to solve a problem?
A.4 How does one use the formula for circumference to solve a problem?
B.1 How does one derive the relationship between the circumference and area of a circle?
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Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problems
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3 - Use (Facts about supplementary angles)
3 - Use (Facts about complementary angles)
3 - Use (Facts about vertical angles)
3 - Use (Facts about adjacent angles)
3 - Write (Equation)
3 - Solve (Equation)
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3 - I can use facts about supplementary angles.
3 - I can use facts about complementary angles.
3 - I can use facts about vertical angles.
3 - I can use facts about adjacent angles.
3 - I can write a simple equation for an unknown angle in a figure.
3 - I can solve a simple equation for an unknown angle in a figure.
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A. One can write and solve an equation for an unknown angle in a figure using facts about supplementary, complementary, vertical and adjacent angles.
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A.1 What is a supplementary angle?
A.2 What is a complementary angle?
A.3 What is a vertical angle?
A.4 What is an adjacent angle?
A.5 What facts does one know about supplementary angles?
A.6 What facts does one know about complementary angles?
A.7 What facts does one know about vertical angles?
A.8 What facts does one know about adjacent angles?
A.9 How does one write a simple equation for an unknown angle in a figure?
A.10 How does one solve a simple equation for an unknown angle in a figure?
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Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problems
Measures
Figures
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3 - Solve (Problems involving area of a triangle)
3 - Solve (Problems involving area of a quadrilateral)
3 - Solve (Problems involving area of a polygon)
3 - Solve (Problems involving volume of a cube)
3 - Solve (Problems involving volume of a right prism)
3 - Solve (Problems involving surface area of a cube)
3 - Solve (Problems involving surface area of a right prism)
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3 - I can solve real life and mathematical problems involving the area of a triangle.
3 - I can solve real life and mathematical problems involving the area of a quadrilateral.
3 - I can solve real life and mathematical problems involving the area of a polygon.
3 - I can solve real life and mathematical problems involving the volume of a cube.
3 - I can solve real life and mathematical problems involving the volume of a right prism.
3 - I can solve real life and mathematical problems involving the surface area of a cube.
3 - I can solve real life and mathematical problems involving the surface area of a right prism.
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A. One can solve real life or mathematical problems involving the area of a triangle, quadrilateral or polygon, the volume of a cube or a right prism, or the surface area of a cube or right prism.
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A.1 What is a two dimensional figure?
A.2 What is a three dimensional figure?
A.3 What are the different polygons?
A.4 What are right prisms?
A.5 How does one find the area a triangle?
A.6 How does one find the area of a quadrilateral?
A.7 How does one find the area of a polygon?
A.8 How does one find the volume of a right prism?
A.9 How does one find the surface area of a right prism?
A.10 How does one solve problems involving area?
A.11 how does one solve problems involving volume?
A.12 How does one solve problems involving surface area?
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