HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 8

Unit 8: Volume

Students explore the concept of volume by building rectangular prisms with an online cube tool and by creating models with cubes (Activity 1 and Parent Plan). The student sheet and answer key ask students to identify that volume requires length, width, and height and that volume is measured in cubic units. Students practice representing 3D shapes by drawing cubes and rectangular prisms on isometric dot paper, showing all three dimensions (Activity 2).
Students build rectangular prisms with centimeter cubes and record length, width, and height (Activity 2 and Making Prisms), with parent notes requiring that the product of the dimensions equal the number of cubes. The Finding Volume activity has students color one layer, count cubes in that layer, count layers, and multiply the two numbers (Step 3), explicitly using multiplication to get volume. Activity 6 shows finding the area of one layer (14 x 11 = 154) and then multiplying by the height (154 x 6 = 924), and explains that repeated addition equals multiplication. The Unit 8 quiz and the Volume and Cubes sheet present mathematical and real-world word problems (garden wall, shipping boxes, etc.) that require students to compute volumes of right rectangular prisms with whole-number edge lengths.
Students build right rectangular prisms from unit (centimeter) cubes (Making 24 activity) and record whole-number edge lengths and volumes. Students test and observe that multiplying the three dimensions gives the volume (Activity 2 asks students to compute 8 × 3 × 1 = 24 and to test other rows). Students use the volume formula l × w × h to compute volumes (example: 8 × 4 × 5 = 160) and complete practice problems using whole-number edge lengths.
Students are shown and practice the formula l × w × h = V in multiple places: the introduction and Activities 1–4 explicitly present the formula and worked examples (e.g., 6 × 6 × 2 = 72, 10 × 3 × 5 = 150). Students complete practice sheets and a quiz that require them to write volume equations and compute volumes for rectangular prisms with whole-number edge lengths, including real-world contexts (stone monument, gift box, shipping container) and a measurement activity where they measure and compute volumes of found boxes. The materials also emphasize labeling answers in cubic units and use the commutative/associative properties to show order of multiplication does not affect volume.
Students build rectangular prisms with centimeter cubes and use an online isometric tool to make three different prisms of volume 20 cubic cm, showing use of whole-number edge lengths. The materials explicitly present and use the formulas V = l × w × h and V = B × h (with B = l × w), and students complete worksheets (Using Base Area to Find Volume, Think About It) computing volumes with given integer dimensions. Students apply the formulas to solve missing-dimension problems (Something's Missing), solve word problems about boxes (Maria's gift boxes, nesting boxes), and find volumes of composite prisms by breaking shapes into right rectangular prisms and adding volumes.
Students solve multiple real-world problems that require computing V = l × w × h (e.g., Diego's 20 × 20 × 15 box, Danielle's 10 × 10 × 10 popcorn box, Sasha and Emilia toy boxes, Lilia and Noah prisms, toolbox selection). One problem uses base area and height explicitly and directs students to use V = b × h (container with base area 24 cm² and height 7 cm). The parent plan and answer key state the formulas V = l × w × h and V = b × h and instruct students to write math sentences with units; Activity 2 has students compute volumes after doubling/tripling dimensions to practice applying the formula in mathematical contexts.
The Skills section explicitly lists applying the formulas V = l × w × h and V = b × h for rectangular prisms. Activities ask students to write the two formulas, compute volumes from given whole-number dimensions (e.g., 4 cm × 5 cm × 2 cm, 8 in × 8 in × 8 in), and use base area with height (b × h) to find missing dimensions. Multiple student pages present real-world word problems (jewelry box, garden bed, boxes, sandbox) and composite-prism problems that require using the formulas and adding volumes; the answer key shows calculations using l×w×h and b×h.
The Parent Plan explicitly lists the skill: "Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes..." Step 4 directs students to measure length, width, and height in centimeters (rounding to the nearest whole centimeter), record dimensions as l × w × h, and compute volumes, labeling results in cubic cm. The student activity pages include columns for recording Dimensions (L × W × H) and Volume, and the project requires at least two composite buildings whose total volumes students must find by adding component volumes.
Unit 9

Unit 9: Skills Review

Students label dimensions and write math sentences to compute volumes for rectangular prisms with whole-number edge lengths in Activity 1 (examples: 8×4×5 = 160 m³; 3×6×1 = 18 in³; 5×5×5 = 125 cm³). Problems 5 and 6 explicitly require students to use V = b × h (given base area and height) to find volumes (36×6 = 216 cm³; base 18 m² × height 5 m = 90 m³). Activity 2 has students solve for missing edge lengths from a given volume in real-world contexts (Bilal's toy box and Heidi's shipping box), applying inverse use of the volume formula in contextual problems.