Students are asked to round numbers (to the nearest 10 and 100) and to use rounding to check the reasonableness of addition (for example comparing 359+132 with 360+130 and noting the sums 491 and 490). Students complete contextual rounding items (Maria's 242 pieces of candy and Jasmine's $128) that require estimating answers by rounding. Students also practice mental rounding with time (rounding times to the nearest hour, quarter hour, or five minutes).

Students practice fluently adding and subtracting multi-digit whole numbers using the standard algorithm through many vertical practice problems and guided examples. Students use rounding to estimate sums (e.g., rounding to the nearest 100 or 1,000) and compare estimated and actual sums on the "Adding Big Numbers" activities and answer key. Students solve one-step subtraction word problems by writing the subtraction equation and computing the difference (e.g., cupcakes, soccer game, bird counts).

Students practice rounding multi‑digit whole numbers to the greatest place and use that rounding to estimate sums and differences in multiple activities. Students complete exercises where they round numbers, compute estimated sums/differences (e.g., 1,926 + 1,529 → 2,000 + 2,000 → 4,000), and then find the true sum or difference to compare. Students also use estimation to decide whether expressions are greater than or less than given benchmarks (e.g., 761 + 308 ____ 1,000).

Students solve multistep word problems involving whole numbers in the "Are They There Yet?" tasks where they add totals (465 + 614 = 1,079), subtract to find how many more are needed (2,000 - 1,079 = 921), and use multiplication and division (Sophie sold twice as many as Samuel; dividing remaining tickets among three). The activity explicitly asks students to use rounding and estimation to assess closeness to goals (use estimation to judge whether 365 + 524 is close to 1,000 and directions to use rounding to estimate). Skills and directions also prompt students to fluently add/subtract multi-digit numbers and to round multi-digit whole numbers.

Students solve several whole-number word problems using addition and subtraction (e.g., adding babysitting earnings for June, July, and August; finding the difference in attendance between two days; totaling stamps and finding how many more are needed). Students practice multi-digit addition and subtraction problems and perform numerous rounding exercises (rounding to the nearest hundred, thousand, ten thousand).

The Skills section explicitly lists assessing the reasonableness of answers using mental computation and estimation strategies including rounding. The Introduction asks students to use estimation to judge whether a difference is greater than or less than benchmark values and to check subtraction using addition. Multiple student activity pages provide word problems that require computing whole-number differences (e.g., notebooks remaining, bank withdrawal, marathon finishers, whale weight difference).

Students are asked to complete a "Multiplication and Division Word Problems" page and to write out the multiplication or division sentence for each question and then solve the problem. The problem set includes division problems that require interpreting remainders (e.g., Hannah with 38 yards and 5 yards per costume) and division-to-find-count problems (e.g., Alex sells $8 tickets and earns $56). Students also practice forming multiplication sentences for multiplicative comparison problems in the Introduction (e.g., writing 7(x)3 for "7 groups of 3").

Students practice dividing whole numbers and interpreting remainders through multiple activities (e.g., Division With Remainders problems 9÷4, 16÷5, 20÷7 and long-division practice). Students check division by using multiplication and addition (steps shown: multiply quotient by divisor and add remainder to match the dividend). The lesson includes word problems that require division and remainder interpretation (Hannah's cloth: how many costumes and how much cloth is left; Jake's stuffed animals: how many per patient and how many left over). A basic skills review includes a rounding problem, giving students practice with rounding.

Students represent unknowns with letters and solve for variables (e.g., 12+n=18, x+3=10, 28 ÷ y = 4). Students solve and balance equations across all four operations via activities and worksheets that require filling in missing addends, factors, quotients, and differences. Students use a pan-balance model and interactive tool to make both sides equal and to find numbers that balance an equation.

Students practice writing and solving equations with a letter for the unknown as shown by problems like 53 + 21 = n, 5 x a = 25, 3 x 7 = b, and n ÷ 3 = 8. The Skills list explicitly states students will "Solve word problems posed with whole numbers...using the four operations" and "Represent word problems using equations with a letter standing for the unknown quantity." Matching and activity pages require students to read word problems, choose or match the correct equation, and solve for the variable.

Students practice applying two-step numerical rules in input-output tables and 'What's the Rule?' activities where they multiply, add, subtract, and divide to get outputs from inputs. Students use t-charts to solve word-style problems about sums and differences (e.g., find two numbers given their sum and difference). Students use rounding in number-riddle items (round to nearest 100 or 1000) and follow multi-step procedures on sequences in the 'Think About It!' problems.

Students solve numerous whole-number word problems using the four operations (e.g., population totals, amusement-park expenditure, hospital donations, museum visitors, packages shipped, Lance/Sean cans, Martha's babysitting money, Emily's M&Ms). Students represent and solve equations with a letter for the unknown in several items (e.g., 6 + n = 12; 12 + x = 23; a ÷ 3 = 8; n × 7 = 49). Students perform division problems that display remainders (e.g., 35 ÷ 3 = 11 R2; other quotient exercises showing remainders).

The Skills section explicitly states that students will "Represent problems using equations with a letter standing for the unknown quantity." The Getting Started questions include "How can we use the four operations to figure out unknown numbers?" and the "Who am I?" story prompt asks students to find a number by "solving various puzzles and some math operations." The project checklist and evaluation sheet require that the collection "Teaches about variables in equations."

Students practice basic operations and related skills on the "Basic Skills Review #8" page, including finding a remainder ("What is the remainder when you divide 20 by 8?") and solving for an unknown in an equation ("4 x n = 28. What is n?"). The review also has multi-digit subtraction (416,728 - 335,733) and multiplication (70 x 5) which provide practice with whole-number operations. These items show students computing with whole numbers and using a letter to represent an unknown in a single-step equation.

Students write and solve equations with a letter for an unknown angle (e.g., 90+90=180, 45+45=90, 85-30=n) when finding missing angle measures. Students perform addition and subtraction to find unknown angle sizes on worksheets and in activities (Finding Missing Angles; Adjacent Angles and Equations I/II). Students also estimate and measure angles with a protractor and choose best estimates on the Angles Quiz, practicing basic reasonableness checks for angle measures.

Students solve arithmetic items that include interpreting a remainder ("What is the remainder when you divide 30 by 9?") and perform multi-digit addition (416,728 + 335,733). Students solve equations with a letter for the unknown (40 ÷ x = 8 and 4500 + n = 8000). Students practice estimation via rounding (Round 45,627 to the nearest 1000).

The Basic Skills Review items ask students to compute a remainder (What is the remainder when you divide 40 by 9?), solve equations with a letter for the unknown (54 ÷ x = 9 and 4500 - n = 2000), and perform rounding (Round 462,911 to the nearest 1000). The Sally/Charles item (Sally has 5 times as many books as Charles. Charles has 6 books.) has students translate a simple multiplicative relationship into a numerical answer. These tasks require students to perform whole-number operations and to represent some relationships using equations.

Students complete multiplication problem-solving tasks that require using multiple operations and comparing expressions (e.g., 80 x 2 ? 70 + 70; 15 x 63 ? 2 x 4 x 63; large multi-factor products like 45 x 12 x 76). Students solve a real-world division-with-remainder problem (Carly seating 38 people at tables of 6) and must interpret the remainder to decide the fewest number of tables. Students write and compute group equations (e.g., write an equation for 9 groups of 6, 4 groups of 5, 7 groups of 5) and show repeated-addition equivalence.

Students solve single-step word problems that use whole-number multiplication and division (e.g., Ms. Marcioni: 7 bags × 100 pieces = 700; Mr. Sweet: 2000 ÷ 2 = 1000). Students practice multiplying by 10, 100, and 1000 using place-value strategies and properties (examples, Sal's steps, and many practice problems). Students explain whether equations are true or false and are asked to explain their thinking, which asks for checking results.

Students solve word problems that require more than one step in at least one instance (Marcus has 30 bags of 20 marbles, then 10 more bags are added), requiring multiplication then addition. Students practice assessing reasonableness of products by choosing among plausible answers (e.g., deciding whether 20 x 40 is 8, 80, or 800) and by using place-value reasoning to estimate products. Multiple word problems ask students to scale quantities (e.g., 4, 40, 400 tins) so students practice mental multiplication and checking magnitude.

Students solve multistep multiplication word problems in Activity 3 (e.g., hotel rooms, babysitting pay, and a restaurant seating problem that requires (17×6)+(14×8)). Students model multiplication with arrays and area models and write addition sentences for partial products (examples: 200 + 220 + 48 = 468; 102 + 112 = 214). Basic Skills items include equations with letters (56 ÷ x = 7; 7800 - n = 2000) and an explicit remainder question (remainder of 45 ÷ 8) and a rounding problem.

Students practice multiplying multi-digit whole numbers using the area model and computing partial products (e.g., 64 x 72 broken into 60x70, 4x70, 60x2, 4x2 to get 4608). Students solve single-operation word problems by multiplying whole numbers (e.g., skyscraper: 56 floors x 24 offices = 1344; tournament: 32 teams x 18 players = 576; cookies: 37 x 48 = 1776). Students solve simple equations with a letter/unknown in basic skills (e.g., 700 x N = 2100) and perform a rounding task (round 563,820 to the nearest 10,000).

Students solve multiple single-step multiplication word problems (e.g., "Charlie bought 15 boxes of donuts. Each box contained 24 donuts. How many donuts did he buy in all?" and similar problems about tickets, comic books, and donuts) and practice applying the standard multiplication algorithm to compute those products. Students are prompted to assess reasonableness in at least one place ("Do you think the product is closer to 16 or 160? Why?"), which asks them to use estimation to judge an answer. Students repeatedly represent multiplication problems in stacked (equation) form and compute products mentally or with the algorithm during practice activities.

The Skills section explicitly states students will "Solve multistep word problems posed with whole numbers and having whole-number answers." The student activity pages include multi-step word problems that require multiple whole-number multiplication computations and comparisons (e.g., Sam and Chris driving different miles over multiple days; comparing marbles across bags). The activities ask students to choose methods (arrays, area models, standard algorithm) to compute and explain products.

Students solve whole-number computation problems such as "Miguel has 23 times as many stamps as Dana. Dana has 42 stamps. How many stamps does Miguel have? (966)" and complete problems like 730×100, 5628×7, and finding a remainder for 80÷9. Students write and solve equations with a letter for the unknown in items such as 53×19 = b and 7000×N = 350,000. Students also practice comparison and basic division facts that involve whole numbers and remainders on the Basic Skills Review sheet.

Students solve single-step whole-number problems in the Basic Skills Review (e.g., Susan has 30 times as many marbles as Dan; Dan has 38 marbles — students compute 1,140). Students find a remainder in a division problem (What is the remainder when you divide 40 by 9? → 4). Students solve for an unknown in an equation (3000 × N = 360,000 → N = 120).

Students solve whole-number computation and a remainder question on the Basic Skills Review (e.g., "What is the remainder when you divide 60 by 8?"). Students compute a multi-step perimeter problem (120 ft by 85 ft) that requires using addition and multiplication. Students also encounter an equation with a letter variable when completing 3654 × 7 = b, identifying the unknown b.

Students repeatedly compute quotients and identify remainders when they draw a dividend card and roll a die to form division sentences, finding answers like 26 ÷ 6 = 4 R 2. Students complete cut-and-paste problems that fill in division sentences (e.g., __ ÷ __ = 2) and match division sentences that have the same quotient. Students also practice division facts with an online game to reinforce division and quotients.

Students solve several real-world division word problems that require interpreting remainders (e.g., Mark with 65 tickets ÷ 3, Taft dividing 88 pieces of candy among 7, and the boat/85 people problem that requires rounding up trips). Students are asked to check division answers by multiplying the divisor and quotient and then adding any remainder. One activity (2784 x 7 = b) uses a letter to represent an unknown in a multiplication equation.

The skills list explicitly tells students to solve multistep word problems with whole-number answers including interpreting remainders. Students complete 'Division Word Problems' pages that ask for quotients and remainders (e.g., cookies left over, people on the last bus, pirate coins leftover) and complete long-division exercises and 'What's Missing?' tasks that require setting up long division and checking with multiplication. Students are prompted to use multiplication to check answers and to find and interpret remainders in division contexts.

Students solve many whole-number word problems that require more than one step (for example, Sarah converts 4 dozen to 48 by multiplication and then divides by 7; David divides total dollars by cost per lunch). Students compute quotients and remainders for multi-digit dividends (examples: 6213 ÷ 4, 2589 ÷ 7, 180 ÷ 7) and write numeric equations for their solutions. Students are asked to create a word problem for a division sentence and to find quotients and remainders on multiple practice and test pages.

Students are asked to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, so they practice long division procedures and computing remainders. Students must include "Real-world Problems: Present 3 problems involving long division," which requires creating and solving contextual division problems. Students are instructed to show "Steps to Divide" (how to divide 2 digits by 1 digit and 4 digits by 1 digit) and to go through the steps of long division using the problems shown on their poster.

The Basic Skills Review asks students to solve whole-number division with a remainder (e.g., sharing 109 M&Ms with 10 friends, yielding 10 each and 9 left over), so students interpret remainders. The review includes equations with a letter for an unknown (e.g., "2341 × 7 = b") and a missing-divisor problem (dividend 99, quotient 11), so students solve for unknowns in whole-number operations. The lesson provides practice with whole-number multiplication and division (30 × 700, multi-digit multiplication and division problems), giving students experience with the four operations.

Students solve unit-conversion problems that require multiple steps, such as the 'Think About It' problems where they convert 10 pints to cups and compare to 16 cups and where they convert 3500 mL and add 2 L to find a total in milliliters. Students complete conversion charts and fill-in-the-blank problems that use multiplication and division (e.g., fluid ounces-to-cups, pints-to-cups, liters-to-milliliters) to compute equivalent whole-number quantities. Activities ask students to draw pictures or use grouped representations (e.g., drawing 8 fluid-ounce groups each containing 2 tablespoons) to carry out multistep computations.

Students solve multi-step time-conversion problems that require multiple operations, for example: "3 decades = ? weeks" (decades → years → weeks), "2 days = 2880 minutes" (days → hours → minutes), and converting hours to seconds in word problems (Matthew's 1 1/2 hours to seconds). Students compute pay from time worked and rate (Sarah babysat 3 hours at $11/hr → $33) and complete time-interval problems (Amanda walked from 3:24 to 3:55 → 31 minutes; find start time given duration and end time). Several worksheets require multiplication and division across units and include multi-step numerical work with whole-number results.

Students calculate perimeters and areas for multiple rectangles using P = and A = notation (examples: P = 5+5+6+6 = 20 ft; A = 6×4 = 24 sq ft). Students solve multi-step context problems that require more than one operation, such as finding each room's area then comparing and totaling areas to decide if 140 sq m of flooring is sufficient. Students compare perimeters (garden vs. patio) and determine how much greater one is, and they determine how to change the garden's width to reach a target perimeter of 66 ft, which requires solving for an unknown quantity in the context of the perimeter formula.

Students solve multistep numerical word problems that require using more than one operation: for example, the Mr. Harmon yard problem (perimeter 240 ft, length 50 ft) requires dividing the perimeter by 2 and then subtracting the known length to find the width. The Ms. Scott bedroom problem (area 120 sq ft, long sides 12 ft) requires dividing to find the width and then using multiplication to find the total length of the short sides. Introductory examples show students dividing a square's perimeter by 4 to find side length and dividing area by a known width to find length.

Students are asked to find areas and perimeters and to deduce missing side lengths using both area and equal-perimeter conditions (Activity 1 problems and the worked example that lists steps: find perimeter, calculate unknown side using area, use perimeter values to solve). Students draw rectangles with specified area or perimeter and compute corresponding dimensions and measures in Activity 2 (draw rectangles with given area/perimeter and compute areas or perimeters). The example and problem set require students to perform sequences of calculations (multiplication, division, addition) to determine unknown side lengths.

Students solve measurement word problems that require converting units and using the four operations (for example, converting 3 pints to cups, adding cups of cereal + mixed nuts + pretzels + bagel chips, and doubling ingredient amounts for 2 lasagnas). Students practice multi-step arithmetic when they combine conversions with addition or multiplication (e.g., finding total cups from mixed units, computing ounces of ground beef plus mozzarella). Students compare measurements by converting to a common unit (e.g., converting 2 miles to feet to compare with 9000 ft).

Students solve multistep measurement word problems that require using the four operations and unit conversions, such as adding cups/pints in the Maggie problem, multiplying batches by ounces then converting to pounds in the Cal cookie problem, and converting pounds and ounces to total ounces in the Yuri problem. The Student Activity Pages and answer key include conversion tables and multi-step computation problems (e.g., Daniel adding milliliters and liters; the librarian book-weight problem) that require students to perform successive operations to find whole-number answers.

Students are asked to compute perimeter and area in multiple activities (Perimeter and Area Worksheet with 12 problems, Perimeter and Area Design a Room where each grid square represents one square foot) so they perform addition and multiplication to find perimeters and areas. The Perimeter and Area With Everyday Objects task requires students to measure objects and round measurements to the nearest unit, which has them apply measurement, compute values, and use rounding. The Converting Units Worksheet and Matching Games require numerical unit conversions (including numbers up to 1,000) so students practice multiplication/division for conversions.

Students practice multi-digit multiplication using the standard algorithm by rewriting problems in stacked form and finding missing products (Activity 1). Students solve multi-digit division problems with a one-digit divisor and three- or four-digit dividends by creating division sentences from playing cards and solving them (Activity 2). Students are asked to estimate whether a product (253 x 8) will be greater or less than 1600 before computing, and students check answers using a calculator.

Students round large whole numbers to a specified place value: the Introduction asks students to round 395,578; 2,333,598; 735,999; and 590,053 to the nearest hundred thousand and explain how they determined each rounded number. The Skills list explicitly includes using place value understanding to round multi-digit whole numbers to any place, and the lesson prompts students to underline digits and reason about rounding decisions.