HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 8

Unit 8: Volume

Students are shown a 3-D diagram of a rectangular prism with side lengths labeled 8 in., 5 in., and 4 in. Students are asked "What does volume measure?" and are provided a space labeled "Formula," prompting them to record a volume formula. The unit text and parent notes explicitly state that students will work with calculating the volume of cubes and rectangular prisms later in the unit, and the activity page includes a dedicated "Volume of a Rectangular Prism" section.
Students build rectangular prisms by packing exactly 16 centimeter cubes in Activity 2, using all unit cubes with no gaps or cubes sticking out. Students identify and label parts of prisms (base, face, height) on the activity page and answer parent-guided questions locating bases and height. The wrap-up statement has students observe that different prisms made with the 16 cubes each had the same volume.
Students practice building rectangular prisms by adding and removing unit cubes using the online interactive tool, with instructions that each added cube changes the prism's volume. The lesson's skills and parent notes explicitly state creating rectangular prisms using cubes and suggest using centimeter cubes as a model. Student pages ask for the measurements needed for volume (length, width, height) and identify volume units as cubic units.
Students build right rectangular prisms with centimeter (unit) cubes in Activities 1–4 and Activity 6 and count the cubes to determine volume (Activity 2 and Day 2 Finding Volume). The Finding Volume activity has students color and count the cubes in one layer, count the number of layers, and multiply the number in one layer by the number of layers to get volume. Day 3 explicitly has students find the area of one layer (length x width = area of base) then use repeated addition and multiplication by the number of layers (height) to compute total volume (e.g., 14 x 11 = 154, 154 x 6 = 924). Parent-plan examples and the Making Prisms activity require students to record length, width, and height and check that their product equals the number of unit cubes (L x W x H = V).
Students build rectangular prisms using 24 one-centimeter unit cubes in Activity 1, physically packing cubes to make prisms and recording dimensions that multiply to 24. In Activity 2 students examine the rows they created, test multiplying the three whole-number edge lengths, and write and use the formula l × w × h = V to find volumes. The student pages and answer key show multiple 3-factor dimension sets (for example 8 × 3 × 1 and 8 × 1 × 3) represented as physical volumes.
Students begin by building a rectangular prism out of 24 unit (centimeter) cubes and noting its volume is 24 cubic centimeters, providing an explicit packing-with-unit-cubes activity. Students are taught and repeatedly use the formula l × w × h = V (examples and practice problems such as 10 × 3 × 5 = 150 and many worksheet/quiz items). Students see and practice that reordering the factors and placing parentheses does not change the product (multiple permutations and associative parentheses examples) and sort/identify prisms drawn as unit-cube grids matched to their volumes.
Students are asked in the Getting Started and Activity 4 tasks to use centimeter (unit) cubes to make rectangular prisms (including an L-shaped composite) and count cubes to find volume. Activity 1 and its images explicitly show a 5 × 3 × 4 prism decomposed into layers and present both l × w × h and B × h = V formulations, with student problems that require computing volumes using both forms. Student pages require writing multiple math sentences (e.g., 4 × 4 × 5 = 80 and 16 × 5 = 80) and completing problems that connect counted unit cubes, three-factor products, and base-area-by-height calculations.
The Parent Plan and activities require students to use V = l × w × h and V = b × h and include multiple calculation problems with whole-number edge lengths (e.g., 20 × 20 × 15, 10 × 10 × 10). Problem 4 explicitly asks for the greatest number of 1 cm cubes that can fit in a prism with base area 24 cm2 and height 7 cm, and the answer uses V = b × h = 24 × 7 = 168 cubic cm (counting unit cubes). The Changing Dimensions activity has students compute volumes when dimensions are doubled or tripled and complete a table showing original, doubled, and tripled dimensions and volumes, representing threefold whole-number products as volumes.
The Skills list and review items explicitly require students to measure volume by counting unit cubes and to apply the formulas V = l × w × h and V = b × h. An interactive activity asks students to compute volume from dimensions and then check their answer by adding unit cubes to fill the prism. Multiple student tasks (dice-generated dimensions, Volume Sort matching, review and test problems) ask students to draw models for three numbers and compute threefold products as volumes and to count cubes on the test.
Students select and assemble buildings from rectangular boxes (right rectangular prisms) and are instructed to measure length, width, and height in centimeters and record dimensions in the l × w × h format (Step 4). The Skills section explicitly tells students to apply the formulas V = l × w × h and V = b × h to find volumes and to add volumes for solid figures composed of two non-overlapping right rectangular prisms. Students are required to make at least two composite buildings from more than one prism and to write volumes labeled as cubic cm, implying calculation of whole-number cubic volumes based on measured whole-centimeter dimensions.
Unit 9

Unit 9: Skills Review

Students label dimensions and write math sentences to compute volumes using V = l × w × h for whole-number edge lengths (examples: 8 × 4 × 5 = 160; 3 × 6 × 1 = 18; 10 × 3 × 4 = 120; 5 × 5 × 5 = 125). Students use V = base × height when given a base area (Problem 5) and compute base area then multiply by height (Problem 6). Students solve for missing dimensions by using volume and dividing by the other given dimensions (Missing Dimensions activity). The Parent Plan explicitly states applying the formulas V = l × w × h and V = b × h in context of real-world and mathematical problems.