Fourth Grade - MATH
5: Math
Unit 1: Place Value to 1,000,000
Lesson 1
Numbers to 10,000 Review
Students practice telling time and answer a time-interval question in the Basic Skills Review (e.g., "What time will it be in an hour? (3:45)"), and they compute perimeter and area by multiplying side lengths in the Perimeter and Area Review. Students also work with simple fractions on Fraction Review (identifying and shading fractions) and complete multiplication facts (7×10, 5×9) that support computation.
Lesson 9
Problem Solving
Students solve multi-step word problems that require addition and subtraction (e.g., totaling Carly and Caleb's cans, finding how many more cans are needed, comparing Caleb and Carly, summing pages read across months). Students use multiplication and subtraction in context (e.g., Sophie has sold twice as many tickets as Samuel; Simon has sold 150 fewer tickets). Students practice estimation and rounding to judge closeness to goals and to estimate sums and differences.
Lesson 10
Unit Test
Students solve money word problems that require addition (e.g., babysitting earnings of $126, $515, and $517 are totaled to determine if a purchase is affordable) and solve difference problems (e.g., attendance difference between Saturday 1,152 and Sunday 1,008). Students compute totals and differences in several exercises (e.g., stamp counts 459+255+388 and finding how many more to reach a goal), and complete many addition and subtraction problems with large whole numbers to build fluency.
Unit 2: The Four Operations
Lesson 1
Addition Practice and Problem Solving
Students practice adding multi-digit whole numbers using the standard algorithm and place-value alignment through examples (e.g., 4,738+2,786; 46,309+37,829; nine-digit and million-making activities). Several word problems require adding measurement and money quantities: totaling zoo visitors (23,652 + 30,122), combining water volumes in gallons (297,000 + 352,000), and adding car costs ($34,661 + $46,233). The "Making One Million" and other addition sheets ask students to form pairs or sums that reach a specified measurement total (1,000,000), reinforcing addition of large measurement-like numbers.
Lesson 2
Subtraction Practice and Problem Solving
Students solve subtraction word problems that involve money (Pablo withdrawing $11,360 from $16,220) and masses (comparing average whale weights of 300,000 and 60,000 pounds). Students practice multi-digit subtraction with five- and six-digit numbers (Subtracting Five-Digit and Six-Digit Numbers sheet) and use subtraction in sequential contexts (Subtraction Ladders). Students check subtraction answers using addition and use estimation and mental computation to assess reasonableness (whiteboard activities and estimation questions).
Lesson 3
Multiplication and Its Properties
Students solve a set of multiplication and division word problems that include money (e.g., Sam earns $9/hour for 11 hours; Alex sold $8 tickets and earned $56) and a measurement context in yards (Hannah has 38 yards and each costume needs 5 yards). In the introduction, students are asked to model 5 × 6 using drawings, arrays, counters, or a number line, giving explicit opportunity to represent quantities with a diagram. The activity set also has students write multiplication or division sentences for story problems and solve them (e.g., teams × players, octopus legs).
Lesson 4
Reviewing and Writing Division
Students solve word problems that use multiplication and division with measurement contexts such as money (Alex sold $56 of $8 tickets; posters $96 at $12 each) and time (What time will it be in a quarter hour?). Students compute with measured quantities in the yardage problem (38 yards ÷ 3 yards per costume) and find leftovers using division with remainders. Students practice the four operations in the basic skills review and use multiplication to check division answers; they also work with a fraction shading task (5/12).
Lesson 5
Playing With the Four Operations
Students practice using all four operations in word problems on the "Four Operations Word Problems" page (addition, subtraction, multiplication, division) and solve example problems such as cups of lemonade, dividing gum, and counting toy cars. Students create two addition, subtraction, multiplication, and division problems to reach a chosen target number on the "Creating Problems" page, and they identify key words that indicate which operation to use. Students also use a calculator game and practice moving multiplication facts among bags and tracking facts on a multiplication table.
Lesson 8
Prime and Composite Numbers
Students perform addition and subtraction with money (examples: $4092+$3146 and $6714−$4380) and are reminded to label amounts with a dollar sign. Students answer a time-interval question ("What time was it 25 minutes ago?") that requires working with minutes. Students work with a simple fraction (shade 4/10) and basic operations (e.g., 7 x 80) on the Basic Skills Review.
Lesson 11
Working With Equations
Students solve for missing numbers using all four operations in scaffolded worksheets (addition, subtraction, multiplication, division panels) and practice balancing equations with a pan-balance model. Students solve word problems that use operations in measurement contexts such as money (Renata saves $2 per day to reach $20) and time (finding what time it was 20 minutes ago). Students also apply operations to group/partition problems (players divided into teams) and complete mixed-operation equation problems.
Lesson 12
More Work With Equations
Students solve whole-number word problems using all four operations and write equations with a letter for the unknown (e.g., 53 + 21 = n; 5 × a = 25; n ÷ 3 = 8). The materials include money contexts (Beth earned $12 babysitting; find how much she started with) and a time context (Marty reads 5 books every month; determine how many months have passed). Students match word problems to equations, create equations from problems, and produce word problems to match given equations.
Lesson 14
Unit Test
Students solve multi-digit addition and subtraction word problems with money and counts (e.g., adding city populations, subtracting ride cost from a budget, hospital donation totals, packages remaining in a warehouse). Students solve multiplication and division word problems about repeated groups and sharing (e.g., Lance collected four times as many cans, Susie walked three times as many dogs, Emily giving 6 friends 8 M&Ms each). Students set up and solve equations using the four operations to find unknowns (e.g., 12 + x = 23, a ÷ 3 = 8, 6 + n = 12, n × 7 = 49).
Unit 3: Geometry
Lesson 2
Points, Lines, Line Segments, Rays
The Basic Skills Review asks a time-interval question: "What time was it 40 minutes ago? (10:52)," which requires students to subtract minutes. The review and other exercises ask students to perform addition and division (e.g., 356,119 + 257,874 and remainder when dividing 16 by 3), so students practice the four operations. Students are also asked to draw lines, line segments, and rays on laminated dot paper (a grid) and are told a line is like a number line, connecting the geometric drawing activities to the idea of a measurement diagram.
Unit 4: Multi-Digit Multiplication
Lesson 3
Multiples of 10, 100, and Beyond!
Students solve multiple word problems that require multiplication with measurement contexts such as money (Alex selling tins for $8; Patty selling ornaments for $7) and mass (the pet shelter needing pounds of cat food for 3, 30, 300 cats). Students compute multi-step and single-step quantities (Marcus with 30 bags of 20 marbles, then 10 more bags; calculating totals for tables seating 6 people for 2, 20, 200 tables). Students practice scaling whole-number measurements by factors of 10, 100, 1000 across many problems and match equivalent products using place-value reasoning.
Lesson 4
Multi-Digit Multiplication Using Arrays
Students solve multistep word problems involving whole-number multiplication (Activity 3 word problems: hotel rooms, babysitting pay, seating capacity). Students represent multiplication quantities using diagrams: arrays, base-10 blocks, and area models throughout Activities 1–3 and the example breakdowns (e.g., 26 x 18 shown with base-10 arrays and partial products). The Skills section explicitly lists solving multistep word problems with whole-number answers and illustrating calculations using rectangular arrays or area models.
Lesson 7
Multiplication Practice
Students solve multi-digit multiplication word problems such as "Chef Charles bought 96 boxes of meatballs. Each box contained 58 meatballs. How many meatballs did he buy in all?" and "At the sporting good warehouse, each shipment of tennis balls contains 89 balls. How many tennis balls will there be in 76 shipments?" Students also solve a time-interval problem in Basic Skills Review (Kathleen started running at 11:24 and stopped at 12:05; how long did she run?). The materials include practice with multiplication, some division/remainder items, and problems that require using multiplication to find totals from measured counts.
Lesson 8
Unit Test
Students solve multiplication word problems that involve money (55 shirts at $20; Mrs. Planter bought 33 bags at $12) and mass (18 bags × 55 grams of jellybeans). Students solve a distance problem (124 miles/day × 14 days and 164 miles/day × 12 days) and determine who drove more, which involves multiplication and comparison. Students also use visual methods (arrays, area models, grids) and standard algorithms to represent and compute measurement quantities.
Final Project
Multiplication Contract
Students are required to create and explain multi-digit multiplication strategies using equations, rectangular arrays, and area models (Skills and contract choices), which gives practice representing measurement-like quantities with diagrammatic models. The rubric explicitly requires the student product to include at least one word problem involving a real-world use of multi-digit multiplication (Explaining the Strategies Evaluation: Examples). The 'How to Subtract' page includes a number line strategy that has students place and hop on a number line to solve subtraction, demonstrating use of a diagram to represent quantities.
Unit 5: Fractions
Lesson 3
Comparing Fractions
Students place and label fractions on number line diagrams (several activities ask them to mark fractions such as 3/8, 5/6, 5/4, 1/3, 3/4, etc.) and use those number lines to decide which fraction is larger or smaller. Students draw pictures and use benchmark reasoning (using 1/2) and fraction charts to compare fractions and record comparisons with <, >, or =. The activities explicitly use number line diagrams as a representation to visualize and compare measurement quantities (fractions).
Lesson 6
Adding Fractions
Students practice adding simple fractions with like denominators across multiple activities and worksheets (calculation problems, visual fraction circles, and interactive tool exercises). Students are asked to represent fractions on a number line and an image explicitly shows a number line divided into sixths with a point at 3/6 and an arrow indicating a 1/6 increment. Students use number-line diagrams and fraction visuals to model and visualize fractional quantities and their sums.
Lesson 7
Subtracting Fractions
Students practice subtracting fractions with like denominators using fraction strips and worksheets (examples: 7/8 - 5/8 = 2/8 and many practice problems with like denominators). Students represent fractional differences on number lines and are asked to label and show problems such as 3/6 - 1/6 and to circle number lines that show 6/8 - 3/8. Students also use interactive fraction-subtraction tools and games to visualize and practice the subtraction of fractions with common denominators.
Lesson 9
Solving Fraction Problems
Students solve word problems that use fractions in measurement contexts: problems explicitly reference miles (walking/running distances) and gallons of milk, and items like pizza and candy bars. Students are instructed to read each word problem, write an equation using fractions with like denominators, compute sums or differences, and simplify results. The Fraction Maze and practice sheets require students to choose paths or answers by solving fraction addition and subtraction problems.
Lesson 11
Subtracting Mixed Numbers
Students solve word problems that use mixed-number addition and subtraction with measurement contexts: one word problem asks for total pounds of candy (mass) and another asks for the difference in miles to the park (distance). Students practice adding and subtracting mixed numbers in the Addition and Subtraction Practice page and in Activity 1 and Activity 2, including verifying answers by addition and using stacking and regrouping. Students represent fractional measurement quantities using pictorial circle diagrams in the Subtracting Mixed Numbers activity and answer keys.
Lesson 13
More Practice and Problem Solving
Students solve numerous measurement word problems that use fractions: cooking problems require adding and multiplying cups (liquid volume), a drive-of-360-miles problem asks students to compute remaining distance, and hay/ pumpkin problems ask students to compute pounds (mass). Students perform addition, subtraction, and multiplication with fractions and mixed numbers (e.g., totals of cheese, tripling recipes, 3/8 of 32 players). Several problems include or encourage diagrams and number-line visuals (the driving problem and instructions to use number lines for problems 1–3).
Lesson 14
Unit Test
Students solve multiple word problems that use fractions and the four operations of addition, subtraction, and multiplication, e.g., running distances (miles), milk measured in gallons, teaspoons of salt, and cups of ingredients. Students are asked to write equations and draw pictures to solve problems such as comparing distances (How much farther did one student run?), combining amounts of pizza or snack mix, and scaling recipes (3/4 x 7 batches). One item explicitly asks students to convert 3/5 gallon into cups, indicating work with expressing a larger unit in terms of a smaller unit.
Unit 6: Multi-Digit Division
Lesson 3
Getting Started With Long Division
Students solve multi-step word problems that require division and checking with multiplication, including a money problem where Katrina has $78 and buys $5 sticker books to determine how many she can buy and what remains. Students solve other real-world division problems (e.g., 65 fair tickets at 3 tickets per ride, dividing cookies among friends, dividing candy among people) and practice interpreting remainders. Students also perform and simplify fraction computations (5/8 + 1/8, 2 × 2/3, 7/12 − 1/12) and are instructed to check division answers using multiplication.
Lesson 5
Division Problem Solving
Students solve a variety of division word problems that involve money (the $3-per-car-wash problem with $261), distance/time (Erin ran 120 miles over 6 weeks to find miles per week), and grouping/units (people per bus, groups through a corn maze). Students set up long-division computations, interpret quotients and remainders, and check answers with multiplication or a calculator. Students also practice forming and solving three- and four-digit dividend ÷ one-digit divisor problems and apply division to contextual situations.
Lesson 6
Unit Test
Students solve multiple real-world division word problems that involve money and grouping (e.g., David has $130 and each lunch costs $9; the concert raised $582 at $4 per ticket; Sarah's donuts shared among people). Students compute quotients and remainders for multi-digit dividends (examples: 6213 ÷ 4, 581 ÷ 3, 2799 ÷ 9) and write division equations and interpret remainders in context (donuts left over, chairs in last row, tickets left over). Students practice writing division sentences and finding quotients using long division representations.
Unit 7: Decimals
Lesson 2
Fractions With Denominators 10 and 100
Students convert fractions with denominator 10 to equivalent fractions with denominator 100 (e.g., 3/10 -> 30/100, 4/10 -> 40/100) in multiple activities and worksheets. Students add fractions in measurement contexts, solving addition problems and a cake word problem that sums fractional parts (e.g., total eaten = 77/100). Students compare fractional amounts of money using coins (3/10 of a dollar as 3 dimes vs 3/100 as 3 pennies) and are prompted to use coins to reason about dollar amounts.
Lesson 4
Fractions and Decimals
Students count and combine coins on the "Working With Money" pages to make specified cent amounts (e.g., 54¢, 98¢) and write those amounts as fractions of a dollar, decimals, and percents. Students convert fractions with denominators 10 or 100 into decimal and percent form in the Base-10 Fractions and Decimals table and in multiple converting exercises. Students create and match fraction-decimal card pairs and complete practice items that link fractions (like 11/20 or 3/10) to their decimal equivalents.
Lesson 6
Decimals on Number Lines and Grids
Students locate and label decimals (tenths and hundredths) on multiple number lines, including values between 0 and 1 and decimals greater than 1, by writing numbers under hash marks and placing flags in online games. Students represent decimals with grids by shading tenths and hundredths to model values like 0.3, 0.41, 0.95, and mixed decimals such as 1.23. Students also practice decimal and fraction equivalence (e.g., 0.2 = 0.20) and complete basic arithmetic and fraction problems on the Basic Skills Review.
Lesson 8
Unit Test
Students solve word problems that use decimals and fractions: e.g., the cake problem where students compare amounts (2/8, 0.2, 0.1, 1/10) and add them to find the total eaten. Students compare distances using decimals in the running problem (0.07 vs 0.7) and compare monetary amounts in the intro (choose $5.50 vs $6.50). Students practice adding and subtracting decimals and fractions on worksheets and are invited to use a laminated number line and linked online number-line activities to place decimals.
Unit 8: Measurement
Lesson 1
Customary and Metric Units
Students practice converting between metric units using the staircase/moving-decimal method (for example, converting 100 meters to .1 km, 1 hm, 10 dam, 1000 dm, 10,000 cm, 100,000 mm). Students identify and classify customary and metric units of length, weight/mass, and capacity in multiple activities and sort/cut-and-paste the appropriate unit for given items (Which Unit Is Best? activities). Students use and record specific conversion facts (e.g., 1 cup = 8 fl oz, 12 in = 1 ft, 1000 ml = 1 L) in fill-in-the-blank and matching exercises.
Lesson 2
Converting Units of Length
Students complete conversion charts and tables for customary and metric lengths (inches, feet, yards, miles; millimeters, centimeters, meters, kilometers) and use rules that going from a large unit to a small unit means multiply and vice versa. Students perform numeric conversions that include decimals (e.g., 5 m → 0.005 km, 0.5 m → 50 cm) and practice multiplying and dividing by unit factors. Students measure real objects with a ruler and convert those measurements (e.g., centimeters to millimeters) and order index cards of mixed metric measures from shortest to longest.
Lesson 3
Converting Units of Weight
Students convert between customary weights (ounces, pounds, tons) using provided tables and fill-in-the-blank items (e.g., 16 oz = 1 lb, 2000 lb = 1 ton) and complete matching and ordering exercises with half- and quarter-pound amounts. Students use multiplication and division explicitly to change between larger and smaller units (rules stated and practiced) and complete metric conversions including decimals (e.g., 300 g = 0.3 kg) and milligram/gram/kilogram conversions. Students create a metric flip chart and use the King Henry mnemonic to write and test equivalent measures for metric units.
Lesson 4
Converting Units of Capacity
Students are given facts and practice converting between customary and metric capacity units and are instructed to use multiplication and division to convert between units. Students solve volume word problems such as comparing Marcie (16 cups) and Francie (10 pints) and adding 3500 mL + 2 L, requiring addition and comparison. Students draw pictures or use shaded grids and visual boxes (cup, pint, quart, gallon) to represent how smaller units fit into larger ones.
Lesson 5
Practice and Problem Solving
The Skills list and Activities direct students to use the four operations and to convert within a measurement system. Activity 2 provides multiple word problems that require operations and unit conversion (e.g., pints/quart to cups; inches/feet remaining length; ounces to pounds; liters and milliliters totaled; kilograms to grams; feet/inches difference; meters to kilometers; meters to centimeters). Activities 3–4 and the wrapping up pages require students to create and interpret line plots on number lines with fractional scales (insects, rabbit weights, distances in fractions), and the Introduction explains when to multiply or divide to convert units.
Lesson 6
Working With Time
The Skills section explicitly states students will "use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money." Multiple activities have students convert time using multiplication and division (e.g., converting hours → minutes → seconds, decades → weeks) and solve time word problems such as Carlie (minutes → seconds), Matthew (1 1/2 hours → seconds), and Sarah (hours × $11 per hour). The Basic Skills Review and other pages include work with fractions and decimals (e.g., 1 1/2 hours, 24.72 expanded form, comparisons between decimals and fractions).
Lesson 7
Reviewing Perimeter and Area
Students calculate perimeter by adding side lengths for several rectangles (e.g., P = 5 + 5 + 6 + 6 = 20 feet) and complete a 'Finding Perimeter' sheet with specific numeric perimeter problems in units like cm, feet, meters, and yards. Students compute area by multiplying length and width for rectangles on the 'Finding Area' sheet (e.g., A = 6 × 4 = 24 square feet) and solve contextual area problems about rooms requiring flooring. Students solve comparative and adjustment problems that use subtraction or addition reasoning (e.g., 'How much greater is it?' and 'what must he do to the width...') to compare perimeters and change a dimension to reach a target perimeter.
Lesson 8
Working With Perimeter and Area
Students solve perimeter and area word problems using all four operations: they add side lengths to find perimeters, subtract known side sums from a total perimeter and divide to find missing side lengths, and divide area by width to find length. Activity problems require students to compute areas of composite figures by multiplying dimensions and subtracting removed sections (e.g., finding patio area by subtracting pool area). The Basic Skills Review asks students to calculate time intervals (e.g., 6:54 to 7:19 and working back 35 minutes), work with decimals and fractions (write 8.07 in expanded form, compare decimals and fractions, add 5/100 + 2/10), and perform multi-step numeric computations.
Lesson 9
Connecting Perimeter and Area
Students compute areas and perimeters of rectangles with given side lengths (e.g., 1×16 cm, 4×4 cm) and record answers with units such as cm, ft, and in. Students solve for missing side lengths by using area and perimeter relationships on the activity pages (e.g., deducing an unknown side when area and equal perimeter are given). Students draw and label rectangles on a grid and use arithmetic (addition, multiplication, division) to find dimensions, areas, and perimeters.
Lesson 10
More Practice and Problem Solving
The lesson's Skills section explicitly tells students to "express measurements in a larger unit in terms of a smaller unit" and to "use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money." Activity 1 has students convert and compare measurements (e.g., 9000 ft vs 2 miles, 3 cm vs 30 mm, many paired comparisons on the student page). Activity 2 (Working With Recipes and Lasagna) has students add and subtract fractional and decimal measurements (cups, tablespoons, teaspoons, ounces, pounds) and scale a recipe (doubling lasagna), with answer keys showing fractional and decimal conversions (e.g., 0.5 liters < 5000 milliliters).
Final Project
Measurement Think-Tac-Toe
Students choose converting-units activities (matching games, a teaching poster, and a converting worksheet) that require them to change measurements within and between metric and customary systems and to express larger units in terms of smaller ones. The skills list explicitly says students will express measurements in a larger unit in terms of a smaller unit, and the Perimeter and Area tasks ask students to measure everyday objects, use a grid (square feet), and compute perimeter and area. The materials mention using rulers, a yardstick, meter stick, and tape measure so students will gather and use measurement tools to produce numerical measurements.
Unit 9: Skills Review
Lesson 3
Fractions and Decimals
Students solve word problems that add and subtract fractions in measurement contexts (e.g., Carlie walks fractional parts of a mile; 3/10 + 2/10 = 10/10 of a mile). Students solve a liquid-volume word problem (7/8 - 2/8 = 5/8 of a gallon of milk). Students practice converting fractions and decimals and ordering decimals, which connects fractional/decimal measurement notation.