Section	Teacher-facing learning goals
Reasoning to Find Area	Lesson 1 Compare (orally) areas of the shapes that make up a geometric pattern. Comprehend that the word “area” (orally and in writing) refers to how much of the plane a shape covers. Lesson 2 Calculate the area of a region by decomposing it and rearranging the pieces, and explain (orally and in writing) the solution method. Recognize and explain (orally) that if two figures can be placed one on top one other so that they match up exactly, they must have the same area. Show that area is additive by composing polygons with a given area. Lesson 3 Calculate the area of a region by decomposing it and rearranging the pieces, and explain (orally and in writing) the solution method. Recognize and explain (orally) that if two figures can be placed one on top one other so that they match up exactly, they must have the same area. Show that area is additive by composing polygons with a given area.
Parallelograms	Lesson 4 Compare and contrast (orally) different strategies for determining the area of a parallelogram. Describe (orally and in writing) observations about the opposites sides and opposite angles of parallelograms. Explain (orally and in writing) how to find the area of a parallelogram by rearranging or enclosing it in a rectangle. Lesson 5 Comprehend the terms “base” and “height” to refer to one side of a parallelogram and the perpendicular distance between that side and the opposite side. Generalize (orally) a process for finding the area of a parallelogram, using the length of a base and the corresponding height. Identify a base and the corresponding height for a parallelogram, and understand that there are two different base-height pairs for any parallelogram. Lesson 6 Apply the formula for area of a parallelogram to find the area, the length of the base, or the height, and explain (orally and in writing) the solution method. Choose which measurements to use for calculating the area of a parallelogram when more than one base or height measurement is given, and explain (orally and in writing) the choice.
Triangles	Lesson 7 Describe (orally and in writing) ways in which two identical triangles can be composed, i.e., into a parallelogram or into a rectangle. Show how any parallelogram can be decomposed into two identical triangles by drawing a diagonal, and generalize (in writing) that this property applies to all parallelograms, but not all quadrilaterals. Lesson 8 Draw a diagram to show that the area of a triangle is half the area of an associated parallelogram. Explain (orally and in writing) strategies for using the base and height of an associated parallelogram to determine the area of a triangle. Lesson 9 Compare, contrast, and critique (orally) different strategies for determining the area of a triangle. Generalize a process for finding the area of a triangle, and justify (orally and in writing) why this can be abstracted as \(\frac12 \cdot b \cdot h\). Recognize that any side of a triangle can be considered its base, choose a side to use as the base when calculating the area of a triangle, and identify the corresponding height. Lesson 10 Draw and label the height that corresponds to a given base of a triangle, making sure it is perpendicular to the base and the correct length. Evaluate (orally) the usefulness of different base-height pairs for finding the area of a given triangle.
Polygons	Lesson 11 Compare and contrast (orally) different strategies for finding the area of a polygon. Describe (orally and in writing) the defining characteristics of polygons. Find the area of a polygon, by decomposing it into rectangles and triangles, and present the solution method (using words and other representations).
Surface Area	Lesson 12 Calculate the surface area of a rectangular prism and explain (orally and in writing) the solution method. Comprehend that the term “surface area” (in written and spoken language) refers to how many square units it takes to cover all the faces of a three-dimensional object. Lesson 13 Compare and contrast (orally and in writing) features of prisms and pyramids. Comprehend and use the words “face”, “edge”, “vertex”, and “base” to describe polyhedra (in spoken and written language). Understand that the word “net” refers to a two-dimensional figure that can be assembled into a polyhedron, and create a net for a given polyhedron. Lesson 14 Match polyhedra with their nets and justify (orally) that they match. Use a net with gridlines to calculate the surface area of a prism or pyramid and explain (in writing) the solution method. Visualize and identify the polyhedron that can be assembled from a given net. Lesson 15 Draw and assemble a net for the prism or pyramid shown in a given drawing. Interpret (using words and other representations) two-dimensional representations of prisms and pyramids. Use a net without gridlines to calculate the surface area of a prism or pyramid and explain (in writing) the solution method. Lesson 16 - Optional Comprehend that surface area and volume are two different attributes of three-dimensional objects and are measured in different units. Describe (orally and in writing) shapes built out of cubes, including observations about their surface area and volume. Determine the surface area and volume of shapes made out of cubes.
Squares and Cubes	Lesson 17 Generalize a process for finding the volume of a cube, and justify (orally) why this can be abstracted as \(s^3\). Include appropriate units (orally and in writing) when reporting lengths, areas, and volumes, e.g. cm, \(cm^2, cm^3\). Interpret and write expressions with exponents \(^2\) and \(^3\) to represent the area of a square or the volume of a cube. Lesson 18 Generalize a process for finding the surface area of a cube, and justify (orally) why this can be abstracted as \(6 \cdot s^2\). Interpret (orally) expressions that include repeated addition, multiplication, repeated multiplication, or exponents. Write expressions, with or without exponents, to represent the surface area of a given cube.
Let's put it to work!	Lesson 19 Apply understanding of surface area to estimate the amount of fabric in a tent, and explain (orally and in writing) the estimation strategy. Compare and contrast (orally) different tent designs. Interpret information (presented in writing and through other representations) about tents and sleeping bags.

6.1 Area and Surface Area