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In this section, students explore strategies for reasoning about the area of two-dimensional figures. The explorations highlight two principles about area:
In this section, students explore ways to find areas of triangles, generalize their observations as a formula, and use the formula to find the area of any triangle. They also apply their insights regarding triangles and parallelograms to find areas of other polygons.
Students begin by investigating the relationship between triangles and parallelograms. They see that a parallelogram can always...
Let’s compare parallelograms and triangles.
Let’s use what we know about parallelograms to find the area of triangles.
Let’s write and use a formula to find the area of a triangle.
Let’s use different base-height pairs to find the area of a triangle.
Let’s investigate polygons and their areas.
This section introduces students to polyhedra and surface area. Students apply their knowledge about areas of polygons to create nets and find surface areas of three-dimensional figures.
First, students learn that surface area is the number of unit squares that covers all the faces of a three-dimensional figure, without gaps or overlaps. They reason about the surface areas of rectangular...
In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions. The lesson in this section is optional because it offers additional opportunities to practice standards that are not a focus of the grade.
Let’s find out how much material is needed to build some tents.
In this section, students reason about areas of parallelograms. They learn about bases and heights and analyze the measurements that can be used to find the area of any parallelogram.
First, students use strategies they learned earlier in the unit to find the areas of given parallelograms. They see that one way to find the area of a parallelogram is...
In this short section, students learn to use exponents to express areas of squares and surface areas and volumes of cubes.
Students first explore perfect squares as areas of squares and perfect cubes as volumes of cubes with whole-number edge lengths. Next, they learn that the exponents 2 and 3 can be used to express the multiplication of edge lengths...
Let’s investigate perfect squares and perfect cubes.
Let’s write a formula to find the surface area of a cube.