Fifth Grade - MATH
5: Math
Unit 5: Multiplying Fractions
Lesson 3
Using Area Models
Students read and model fraction-of-a-fraction situations using area models and fraction strips (for example, the lesson states "1/3 × 1/2 means 1 part when 1/2 is divided into 3 parts" and has an example showing 1/3 × 1/2 = 1/6). Students use fraction strips to rephrase 3/4 of 1/2 as "3 parts when 1/2 is divided into 4 parts" and produce the visual result 3/8. Multiple activities (paper folding, area-model grids, and interactive tools) require students to divide one fractional part into equal subparts and count overlapping regions to compute products of unit fractions and other fractions.
Lesson 4
Area Models to Algorithm
Students divide a unit fraction on a number line when they are asked to split the interval from 0 to 1/2 into four equal parts and identify the intermediate marks as 1/8, 1/4, 3/8, etc. Students use fraction strips and number-line markings to see that one part of 1/2 divided into 4 parts equals 1/8 and then count three such parts to get 3/8. The student activity pages prompt questions like "How much is 1 part when 2/3 is divided into 2 parts?" that practice partitioning a fraction by a whole number.
Unit 7: Dividing Fractions
Lesson 3
Dividing Unit Fractions by Whole Numbers
Students model and solve division of unit fractions by whole numbers using story contexts and visuals (pie shared among friends, 1/5 of a bag of treats divided among 4 dogs). The lesson includes a specific visual example for 1/3 ÷ 4 showing the whole divided into 12 parts and concluding each part is 1/12. Students learn and practice the algorithm Keep–Switch–Flip–Solve (keep the fraction, switch ÷ to ×, flip the whole number to its reciprocal, then multiply) and complete problems and a quiz that require writing reciprocals and computing quotients. Multiple activities ask students to create, color, and count grid-based models and to solve word problems that require interpreting and computing unit-fraction ÷ whole-number quotients.
Lesson 5
More Division Practice
Students interpret and compute unit-fraction ÷ whole-number problems such as 1/3 ÷ 5 and are shown a visual model that represents 1/3 of a pitcher divided among 5 people resulting in 1/15. The Student Activity Pages include many unit-fraction ÷ whole-number problems (e.g., 1/3 ÷ 6, 1/3 ÷ 3) for students to solve and sort with matching visuals and word problems. Activity 2 and the Parent Plan ask students to create a story context for division problems (explicitly citing 1/3 ÷ 4 as an example), produce corresponding visual representations, and write related multiplication problems, and the Wrap-Up reviews the Keep-Switch-Flip steps and use of reciprocals.
Lesson 6
Unit Review and Test
Students watch a video titled "Dividing Unit Fractions by Whole Numbers" and complete practice problems that include unit-fraction ÷ whole-number expressions such as 1/3 ÷ 4. The matching activity lists 1/3 ÷ 4 with the correct quotient 1/12, and the Unit Test asks students to draw a visual representation for 1/3 ÷ 4. Multiple word problems present real contexts (e.g., "Cameron has 1/3 box of crayons and wants to divide it among his 4 brothers") that ask students to interpret and set up unit-fraction ÷ whole-number expressions, and answer keys show division written as multiplication by the reciprocal (e.g., 1/3 ÷ 7 = 1/3 × 1/7 = 1/21).
Final Project
Fraction Division Pamphlets
Students are instructed to create one pamphlet that teaches how to divide a unit fraction by a whole number and to place a division problem on the title page. The activity requires students to draw a visual representation of the problem, show a corresponding division word sentence, write a word problem based on the original division problem, and "show the step using numbers." The Parent Plan skills explicitly list using visual fraction models and equations to represent and solve real-world problems involving division of unit fractions by non-zero whole numbers. The pamphlet prompts also ask students to explain what a reciprocal is and to explain each step in their own words.
Unit 8: Volume
Lesson 3
From Area to Volume
Students complete Basic Skills Review problems that include the computation 1/8 ÷ 7 = 1/56, and the answer key records that result. The materials also include division problems involving unit fractions (for example, 6 ÷ 1/8 = 48), so students practice dividing with unit fractions and whole numbers on worksheets.
Lesson 4
Volume and Unit Cubes
Students complete Basic Skills Review problems that include computing unit-fraction ÷ whole-number (answer key shows 1/9 ÷ 5 = 1/45 and the algebraic steps 1/9 ÷ 5/1 = 1/9 × 1/5 = 1/45). The review also includes division of a whole number by a unit fraction (12 ÷ 1/6 = 72), showing students practice related fraction-division computations. Multiple sections show students using multiplication as repeated addition (e.g., 154 + 154 + ... = 154 × 6) which reinforces multiplicative reasoning connected to division.
Lesson 6
Practicing the Algorithm
The Basic Skills Review answer key includes the computation 1/8 ÷ 6 = 1/48 and shows the work 1/8 ÷ 6 = 1/8 × 1/6 = 1/48. The review problems and answers show students performing division of a unit fraction by a whole number and converting the division to multiplication by the reciprocal.
Unit 9: Skills Review
Lesson 1
Fraction Operations
Students solve word problems that require dividing a fraction by a whole number (the Kurt problem) and the answer key explicitly computes a unit-fraction quotient: 1/5 ÷ 3 = 1/15, showing 1/5 ÷ 3 = 1/5 × 1/3. Students complete input/output tables for rules including "Divide by 4," requiring them to compute outcomes such as 1 ÷ 4 and other divisions that produce fractional quotients. The parent notes and answer key emphasize that students only need to know how to divide fractions and whole numbers, reinforcing practice with division of fractions by whole numbers.
