Fifth Grade - MATH
5: Math
Unit 1: Place Value
Lesson 9
Roman Numerals
Students encounter fractional quantities in Basic Skills Review #3 where they convert ounces to cups (8 oz = 1 cup, 16 oz = 2 cups) and then add fractional cup amounts (1/2 cup, 1/4 cup, etc.) to find a total amount of trail mix. The answer key shows the converted cup amounts being added (1 + 2 + 1/2 + 1/4 + 1/2 + 1/2 + 1/2 = 5 1/4 cups). These tasks require students to combine fractions with unlike denominators (halves and quarters) within a word problem context.
Unit 3: Measurement
Lesson 4
Working With Time
Students practice adding and subtracting mixed units of time in multiple activities (e.g., Example 1: 1 hour 45 minutes + 2 hours 40 minutes converted to 3 hours 85 minutes then to 4 hours 25 minutes; subtraction example borrowing an hour to convert minutes). Activity 3 includes a problem with a fractional week (2/3 weeks 5 days + 6 days) that requires converting the fractional week into days before adding. Several word problems ask students to convert units and then add or subtract (e.g., adding hours and minutes, adding days/months/years, converting before combining).
Lesson 5
Working With Line Plots
The Skills section states that students will "Use operations on fractions to solve problems involving information presented in line plots." Students create line plots that use fractional measurements in quarters (1/4, 1/2, 3/4) and place Xs to represent data points. The activity asks students to compute totals and differences from the plotted data (for example, "What is the total weight of all the packages that weigh 4 1/4 pounds?" and "What's the difference between the heaviest package and the lightest package?").
Lesson 6
Unit Test
Students work with fractions and mixed numbers in line-plot tasks and word problems: they add three 1 1/4 cm lengths to get 3 3/4 cm and subtract 3 3/4 cm - 1 1/4 cm = 2 1/2 cm. The Unit Review and Parent Plan state that students should "use operations on fractions to solve problems involving information presented in line plots" and the guitar practice and insect length plots use fractional and mixed-number measurements (e.g., 1 1/4, 1 1/2, 3/4).
Final Project
Measurement Book
Students are asked to show equivalent measurements on multiple pages (e.g., Page 2 asks for examples like 3 feet = 1 yard; Page 5 asks for 1 meter = 100 centimeters; Page 6 asks for 1000 grams = 1 kilogram; Page 7 asks for 1000 milliliters = 1 liter). Page 8 requires students to create and solve conversion questions, including "converting between units in the same system," and the "Questions to Consider" list explicitly mentions problem-solving using strategies like adding and subtracting. Several pages require students to create word problems and provide solutions related to measurement and conversion, which may involve numeric operations.
Unit 4: Adding and Subtracting Fractions
Lesson 1
Reviewing Fractions
Students repeatedly generate and identify equivalent fractions using fraction strips and worksheets (Activities 3, 4, 5). They complete equivalent-fractions exercises, create equivalent-fraction chains, simplify fractions, and explain that multiplying or dividing numerator and denominator by the same number produces equivalent fractions. The quiz and flipbook tasks require students to find and match equivalent fractions and to simplify fractions.
Lesson 5
Working With Unlike Denominators
Students use fraction strips and interactive fraction-strip activities to create sums using unit fractions with different denominators, showing how different equivalent fractions combine to make the same total. The "Easiest Common Denominator" activity and video have students multiply denominators, multiply each fraction by a whole fraction (e.g., 2/5 x 3/3 and 1/3 x 5/5), and convert 2/5 + 1/3 into 6/15 + 5/15 = 11/15. The unit quiz asks students to add and subtract problems with unlike denominators (for example 4/5 + 5/6 and 2 6/10 - 1/9) and to simplify and convert improper fractions to mixed numbers.
Lesson 6
Adding Fractions With Different Denominators
Students convert unlike denominators to like denominators using visual fraction strips (e.g., showing 2/3 = 4/6 and adding 1/6 to get 5/6). Multiple activity pages ask students to find least common multiples, create equivalent fractions (e.g., change 5/6 and 3/8 to /24 to get 29/24), add the resulting like-denominator fractions, simplify, and convert improper fractions to mixed numbers. The answer key and practice problems explicitly show rewriting fractions with common denominators (for example, 2/3 + 3/4 = 8/12 + 9/12 = 17/12).
Lesson 7
Subtracting Fractions With Different Denominators
Students convert unlike denominators to a common denominator and create equivalent fractions, as shown when they change 3/4 into 6/8 using the laminated fraction chart and then subtract 3/8 to get 3/8. Students are taught step-by-step procedures: find a common denominator (LCD or easiest method), rewrite fractions with that denominator, subtract numerators, and simplify. Students practice these actions with multiple worked examples and a set of practice and quiz problems that require finding common denominators and subtracting numerators.
Lesson 8
Mixed Numbers With Unlike Denominators
Students are instructed to "Find the common denominator and create equivalent fractions" and shown worked examples such as converting 2/3 and 1/5 to 10/15 and 3/15 before adding to get 7 13/15. Student activity pages give multiple practice problems that require converting mixed numbers to equivalent fractions with like denominators (e.g., 2 2/3 + 5 1/6 example converting to sixths). The lesson also shows the alternative method of converting mixed numbers to improper fractions, finding a common denominator, and then adding or subtracting (example: 7/5 + 7/2 -> 14/10 + 35/10).
Lesson 9
Problem Solving With Fractions
Students are asked to add and subtract mixed numbers in multiple places: the walking contest problems require comparing and subtracting 4 3/4, 4 2/8, and 5 1/2 and then adding the three distances together. Activity 3 is explicitly titled "Adding and Subtracting Mixed Numbers" and directs students to use fraction boxes to complete mixed-number addition and subtraction problems. The Parent Plan and Things to Review list the skill "Add and subtract fractions with like and unlike denominators (including mixed numbers)" and include conversion between improper fractions and mixed numbers practice.
Lesson 10
Unit Review and Test
The lesson explicitly lists "Add and subtract fractions with like and unlike denominators" and "Add and subtract mixed numbers with like and unlike denominators" as required skills. Students are assigned a video titled "Adding Fractions With Different Denominators," an online quiz on fraction addition and subtraction, and practice pages with problems such as 3/7 - 2/11, 2/5 + 13/15, 16/7 + 3/2, 1/2 + 1/7, 4 5/6 - 2 2/3, and 5 1/5 + 3 5/6. Students are also asked to write least common denominators and to "simplify and convert as needed," and the answer key shows converted/common-denominator computations (e.g., 3/7 - 2/11 = 16/33).
Final Project
Adding and Subtracting Fractions BINGO
Students are required to create and solve problems that include additions and subtractions of fractions and mixed numbers with unlike denominators (checklist items: 2 addition problems using fractions with unlike denominators; 2 addition problems using mixed numbers with unlike denominators; corresponding subtraction items). Students must also convert between improper fractions and mixed numbers, and use scratch paper and pencils to figure out answers during gameplay (Step 6). The game play instructs students to mark answers that match caller problems, so students will practice computing sums and differences of fractions with different denominators during play.
Unit 5: Multiplying Fractions
Lesson 4
Area Models to Algorithm
Students convert unlike denominators to equivalent fractions and add/subtract them in the brownies example where 2/3 is rewritten as 8/12 and 1/4 as 3/12 to get 11/12. The "Adding, Subtracting, and Multiplying Fractions" activity asks students to create addition and subtraction problems and solve them, and the Student/Parent notes instruct students to find a common denominator before adding or subtracting. The explanatory text and answer key explicitly show work rewriting fractions with common denominators (e.g., 2/3 → 8/12, 1/4 → 3/12) and then performing the addition/subtraction.
Lesson 6
Multiplying Mixed Numbers
Students practice converting between improper fractions and mixed numbers in Activity 1 through matching, conversion items, and a comparison word problem. The Basic Skills Review and Student Activity Pages include explicit addition and subtraction problems with mixed numbers (e.g., 5 2/3 - 3 1/2 and 2 1/2 + 3 3/6) that require working with unlike denominators. The materials require students to manipulate fraction forms (improper ↔ mixed) which supports fraction work.
Lesson 7
More Fraction Multiplication
Students are asked to add fractions with unlike denominators in Real World Problem 1 (3/4 cup + 5/12 cup) and to subtract mixed numbers with unlike denominators in Real World Problem 3 (3 1/4 − 1 5/6). Students also encounter other problems that require combining fractional amounts (e.g., finding remaining cupcakes after taking fractional parts), which necessitate addition or subtraction of fractions. These tasks require working with mixed numbers and unlike denominators to find totals or differences.
Lesson 8
Finding Fractional Area
Students repeatedly add fractional areas by counting and summing partial tiles (for example, Activity 2 combines 1/2 + 1/2 + 1/6 = 1 1/6 and the table example sums 6 + 1 + 1/2 + 1/4 = 8 3/4). Students add mixed numbers when finding perimeter (e.g., 2 1/2 + 4 1/4 + 2 1/2 + 4 1/4 = 13 1/2) and complete practice problems that require adding fractional and mixed-number areas and perimeters. Several student activity pages and answer keys show worked sums of fractional parts resulting in mixed-number totals.
Lesson 9
Unit Review and Test
Students solve several word problems that require adding and subtracting mixed numbers and fractions (e.g., Jamie walking 3 1/2 miles and having walked 1 2/3 miles; Basha's total yard-work time 1 3/4 + 2 1/2; rope problem 7 1/2 − 5 3/8). The answer key shows computed sums and differences for these problems, indicating students will practice computing with mixed numbers and fractional parts. Additional problems (coffee mixing, remaining amounts) require combining and subtracting fractional amounts.
Unit 6: Geometry
Lesson 2
Identifying and Classifying Polygons
Students complete the Basic Skills Review #17 which includes problems that add and subtract mixed numbers and fractions (e.g., 2 3/4 + 2 1/3 + 1/6 and 9 1/5 - 2 2/3). The provided answer key shows converting fractions to common denominators (e.g., converting to twelfths or fifteenths) and then performing the addition or subtraction to produce the final mixed-number answers. These worked solutions demonstrate replacing given fractions with equivalent fractions to produce like denominators before adding or subtracting.
Lesson 6
More Work With Ordered Pairs
The Basic Skills Review #18 includes problems that require adding and subtracting mixed numbers and fractions with unlike denominators (e.g., 8 2/5 - 3 2/3 and 2 1/8 + 2 4/5 + 1/10). The Parent Plan answer key shows students converting mixed numbers to improper fractions and replacing fractions with equivalent fractions having a common denominator (126/15 - 55/15 and 85/40 + 112/40 + 4/40). The answer key gives final converted sums and differences (71/15 = 4 11/15 and 201/40 = 5 1/40), demonstrating the method of producing like denominators to compute results.
Lesson 7
Coordinate Plane Pictures
Students are asked to complete Basic Skills Review #19 which includes fraction problems such as 1/5 + 2/3 + 1/10 and 6 3/4 − 2 2/3. The answer key shows these problems worked by replacing fractions with equivalent fractions having a common denominator (e.g., 1/5 + 2/3 + 1/10 = 6/30 + 20/30 + 3/30 = 29/30; 6 3/4 − 2 2/3 converted to improper fractions and then to twelfths). Students also solve related fraction equations and comparisons elsewhere on the review sheet.
Unit 7: Dividing Fractions
Lesson 2
Getting Ready to Divide Fractions
Students encounter addition and subtraction of fractions in the Basic Skills Review items and answer key: the pizza problem shows 3/8 + 1/4 converted to 3/8 + 2/8 = 5/8 and subtraction from 1 to get 3/8, and the distance problem shows subtraction of mixed numbers (8 2/5 - 6 1/10) with conversion to improper fractions and common denominators. Activity 2 explicitly instructs students to "convert any improper fractions to mixed numbers," indicating attention to mixed-number form. The answer keys display the procedure of creating equivalent fractions (e.g., converting 1/4 to 2/8) in worked solutions.
Unit 8: Volume
Lesson 1
Perimeter and Area Review
Students solve problems with fractional and mixed-number side lengths (for example, a rectangle with sides 3 1/3 ft and 2 1/4 ft) where they compute perimeter by adding mixed numbers and compute area using multiplication of converted improper fractions (answer key shows 2 1/4 × 3 1/3 = 9/4 × 10/3 = 7 1/2). Several tasks (the package, sandbox, and other problems) require working with mixed numbers and fractions (e.g., 4 1/2 yards, 1/3 ft). The answer key demonstrates converting mixed numbers to improper fractions and finding common denominators when adding (for perimeter calculation resulting in 11 1/6 ft).
Lesson 3
From Area to Volume
Students are asked to add fractions with unlike denominators in Basic Skills Review: Tanner ate 1/6 and Bess ate 1/4 of the same pizza, and students compute 1/6 + 1/4 = 5/12 and then subtract from 1 to find 7/12. Another item asks students to work with a fraction and a whole number (1/8 and 7), indicating at least one other fraction addition task. The answer key shows the correct combined result for the unlike-denominator addition, indicating students produce a common-denominator result.
Lesson 4
Volume and Unit Cubes
Students complete the Basic Skills Review that includes adding fractions with unlike denominators (e.g., 4/5 + 1/3 + 2/3) and then subtracting the result from a whole number (2 − 1 4/5). The provided answer key shows students converting to equivalent fractions with a common denominator (4/5 = 12/15, 1/3 = 5/15, 2/3 = 10/15) and adding to get an improper fraction, then converting to a mixed number and performing the subtraction.
Lesson 6
Practicing the Algorithm
Students complete a Basic Skills Review that requires adding and subtracting fractions and mixed numbers (for example, 2/5 + 2/3 + 2/3 = 26/15 = 1 11/15 and then 2 − 1 11/15 = 4/15). The Marcus mini-pizza problem also has students convert and subtract mixed numbers (1/3 × 17 = 17/3 = 5 2/3; 5 2/3 − 4 1/2 = 1 1/6). These tasks show students practice computations that involve unlike denominators and mixed-number subtraction.
Unit 9: Skills Review
Lesson 1
Fraction Operations
Activity 1 is titled "Adding and Subtracting Fractions" and directs students to play two online games (Fruit Splat Fraction Addition and Fruit Splat Fraction Subtraction). The Parent Plan explicitly states that "your child will play two games to review the use of equivalent fractions in the addition and subtraction of fractions" and tells students to focus primarily on working with unlike denominators. The Skills list also names "Add, subtract, multiply, and divide fractions with like and unlike denominators (including mixed numbers)."
Lesson 4
Geometry
The Parent Plan explicitly states students will "make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8)" and "use operations on fractions to solve problems involving information presented in line plots," which indicates students will work with fractional measurements and perform fraction operations. The Corn Growth activity provides data with fractional values (1/2, 2 1/2, etc.) and asks students to compute growth amounts (e.g., "How much did the corn grow between week 6 and week 8?"), requiring subtraction of fractional measurements. The Swim Team and line-plot tasks require placing fractional-unit marks on plots in the skills description, supporting practice with fractions in measurement contexts.
