HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 3

Unit 3: Ratios and Percentages

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Students set up and compute divisions to find unit rates in multiple places (e.g., 216 ÷ 4 = 54 for miles per hour; 156 ÷ 12 = 13 calories per chip; 240 ÷ 3 = 80 pages per hour). Students compute decimal quotients for unit price problems (e.g., $5.25 ÷ 3 = $1.75, $6.27 ÷ 3 = $2.09, $3.84 ÷ 12 = $0.32) and one example displays a long-division arrangement for a decimal division. Students are asked to use the division method as an accepted approach alongside equivalent-ratio/diagram methods throughout activities and practice pages.
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Students are asked to calculate unit prices by dividing the total price by the number of units, and the materials include a worked long-division example showing $3.38 ÷ 13 with the standard long-division steps written out. The activity directs students to record ratios and unit prices and to round decimals to the hundredths place, requiring division of decimal amounts by multi-digit whole numbers. Several data-collection and calculation tasks (e.g., converting gallons to fluid ounces and then dividing price by 128 fl oz) create opportunities to perform division with larger divisors.
Unit 5

Unit 5: Algebraic Equations

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Students are instructed to "Divide using the standard algorithm" in the decimal division section and shown examples where they divide both sides of equations (e.g., 8n = 2.4 then divide by 8; solving 0.3a = 15 then divide by 0.3). Student practice pages require division steps when isolating variables (dividing by coefficients such as 5, 4, 3, 10, etc.) and the decimal division guidance describes moving decimals and bringing the decimal into the quotient.
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Students solve equations that require division such as 6m = 42 (m = 7) and n/3 = 4 (n = 12), with answer key steps stating "To solve, divide both sides by 6" and "multiply both sides by 3." Several problems show solving for a variable by isolating it using division or multiplication (for example a/7 - 5 = 9 leading to a = 98). Practice includes solving for variables that involve division and using inverse operations with whole numbers and simple divisors.
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The project checklist and instructions require students to include division in their work (e.g., "Include one example of each operation (addition, subtraction, multiplication, and division)" and examples such as y/5 < 3 and n/2 + 5 ≤ 9). Students are asked to create equations and inequalities that sometimes require solving division to find whole-number answers and to include at least one equation with a fraction or division operation. Sample poster problems and answer-key tasks show students solving for variables in expressions that involve division.
Unit 6

Unit 6: 2D Geometry

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Students are asked to compute quotients in contextual problems and a review: e.g., Basic Skills Review #12 includes "Divide until there is no remainder. 396 ÷ 15 =" and the answer key gives 26.4. Students simplify ratios and scale factors by dividing numerator and denominator (examples: 8/2 → 4/1; 12/3 → 4/1) and solve proportions by multiplying/dividing both parts (e.g., 1 in/5 ft = 6 in/n ft leading to n = 30 ft). Several activities require students to perform division to find scale drawing measures (converting units and computing scale factors).
Unit 7

Unit 7: 3D Geometry

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Students compute a unit price by dividing $3.12 by 24 to find $0.13 per ounce, and they solve for x in 4x + 12 = 24 which requires dividing 12 by 4. Some activity answers show division used to find unit rates and to compute areas that involve numeric division (for example, converting meters to centimeters involves multiplication/division reasoning). These items require students to perform division with multi-digit decimals or to divide during equation solving.
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Students compute multi-digit quotients in several applied problems (for example, 528 ÷ 275 = 1.92 is worked out and 45,000 ÷ 600 = 75 appears in the salt factory example). The lesson instructs students to "add a decimal and zeros to the dividend as you divide" and shows converting 724 ÷ 1.6 into 7240 ÷ 16 to perform the division. Answer keys and activity pages require students to divide multi-digit numbers (e.g., 27,000 ÷ 90 = 300; 27,000/90 = 300) and to interpret remainders by rounding up for real-world contexts.
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Students must perform division in several applied problems that appear in the review and test (for example, finding the height h from V = Bh with 182 = 6.5 × h, solving 6300 ÷ 42 to find prism length, dividing 3000 ÷ 150 to find how many boxes a roll covers, and dividing total surface area by 10 to find number of paint cans). The answer key shows numeric quotients for these problems, indicating students are expected to compute multi-digit quotients and quotients involving decimals. These required computations place division within realistic problem-solving contexts.
Unit 8

Unit 8: Statistics

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Students perform division to compute means in multiple places: e.g., 219 ÷ 15 = 14.6, 418 ÷ 20 = 20.9, and 753 ÷ 9 = 83.666... are presented as steps to find the mean. Activity prompts ask students to add totals and then divide by the number of data values to find the mean, and some practice problems require rounding division results. The materials also note that students may use a calculator to find the mean.
Unit 9

Unit 9: Skills Review

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The Parent Plan explicitly lists "Fluently divide multi-digit numbers using the standard algorithm" as a targeted skill. Students solve division problems that require multi-digit division such as 2184 ÷ 56 and decimal division 994.08 ÷ 2.4, and they apply division in word problems (e.g., 118 ÷ 4 and the cupcake boxes problem). The answer key shows correct quotients for these multi-digit division problems, indicating students are expected to compute and produce accurate results.

3: Math

Unit 1

Unit 1: Numbers

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Students are instructed to convert fractions into decimals by dividing the numerator by the denominator and to use long division (e.g., the example converting 3/4 to 0.75 shows a division procedure and Activity 2 directs students to use long-division for the first four problems). Activity pages provide space for students to show long-division work for fraction-to-decimal conversions (problems include fractions such as 3/4, 2/7, 5/6, 13/40, 7/24). The lesson models long-division in examples of terminating and repeating decimals (e.g., 1/3 → 0.333... and use of long division to reveal repeating patterns).
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Students solve several division problems (e.g., -20 ÷ 4, -30 ÷ 5) on both the review and test pages. The parent/skills sections explicitly state that students should "convert a rational number to a decimal using long division" and include fraction-to-decimal tasks (e.g., 3/8 → 0.375, 5/8 → 0.625) that require use of division procedures.
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The Skills section explicitly states students will "Convert a rational number to a decimal using long division," indicating students are expected to use long division. Task 3 asks students to compute how many 700 kWh fuel cells are needed for large energy shortfalls, and the answer key shows division of multi-digit energy totals by 700 to produce whole-number counts (e.g., 83,220 ÷ 700 = 119). The Parent Plan and other skill bullets reference interpreting quotients of integers and converting scientific notation to decimals, which implicitly requires performing long division on multi-digit numbers.
Unit 2

Unit 2: Proportions

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Students set up and solve backward percent problems that require division, for example solving 0.012 × V = $2,400 by computing V = $2,400 ÷ 0.012 and solving 0.20 × I = $9,000 by computing I = $9,000 ÷ 0.20. Several activity problems ask students to find pre-tax prices by dividing totals by factors such as 1.06 or 1.08 (e.g., p = $374.40 ÷ 1.06 and p = $529.95 ÷ 1.055). The answer keys show numerical division results for multi-digit values (e.g., 2400 ÷ 0.012 = 200,000; 374.40 ÷ 1.06 = 353.21).
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Students perform division in multiple problems that require dividing fractions and decimals (for example, finding unit rates such as 5/6 mile in 2/3 hour and 3/4 mile in 1/2 hour). Students solve decimal division problems to find pre-tax or original prices (e.g., p = 212 ÷ 1.06 and p = 1728 ÷ 0.012) and determine constants of proportionality from tables that require quotients. The answer key gives numerical quotients for these items, indicating students compute multi-digit and decimal divisions as part of problem solving.
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Students are repeatedly asked to compute unit prices by dividing total cost by quantity (e.g., find price per lemon by dividing store price by number of lemons). Step 4 and Step 5 require students to divide a 2 lb sugar price by 2 to get price per pound and to divide a package price by the number of cups to get price per cup. In Part 3 students divide the total cost for 1 gallon by 16 to find the cost per cup and set up proportions that use division to convert tablespoons to lemons or pounds of sugar.