HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 7

Unit 7: Dividing Fractions

Students are asked to consider a real-world whole ÷ unit-fraction situation: "If you have 5 pounds of almonds and you want to make 1/2 pound servings... How many servings...?" Students physically cut sandwich models into thirds, sixths, fifths, and tenths to produce visual fraction pieces and record results in tables (e.g., 4 sandwiches ÷ 3 people = 4/3; 4 ÷ 6 = 4/6 = 2/3). The activities explicitly have students use visual fraction models (cutting and grouping pieces) to represent division outcomes and complete charts showing quotients as fractions or mixed numbers.
Students are asked to create and interpret visual models for dividing whole numbers by unit fractions (e.g., images and activities showing 4 ÷ 1/2 = 8 and 4 ÷ 1/3 = 12). Multiple word problems and student pages (Coach Clark pizzas, Sally's flour, Bobbie's ribbon, Tasha candy bars) require students to set up division of a whole number by a unit fraction and compute the quotient. The lesson teaches the algorithm Change-Switch-Flip-Solve, showing conversion to multiplication by the reciprocal (e.g., 3 ÷ 1/4 → 3/1 × 4/1 = 12) and quizzes require students to find reciprocals and solve using that relationship.
Students solve and interpret whole-number ÷ unit-fraction problems such as 5 ÷ 1/3 = 15 and 6 ÷ 1/3 (listed on activity pages and in the student worksheet). Students match division problems with word-problem situations and visual fraction models in the Fraction Division Sort activity. Activity 2 requires students to create a multiplication problem corresponding to a division problem, and the answer key maps division to multiplication by the reciprocal (for example, 4 ÷ 1/3 -> 4 × 3; 3 ÷ 1/5 -> 3 × 5). The parent notes and wrapping-up questions ask students to use the term "reciprocal" and the steps (Change, Switch, Flip) for dividing a whole number by a unit fraction.
Students are asked to draw visual models for specific whole-number ÷ unit-fraction problems (e.g., 5 ÷ 1/3, 6 ÷ 1/2, 4 ÷ 1/3, 5 ÷ 1/4) on multiple review and test pages. Students create or match story contexts to division expressions (e.g., Marcus cutting 5 pies into fourths, Pam cutting ribbon into 1/3-inch pieces) and write division sentences for word problems. Students compute quotients and answer keys show the conversion of division into multiplication by the reciprocal (for example, 5 ÷ 1/4 = 5 × 4/1 = 20), demonstrating the relationship between multiplication and division.
Students are asked to create a pamphlet that teaches how to divide a whole number by a unit fraction (Parent Plan skills list and instructions for two pamphlets). The student activity pages require students to draw a visual to represent the problem, write a corresponding division word sentence, and write a word problem based on the original division problem. The steps panels prompt students to "show the step using numbers" and to explain each step in their own words, and the teacher prompts ask students to explain what a reciprocal is in each pamphlet.
Unit 8

Unit 8: Volume

Students solve a word problem that directly represents dividing a whole number by a unit fraction: "Zach cuts 6 pizzas into eighths. How many pieces of pizza does he have?" The answer key shows the computation 6 ÷ 1/8 = 6/1 × 8/1 = 48, so students compute the quotient by converting the division to multiplication. The activity list includes this story context as a practical scenario for the operation.
Students solve Basic Skills Review problem 7: "Marley cuts 12 pizzas into sixths. How many pieces of pizza does she have?" The answer key shows work written as 12 ÷ 1/6 = 12 × 6 = 72, demonstrating interpretation of a whole number divided by a unit fraction and using the multiplication relationship to compute the quotient. Additional review items include fraction division problems (e.g., 1/9 ÷ 5) that show students carry out fraction-by-whole-number division procedures.
Students solve a contextual problem that divides a whole number by a unit fraction: in the Basic Skills Review students compute 16 ÷ 1/8 for the pizza problem (16 ÷ 1/8 = 128) and use the reciprocal method shown as 16/1 × 8/1 = 128. The review also shows division of a unit fraction by a whole number rewritten as multiplication by the reciprocal (1/8 ÷ 6 = 1/8 × 1/6 = 1/48), demonstrating the procedural connection between division and multiplication by reciprocals. The pizza scenario is a story context that asks students to interpret the division in a real situation and compute the quotient to decide if there are enough pieces.
Unit 9

Unit 9: Skills Review

Students complete an input/output table titled 'DIVIDE BY 1/3' where they compute whole-number ÷ 1/3 for inputs (2, 3, 10, 7, 11) with answers given (6, 9, 30, 21, 33). Students solve a contextual word problem asking 'Pam has 8 inches of ribbon and needs to cut it into 1/3 inch pieces. How many smaller pieces will she have?' and compute 8 ÷ 1/3 = 24. The parent notes and directions emphasize that at this level students need to know how to divide fractions and whole numbers, focusing practice on those computations.
Students solve conversion problems that require finding how many smaller units fit into a larger unit, for example Ace's Ice Cream: students calculate 8 gallons × 4 quarts/gallon = 32 quarts. The matching and conversion tasks (e.g., cups to pints, kilograms to grams) require students to use and apply unit relationships and perform computations that count equivalent smaller units within larger ones.