Grade 3 · Mathematics
Quarter 2 · Week 5 · TEKS
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This lesson guides Grade 3 students to fluently solve one-step and two-step addition and subtraction problems within 1,000. Students will use strategies based on place value, properties of operations, and the relationship between addition and subtraction. They will also learn to round numbers to the nearest 10 or 100 or use compatible numbers to estimate solutions, and determine the value of collections of coins and bills. The lesson emphasizes understanding and applying mathematical process standards to develop efficient and accurate problem-solving skills.
Students should understand basic addition and subtraction facts, place value concepts up to 1,000, and be familiar with common US coins and bills and their values.
Place value is the value of a digit depending on its position in a number. For example, in 345, the 3 represents 300 because it is in the hundreds place. Using place value helps students break numbers into hundreds, tens, and ones to add or subtract more easily. For example, to add 234 + 145, students can add hundreds (200 + 100), tens (30 + 40), and ones (4 + 5) separately, then combine the sums.
Properties of operations such as the commutative property (changing the order of addends does not change the sum) and associative property (grouping of addends does not change the sum) help students find flexible strategies for addition and subtraction. For example, to solve 345 + 156, students might rearrange addends or group numbers to make easier sums, like (345 + 150) + 6.
Addition and subtraction are inverse operations. Understanding this relationship helps students check their work and solve problems efficiently. For example, if a student knows 500 - 275 = 225, they can check by adding 225 + 275 to see if it equals 500. This relationship also helps in solving two-step problems where one operation leads to the next.
Rounding numbers to the nearest 10 or 100 simplifies calculations and helps estimate sums or differences. Compatible numbers are numbers close to the original numbers that are easy to compute mentally. For example, to estimate 487 + 326, students might round 487 to 490 and 326 to 330, then add 490 + 330 = 820 as an estimate. Estimation helps check if answers are reasonable.
Students learn to identify the value of common coins (pennies, nickels, dimes, quarters) and bills (ones, fives, tens, twenties). They practice counting collections of coins and bills by grouping and adding their values. For example, a collection with 3 quarters, 2 dimes, and 4 pennies is counted by adding 75 cents + 20 cents + 4 cents = 99 cents.
Solve the problem: Sarah has 245 marbles. She buys 136 more marbles. How many marbles does she have now? Use place value to solve.
Break the numbers into hundreds, tens, and ones: 245 = 200 + 40 + 5, 136 = 100 + 30 + 6. Add hundreds: 200 + 100 = 300, tens: 40 + 30 = 70, ones: 5 + 6 = 11. Since 11 ones is more than 10, regroup 10 ones as 1 ten and 1 one. Add tens: 70 + 10 = 80, ones: 1. Total is 300 + 80 + 1 = 381.
381 marbles
Estimate the sum of 478 + 326 by rounding to the nearest 10.
Round 478 to 480 and 326 to 330. Add 480 + 330 = 810. This is an estimate close to the actual sum.
Approximately 810
Determine the value of this collection: 3 quarters, 2 dimes, 4 pennies.
3 quarters = 3 x 25 cents = 75 cents, 2 dimes = 2 x 10 cents = 20 cents, 4 pennies = 4 x 1 cent = 4 cents. Add 75 + 20 + 4 = 99 cents.
99 cents
Solve the two-step problem: John has 500 stickers. He gives 175 to his friend and then buys 120 more. How many stickers does he have now?
First subtract: 500 - 175 = 325 stickers left. Then add: 325 + 120 = 445 stickers. So John has 445 stickers now.
445 stickers
Use compatible numbers to estimate the difference: 652 - 289.
Round 652 to 650 and 289 to 290. Subtract 650 - 290 = 360. This estimate helps check the actual difference.
Approximately 360
Present a real-world story problem involving buying items with money and needing to find the total cost or change.
Listen and discuss what information is needed to solve the problem and what operations might be used.
This engages students by connecting addition and subtraction to everyday situations involving money and problem solving.
Provide students with base-ten blocks and number cards to model addition and subtraction problems within 1,000.
Use the materials to represent and solve one-step addition and subtraction problems, explaining their strategies.
Hands-on materials help students visualize place value and understand how to break numbers apart to add or subtract.
Demonstrate solving a two-step problem on the board using place value strategies and properties of operations.
Watch the demonstration and ask questions to clarify understanding.
Modeling the process shows students how to apply strategies systematically to solve more complex problems.
Present problems that require rounding or using compatible numbers to estimate sums or differences.
Practice rounding numbers and estimating answers before solving the problems exactly.
This deepens understanding of estimation as a tool to check reasonableness of answers.
Give students a mixed set of problems including one-step and two-step addition and subtraction within 1,000, rounding and estimation tasks, and coin/bill value problems.
Solve the problems independently and explain their reasoning in writing or orally.
Assessment of student fluency and understanding across all objectives.
Use the materials to represent and solve one-step addition and subtraction problems, explaining their strategies.
Add 234 and 145 using place value strategies.
234 + 145 = 379. Add hundreds: 200 + 100 = 300, tens: 30 + 40 = 70, ones: 4 + 5 = 9; total 300 + 70 + 9 = 379.
Estimate the sum of 478 + 326 by rounding to the nearest 10.
Round 478 to 480 and 326 to 330. Add 480 + 330 = 810 as an estimate.
Determine the value of 3 quarters, 2 dimes, and 4 pennies.
3 quarters = 75 cents, 2 dimes = 20 cents, 4 pennies = 4 cents. Total = 99 cents.
Solve the two-step problem: John has 500 stickers, gives 175 away, then buys 120 more. How many stickers now?
500 - 175 = 325; 325 + 120 = 445 stickers.
Use compatible numbers to estimate 652 - 289.
Round 652 to 650 and 289 to 290; subtract 650 - 290 = 360 as an estimate.
Use base-ten blocks and visual aids to reinforce place value concepts. Provide step-by-step guided practice with simpler numbers before progressing. Use real coins and bills for hands-on counting practice.
Use visual models and gestures to explain place value and operations. Label coins and bills with their values in English and native language if possible. Use sentence frames to help explain problem-solving steps.
Challenge students with multi-step problems involving larger numbers within 1,000. Encourage students to create their own word problems using addition and subtraction. Explore mental math strategies for addition and subtraction beyond place value.
Encourage students to help count money at home, such as coins in a piggy bank or bills in a wallet, and practice adding or subtracting small amounts with family members.
Students learned to fluently solve one-step and two-step addition and subtraction problems within 1,000 by using place value and properties of operations. They practiced rounding and using compatible numbers to estimate sums and differences, and determined the value of collections of coins and bills. These skills help students develop efficient and accurate problem-solving strategies applicable to real-world situations.
Use the exact standards alignment and retrieved-source provenance stored with this enrichment.