HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 7

Unit 7: 3D Geometry

Students count how many fractional unit cubes fit in a prism (Activity 2 sugar-cube and craft-cube examples) and multiply the number of cubes by the volume of a single fractional cube to find the prism's volume. Students convert mixed numbers to improper fractions and use V = l × w × h with fractional dimensions (examples show 3 1/2 × 2 × 2 and 1 1/2 × 3/4 × 4) and obtain the same results. Student activity pages explicitly instruct students to use the cube-counting method with 1/2-in and 1/4-in cubes and include problems where students both count cubes and compute volumes using formulas. The lesson also has real-world word problems (packaging boxes, aquarium, mailing boxes, lawn dice) that require finding volumes with fractional edge lengths.
Students use and apply the formulas V = l × w × h and V = B × h in multiple real-world problems: Archie's mugs (V = 4 × 4 × 5 = 80 in^3 then 8 × 80 = 640 in^3), the cheese blocks item in Learning Gates where each block measures 12 × 2 1/2 × 5 giving a block volume of 150 cm^3 and box capacity found by division, and the sculptor's triangular prism where V = (1/2 × 5 × 3) × 12 = 90 cm^3 (V = B × h). Several missing-dimension exercises set up and solve equations using fractional edge lengths (for example 11/2 × w × 2 = 44).
The Parent Plan and skills list explicitly instruct students to apply the formulas V = l × w × h and V = B × h to find volumes of right rectangular prisms with fractional edge lengths. Several practice problems require students to compute volumes with fractional dimensions (for example V = 3/4 × 1/2 × 4 4/5 = 1 4/5) and to use V = B × h to solve real-world problems (Bella's flute case and the soap-prism length). A linked interactive activity ("Interactive Cubes") asks students to place cubes to find volume, providing a manipulable tool related to packing cubes to determine volume.
The Volume activity page provides the formulas V = l × w × h and V = B × h and asks students to calculate volumes for a cube, rectangular prism, and triangular prism. The Parent Plan explicitly states that students should "apply the formulas V = l × w × h and V = b × h to find volumes of right rectangular prisms with fractional edge lengths." Day 2 instructs students to measure nets on graph paper and to round measurements to the nearest 1/2 unit, and an example shows multiplying with a half-unit (8 × 4 1/2 = 36) when computing area.
Unit 8

Unit 8: Statistics

The Basic Skills Review includes a problem asking students to find the volume of a rectangular prism and the answer key uses the formula V = l × w × h to compute volume. The provided solution shows a computation involving a fractional edge length (6 × 4 × 3/4 = 18), so students practice multiplying edge lengths when one edge is a fraction.
Unit 9

Unit 9: Skills Review

The Parent Plan skills list explicitly tells students to "Find the volume of a right rectangular prism with fractional edge lengths" and to "Solve real-world and mathematical problems involving ... right prisms," and it states students will review surface area and volume. Activity 2 directs students to complete a surface area and volume quiz, and the parent notes that students may refer to geometric formulas in their Interactive Notebook.