Fifth Grade - MATH
5: Math
Unit 1: Place Value
Lesson 5
Comparing Decimals
Students complete a Basic Skills Review item that asks them to divide 6,452 by 6 and find the remainder, showing practice with a four-digit dividend and a whole-number divisor. The review explicitly labels this as a "Division with Remainder" problem, indicating students perform long-division style computation on a multi-digit dividend.
Lesson 7
Powers of 10
Students complete problems that produce whole-number quotients such as 1,000 ÷ 10 = 100 (Activity 3) and 3,455 ÷ 7 = 493 R 4 (Basic Skills Review). Students practice multiplying and dividing whole numbers and decimals by powers of 10 and use place-value reasoning to move zeros and decimal places (matching exercises and parent/answer keys). Students write exponential form for powers of ten (10^6) and fill number lines showing successive multiplication by 10, reinforcing place-value strategies for division by 10 and other powers of ten.
Unit 2: Four Operations
Lesson 3
Dividing Multi-Digit Numbers
Students practice long division with two-digit divisors and multi-digit dividends in Activity 4, including problems such as 2568 ÷ 12 and 322 ÷ 14 and guided long-division steps for 525 ÷ 15. Students use place-value strategies in Activity 1 by simplifying dividends and divisors that end in zeros (for example, reducing 1,200 ÷ 30 to 120 ÷ 3) and check quotients by turning division into multiplication equations. Students use concrete/models in Activity 2 with base-ten blocks to represent grouping and division visually and are asked to create multiplication tables to support choosing quotients during long division.
Lesson 8
Dividing Decimals
Students model decimal division with base-10 blocks, drawing flats, rods, and units to split quantities (e.g., 2.8 ÷ 4 → 0.7) and use those place-value models to reason about quotients. Students set up and perform long division in vertical (long division) form, move decimal points when divisors are decimals (e.g., convert 6.5)80.6 to 65)806), and check results by multiplying the quotient and divisor. Several practice problems require dividing multi-digit dividends (e.g., 806 ÷ 65 example) and students are instructed to align place value and position decimal points in the quotient.
Lesson 9
Solving Problems Using the Four Operations
Students solve division problems such as 416 ÷ 5 to find sugar per batch and compute shares like 47.4 ÷ 12 for splitting the fruit salad; students also compute unit costs using division (e.g., $1.44 ÷ 12 to find cost per donut). The instructions require students to write number sentences, show work in large blank areas, circle keywords, and are encouraged to draw pictures to help solve problems.
Lesson 13
Unit Test
Students are given whole-number division problems with up to four-digit dividends and two-digit divisors (for example, 2,795 ÷ 65 on the Unit Test and 2,580 ÷ 12 in a word problem) and other division items such as 456 ÷ 24. Several problems require students to compute and write answers (many answer keys show whole-number quotients), and some pages instruct students to "show your work." The review and test include multiple real-world division tasks where students solve for number of groups or units.
Unit 3: Measurement
Lesson 2
Converting Units of Measurement
Students practice deciding when to divide versus multiply in unit conversions and compute quotients in examples such as 36 ÷ 12 = 3 and 36 quarts ÷ 4 = 9. Activity prompts require students to perform divisions to convert measures (e.g., 60 inches = ? feet, How many inches are in 5 miles?) and the Basic Skills Review includes a division reasoning item (dividend 20,000 with quotient 40 asks for the divisor). The materials explicitly state that division and multiplication are inverse operations and ask students to think "what do you multiply by to get..." when solving conversion division problems.
Lesson 3
Measurement Problem Solving
The lesson includes explicit division equations and visual supports for unit-conversion divisions, for example the image and text showing "82 ÷ 16 = 5 R 2" with five full 16-oz bags and a partial bag. Student problems require performing division in conversion contexts such as 20 ft ÷ 3 = 6 R 2, 423 in ÷ 12 = 35 R 3, and 720 in ÷ 36 = 20 (converting inches to yards). Students also convert 7,056 grams to kilograms and grams by grouping into thousands, showing use of division to produce whole-number quotients and remainders in context.
Lesson 4
Working With Time
The materials explicitly tell students that converting from a small unit of time to a large unit requires division and give worked conversion problems that require division (e.g., 600 years ÷ 10 = 60 decades; 154 hours ÷ 24 = 6 days remainder 10 hours; 330 seconds ÷ 60 = 5 minutes 30 seconds). Multiple activity items ask students to convert and compare time by dividing (for example converting minutes to hours and seconds to minutes in the Converting Units of Time and Adding/Subtracting Time pages). The "Things to Know" and answer-key explanations show students carrying out division to find quotients or quotients with remainders in those contexts.
Lesson 6
Unit Test
Students perform whole-number division in multiple word problems and test items (for example, dividing 2,000 milliliters by 10 to get 200 ml per person in Beth's tea problem, dividing 504 inches by 36 to get 14 yards in Mollie's string problem, and dividing 1,800 meters by 600 meters to get 3 laps in Marla's track problem). Students complete conversion and comparison tables and calculations that require dividing measurements (e.g., converting inches to feet, grams to milligrams, and hours to days using division). The Unit 3 Test and review pages contain numerical problems where students compute quotients of multi-digit dividends by two-digit or smaller divisors as part of solving real-world measurement tasks.
Final Project
Measurement Book
Students are asked to solve and create measurement conversion word problems that involve division (for example, the sample time worksheet shows 300 minutes ÷ 60 = 5 hours). The project directions and the 'Questions to Consider' explicitly list problem-solving using strategies like adding, subtracting, multiplying, or dividing. Page 8 requires students to create converting-between-units problems and provide answers, so students will perform division when converting units in context.
Unit 4: Adding and Subtracting Fractions
Lesson 9
Problem Solving With Fractions
Students perform whole-number division in Basic Skills Review problems: they divide 64 ounces by 32-ounce containers to find the number of containers (2), and they divide total ounces of batter (240 oz) by 48 cupcakes to find ounces per cupcake (5). Another problem asks for a quotient when the dividend is 145.2 and the divisor is 8, which asks students to compute a quotient of a division problem.
Unit 5: Multiplying Fractions
Lesson 2
What Does Multiplying by a Fraction Mean?
Students compute fractional parts by dividing whole numbers into equal parts (for example, 1/3 of 15 is shown as 15 ÷ 3 = 5 and students divide a 0–15 number line into three equal parts). Students use visual models such as a 30-circle array to find 1/6 of 30 and number-line arcs to represent 2/3 of 12, linking multiplication by a fraction to division. The materials repeatedly ask students to represent 'fraction of' problems as multiplication and as a division (e.g., showing 1/3 × 15 as 15 ÷ 3).
Unit 7: Dividing Fractions
Lesson 1
Reviewing Division
Students practice finding quotients for multi-digit dividends (e.g., 4810 ÷ 10, 312 ÷ 12, 625 ÷ 5, 536 ÷ 4, 392 ÷ 7) on the "Basic Long Division Review" sheet and are directed to use the "Long Division Steps" and a long-division video. The materials prompt students to use multiplication facts to solve mental division problems and explicitly note that division is the opposite of multiplication. The lesson includes visual images of division as equal groups and grouping (cookies and coins), which model division with physical arrays/groups.
Unit 8: Volume
Lesson 3
From Area to Volume
Students complete Basic Skills Review items that require division, including computing 156 ÷ 12 as part of a comparison problem and finding the quotient 1.92 ÷ 0.06. Students also solve division-related fraction problems (for example, dividing 6 pizzas into eighths to find the total number of pieces).
Lesson 7
Extending Work With Volume
Students set up and solve equations using V = l × w × h and B × h = V to find missing dimensions (for example, 400 = 10 × 8 × h followed by 400 ÷ 80 = 5). Multiple activity pages ("Something's Missing") ask students to solve for a missing measurement by dividing a known volume by a known product (area or product of two dimensions). The lesson also presents visual decompositions of prisms into layers and uses base-area × height reasoning that connects multiplication and its inverse, division.
Lesson 8
Problem Solving
Students compute and use multiplication to find volumes in multiple problems (e.g., 20 × 20 × 15 = 6,000 and 10 × 10 × 10 = 1,000). A few tasks require solving for a missing dimension, which implicitly requires division (e.g., Charlie choosing dimensions for volume 48 with height 6, and Noah's prism where students solve 16 × 6 × ? = 960). The wrap-up questions also include solving for height given base area and volume (36 ÷ 12 = 3).
Unit 9: Skills Review
Lesson 2
Decimal Operations
Students solve division problems that involve two-digit divisors (e.g., 112.2 ÷ 17 and 61.2 ÷ 18) and complete word problems requiring division (e.g., 581.7 ÷ 7 for equal batches). The activity pages provide spaces for students to perform the computations and record quotients, and answer keys show the expected quotients for these division tasks.
Lesson 3
Measurement
Students solve Missing Dimensions problems where they find an unknown side by dividing a prism's volume by the known dimensions (e.g., Bilal's toy box: 24 ÷ (4 × 2) = 3). Students write math sentences using V = l × w × h and use division to undo multiplication when finding missing dimensions (Heidi: 288 ÷ 8 = 36, then find square root to get side length). The activities require students to compute volumes by multiplying whole numbers and then use those multiplication equations to reason back to missing factors.
