HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 1

Unit 1: Place Value

Students practice interpreting a unit fraction as a division sentence (the materials state 1/10 means "1 divided by 10") and answer concrete problems like 400,000 ÷ 10, 4,000 ÷ 10, and 1.2 ÷ 10. The lesson uses visual models (ten dimes, cake grids) to represent one-tenth and one-hundredth and includes exercises that ask students to find one-tenth of groups and move the decimal point when dividing by 10. Students complete problems and fill-in-the-blank items that reinforce dividing whole numbers and decimals by 10 and comparing unit fractions such as 1/10 and 1/100.
Unit 3

Unit 3: Measurement

The project offers an Option 2 in which students must create measurement word problems and provide solutions, and Page 8 explicitly asks students to create questions or word problems that include converting between units. The "Questions to Consider" section tells students to use problem-solving strategies including dividing, and Pages 2–7 require students to show equivalent measurements and give examples of converting between units (which can involve numerical division).
Unit 5

Unit 5: Multiplying Fractions

Students are shown that 1/3 × 15 is the same as 15/3 or 15 ÷ 3 and they divide a number line into three equal parts to find one part, so they use visual models (number lines and arcs) and equations to represent fraction-of-a-whole problems. In the Parts and Divisions and Showing Fraction Multiplication activities, students divide whole numbers into denominator-sized groups (e.g., divide 15 into 5 parts for 2/5 of 15) and shade or count parts to find a/b of a whole. Multiple word problems and number-line/grid visuals ask students to compute fractions of whole quantities (e.g., 1/6 of 30, 2/3 of 12) and to record equations that show those relationships.
Unit 7

Unit 7: Dividing Fractions

Students model and solve division of unit fractions by whole numbers using visual fraction models in multiple examples (e.g., 1/2 ÷ 3 = 1/6 with a pie model; 1/5 ÷ 4 = 1/20 with a shaded grid). Students practice the algorithm Keep–Switch–Flip–Solve for converting division of a unit fraction by a whole number into multiplication by the reciprocal, with worked examples and problems (e.g., 1/4 ÷ 3 → 1/4 × 1/3 = 1/12). Students complete guided activities, word problems, and a quiz that require creating visuals, writing reciprocals, and solving equations that represent dividing unit fractions by whole numbers.
Students create and use visual models (circles, rectangles, pizzas, bars) to represent and solve problems such as 4 ÷ 1/3, 5 ÷ 1/4, and 6 ÷ 1/2, counting fractional parts to find quotients. Students solve real-world word problems (e.g., Coach Clark's pizzas, Jack's flour, Sally's flour, Brianna's apples) and write equations that correspond to the visuals. Students learn and apply the algorithm "Change, Switch, Flip, Solve" to convert whole-number ÷ unit-fraction problems into multiplication by the reciprocal and compute answers, and they complete quizzes and worksheets with answer keys showing these steps.
Students work with explicit real-world examples that divide unit fractions by whole numbers (e.g., 1/2 ÷ 3 for sharing 1/2 lb of chocolate among 3 people) and whole numbers by unit fractions (e.g., 2 ÷ 1/3 for how many 1/3-cup servings in 2 cups). In Activity 1 students sort cards so each group contains a division expression, a matching word problem, and a visual representation, requiring them to interpret dividend/divisor roles and reason about answers. In Activity 2 students create visuals, write situations, and record multiplication problems (reciprocal/multiplication form) to represent given division problems, and answer keys and parent notes explicitly show the equation connections.
Students are asked to draw visual representations for specific problems such as 1/2 ÷ 4, 1/3 ÷ 5, 5 ÷ 1/3, and 6 ÷ 1/2. Multiple real-world word problems ask students to write the division sentence and match or solve situations (e.g., dividing 1/3 of a cake among friends, cutting 6 inches of rope into 1/2-inch pieces, sharing 1/2 box of donuts among 6 brothers, and finding how many 1/3-cup servings are in 4 cups). Worksheets require students to write division math sentences before solving, find quotients for expressions like 4 ÷ 1/4 and 1/3 ÷ 7, and match division problems to their numerical quotients. Answer keys and test items show visual models paired with equations for both unit-fraction ÷ whole-number and whole-number ÷ unit-fraction problems.
The Skills and activity descriptions explicitly require students to create one pamphlet teaching how to divide a unit fraction by a whole number and another teaching how to divide a whole number by a unit fraction. Student pages ask students to draw a visual to represent the problem, show the corresponding division word sentence, "show the step using numbers," and "write a word problem based on the original division problem." Directions also prompt students to explain each step in their own words and to explain what a reciprocal is, and the Skills list explicitly mentions using visual fraction models and equations to represent problems.
Unit 8

Unit 8: Volume

The Basic Skills Review answer key includes the computation 1/8 ÷ 7 = 1/56, showing students perform division of a unit fraction by a whole number. The review also contains a real-world pizza problem: "Zach cuts 6 pizzas into eighths. How many pieces of pizza does he have?" with the solution 6 ÷ 1/8 = 48, showing students compute whole-number ÷ unit-fraction using multiplication by the reciprocal. These items provide explicit practice with both types of fraction division (unit fraction ÷ whole number and whole number ÷ unit fraction).
The Basic Skills Review includes explicit problems and answers that perform division with unit fractions: it shows 1/9 ÷ 5 = 1/45 (division of a unit fraction by a whole number) and Marley cutting 12 pizzas into sixths with the solution 12 ÷ 1/6 = 72 (division of a whole number by a unit fraction). These appear as real-world word problems (cupcakes and pizzas) with numerical equations and worked answers in the answer key.
The Basic Skills Review includes explicit fraction-division problems: students compute 1/8 ÷ 6 = 1/48 (division of a unit fraction by a whole number) and solve a word problem where Tamara cuts 16 pizzas into eighths and computes 16 ÷ 1/8 = 128 (division of a whole number by a unit fraction). The answer key shows students set up equations and use multiplication by the reciprocal to calculate the results, and the pizza problem is presented in a real-world context requiring interpretation (enough pieces for 70 people).
Unit 9

Unit 9: Skills Review

Students complete a Rule: DIVIDE BY 1/3 input/output table and the answer key shows whole-number ÷ 1/3 examples (e.g., 2 → 6, 10 → 30). Students solve the real-world problem asking how many 1/3-inch pieces come from 8 inches of ribbon (Pam), with the answer 24. Students solve a division-of-a-fraction-by-a-whole-number word problem (Kurt: 3/4 ÷ 3 = 1/15).