HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 7

Unit 7: 3D Geometry

Students dismantle a cardboard box and lay it flat to observe faces, edges, and vertices and to see a physical net. Students cut, crease, fold, and tape printed nets (Nets A–F) to construct prisms and pyramids and record the number and shapes of faces (including rectangles and triangles) on the "Geometric Nets" and "Working with Nets" pages. Students draw nets for a rectangular prism and a regular tetrahedron, and they analyze nets that show rectangles and triangles (e.g., square pyramid net with one square and four triangles). Students apply nets to identify real-world solids such as a pizza box and dice in problem-solving tasks.
Students are asked to draw nets, lay kit-built solids flat, and label dimensions on 2D nets (cube, rectangular prism, triangular prism, square pyramid) before measuring and calculating face areas. Student Activity Pages and worked examples show nets made of rectangles and triangles and guide students to find each face area and add them to get surface area (examples: 190 in^2 wrapping paper, 152 cm^2 triangular prism, 84 cm^2 square pyramid). Multiple real-world tasks (wrapping a package, painting a pyramid-shaped roof, covering a box with tape) require students to apply nets-and-surface-area methods to solve contextual problems.
Students are asked to refold and use nets (referenced Net C and Net D) to reconstruct rectangular and triangular prisms and to measure those solids. The unit includes tasks where students draw a net of a triangular prism on the quiz and identify a solid from a shown net. The quiz and answer key contain surface-area problems (e.g., square pyramid and rectangular prism) with calculations that sum areas of triangular and rectangular faces.
Students are shown unfolded box nets for three candidate shipping boxes (Box A, B, and C) and are prompted to use those nets (and the face dimensions) to compute volume and choose an appropriately sized box. Students use a net of the chosen rectangular prism to compute surface area step-by-step (SA = 2LW + 2LH + 2WH) and then apply that surface area to a real-world task (how many rolls of mailing paper to buy). The lesson repeatedly places these net-based calculations in real-world contexts (shipping mugs, painting a dresser, buying wrapping paper).
Students match and circle 2D nets to their corresponding 3D solids in multiple sections (e.g., cubes, pyramids, rectangular and triangular prisms). Students sketch nets (Josie's cereal box, cube nets) and are given unfolded nets with dimensions (Problems 4, 5 and others) and compute surface area using those nets. Students apply these techniques to real-world problems (painting a storage box, covering boxes with decorative paper, soap molds, cereal box craft) where they use nets and surface-area calculations to find quantities like paint cans or paper needed.
Students select, cut out, assemble, and arrange preprinted nets (cube, rectangular prism, triangular prism, square pyramid, tetrahedron) to represent three-dimensional figures and build a model. Step 3 directs students to choose three full-size preprinted nets and use the provided "Surface Area" and "Volume" sheets and formulas to measure faces (using graph paper) and calculate surface area and volume. The Parent Plan and Skills list explicitly state that students will "represent three-dimensional figures using nets made up of rectangles and triangles" and will solve real-world/mathematical problems involving surface area and volume as part of the project.
Unit 8

Unit 8: Statistics

The Basic Skills Review includes Problem 8: "A cube-shaped box has a volume of 27 ft^3. What is the surface area of the box?" The answer key shows students find the side length (s = 3 ft) and compute surface area using SA = 6s^2 = 54 ft^2, so students practice computing surface area of a cube from given information.