Trailblazer Division WorksheetTrailblazer Division Grade 4 Math • Estimating Quotients with Compatible Numbers Name: Date: Field Guide: What Are Compatible Numbers? Compatible numbers are numbers that are easy to divide mentally because they match a basic multiplication fact. Estimate \( 253 \div 6 \) 1. Find a basic fact: Think of a multiple of \( 6 \) close to \( 25 \): \( 6 \times 4 = 24 \). 2. Swap the dividend: Replace \( 253 \) with the compatible number \( 240 \). 3. Divide mentally: \( 240 \div 6 = \) \( 40 \) PART 1 Spot the Compatible Fact Rewrite each problem using a compatible number, then write the estimated quotient. 1. \( 192 \div 5 \) \( \div \) 5 \( = \) 2. \( 348 \div 7 \) \( \div \) 7 \( = \) 3. \( 415 \div 6 \) \( \div \) 6 \( = \) 4. \( 274 \div 3 \) \( \div \) 3 \( = \) PART 2 Estimate the Quotient Use compatible numbers to estimate each quotient. Show the compatible division problem you used. 5. \( 143 \div 7 \) Estimate: 6. \( 318 \div 8 \) Estimate: 7. \( 535 \div 9 \) Estimate: 8. \( 2,380 \div 4 \) Estimate: 9. \( 4,815 \div 6 \) Estimate: 10. \( 6,342 \div 9 \) Estimate: Trailblazer Division — Page 2 Name: PART 3 Pick the Best Estimate Circle the letter of the most reasonable compatible estimate for each problem. 11. \( 472 \div 8 \) A. \( 50 \) B. \( 60 \) C. \( 70 \) 12. \( 2,135 \div 7 \) A. \( 30 \) B. \( 300 \) C. \( 400 \) 13. \( 3,580 \div 6 \) A. \( 500 \) B. \( 600 \) C. \( 700 \) PART 4 Trail Word Problems Use compatible numbers to solve each problem. Show your work in the box. A camp counselor packs 284 granola bars equally into 7 supply crates. About how many granola bars go into each crate? A park ranger drives 3,165 miles over 8 weeks checking mountain trails. About how many miles does the ranger drive each week? 16. Explorer Challenge: Two Trails to One Answer Mia estimated \( 295 \div 4 \) using \( 280 \div 4 = 70 \). Leo estimated \( 295 \div 4 \) using \( 320 \div 4 = 80 \). Did both students use reasonable compatible numbers? Explain why.
Trailblazer Division Answer KeyTrailblazer Division — Answer Key Grade 4 Math • Teacher Reference (Compatible Numbers) Note: Accept other reasonable compatible facts if justified. PART 1 Spot the Compatible Fact 1. \( 192 \div 5 \) \( 200 \div 5 = 40 \) 2. \( 348 \div 7 \) \( 350 \div 7 = 50 \) 3. \( 415 \div 6 \) \( 420 \div 6 = 70 \) 4. \( 274 \div 3 \) \( 270 \div 3 = 90 \) PART 2 Estimate the Quotient 5. \( 143 \div 7 \) \( 140 \div 7 = 20 \) 6. \( 318 \div 8 \) \( 320 \div 8 = 40 \) 7. \( 535 \div 9 \) \( 540 \div 9 = 60 \) 8. \( 2,380 \div 4 \) \( 2,400 \div 4 = 600 \) 9. \( 4,815 \div 6 \) \( 4,800 \div 6 = 800 \) 10. \( 6,342 \div 9 \) \( 6,300 \div 9 = 700 \) PART 3 Pick the Best Estimate 11. \( 472 \div 8 \) B. \( 60 \) (\( 480 \div 8 \)) 12. \( 2,135 \div 7 \) B. \( 300 \) (\( 2,100 \div 7 \)) 13. \( 3,580 \div 6 \) B. \( 600 \) (\( 3,600 \div 6 \)) PART 4 Trail Word Problems 14. Granola Bars (\( 284 \div 7 \)) \( 280 \div 7 = 40 \) — About 40 granola bars go into each crate. 15. Park Ranger Miles (\( 3,165 \div 8 \)) \( 3,200 \div 8 = 400 \) — The ranger drives about 400 miles each week. 16. Explorer Challenge — Sample Response Yes, both students used reasonable compatible numbers. Both \( 280 \) and \( 320 \) are multiples of \( 40 \) that are close to \( 295 \) and easy to divide by \( 4 \) mentally. Since \( 295 \) is between \( 280 \) and \( 320 \), the exact quotient is between \( 70 \) and \( 80 \) (slightly closer to \( 70 \)).
Summit Division WorksheetSummit Division Grade 4 Math • Estimating Quotients with Compatible Numbers Name: Date: Field Guide: What Are Compatible Numbers? Compatible numbers are numbers that are easy to divide mentally because they match a basic multiplication fact. Estimate \( 342 \div 8 \) 1. Find a basic fact: Think of a multiple of \( 8 \) close to \( 34 \): \( 8 \times 4 = 32 \). 2. Swap the dividend: Replace \( 342 \) with the compatible number \( 320 \). 3. Divide mentally: \( 320 \div 8 = \) \( 40 \) PART 1 Spot the Compatible Fact Rewrite each problem using a compatible number, then write the estimated quotient. 1. \( 236 \div 4 \) \( \div \) 4 \( = \) 2. \( 485 \div 7 \) \( \div \) 7 \( = \) 3. \( 294 \div 6 \) \( \div \) 6 \( = \) 4. \( 628 \div 9 \) \( \div \) 9 \( = \) PART 2 Estimate the Quotient Use compatible numbers to estimate each quotient. Show the compatible division problem you used. 5. \( 178 \div 6 \) Estimate: 6. \( 412 \div 5 \) Estimate: 7. \( 645 \div 8 \) Estimate: 8. \( 1,590 \div 4 \) Estimate: 9. \( 3,520 \div 7 \) Estimate: 10. \( 5,430 \div 9 \) Estimate: Summit Division — Page 2 Name: PART 3 Pick the Best Estimate Circle the letter of the most reasonable compatible estimate for each problem. 11. \( 354 \div 6 \) A. \( 50 \) B. \( 60 \) C. \( 70 \) 12. \( 2,780 \div 4 \) A. \( 600 \) B. \( 700 \) C. \( 800 \) 13. \( 4,215 \div 7 \) A. \( 60 \) B. \( 600 \) C. \( 700 \) PART 4 Trail Word Problems Use compatible numbers to solve each problem. Show your work in the box. A hiking club collects 368 water bottles and packs them equally into 9 coolers. About how many water bottles go into each cooler? A mountain lodge orders 2,430 pinecones for 6 craft tables to share equally. About how many pinecones does each table get? 16. Explorer Challenge: Two Trails to One Answer Noah estimated \( 465 \div 7 \) using \( 420 \div 7 = 60 \). Maya estimated \( 465 \div 7 \) using \( 490 \div 7 = 70 \). Did both students use reasonable compatible numbers? Explain why.
Summit Division Answer KeySummit Division — Answer Key Grade 4 Math • Teacher Reference (Compatible Numbers) Note: Accept other reasonable compatible facts if justified. PART 1 Spot the Compatible Fact 1. \( 236 \div 4 \) \( 240 \div 4 = 60 \) 2. \( 485 \div 7 \) \( 490 \div 7 = 70 \) 3. \( 294 \div 6 \) \( 300 \div 6 = 50 \) 4. \( 628 \div 9 \) \( 630 \div 9 = 70 \) PART 2 Estimate the Quotient 5. \( 178 \div 6 \) \( 180 \div 6 = 30 \) 6. \( 412 \div 5 \) \( 400 \div 5 = 80 \) 7. \( 645 \div 8 \) \( 640 \div 8 = 80 \) 8. \( 1,590 \div 4 \) \( 1,600 \div 4 = 400 \) 9. \( 3,520 \div 7 \) \( 3,500 \div 7 = 500 \) 10. \( 5,430 \div 9 \) \( 5,400 \div 9 = 600 \) PART 3 Pick the Best Estimate 11. \( 354 \div 6 \) B. \( 60 \) (\( 360 \div 6 \)) 12. \( 2,780 \div 4 \) B. \( 700 \) (\( 2,800 \div 4 \)) 13. \( 4,215 \div 7 \) B. \( 600 \) (\( 4,200 \div 7 \)) PART 4 Trail Word Problems 14. Water Bottles (\( 368 \div 9 \)) \( 360 \div 9 = 40 \) — About 40 water bottles go into each cooler. 15. Pinecones (\( 2,430 \div 6 \)) \( 2,400 \div 6 = 400 \) — Each table gets about 400 pinecones. 16. Explorer Challenge — Sample Response Yes, both students used reasonable compatible numbers. Both \( 420 \) and \( 490 \) are multiples of \( 70 \) that are close to \( 465 \) and easy to divide by \( 7 \) mentally. Since \( 465 \) is between \( 420 \) and \( 490 \), the exact quotient is between \( 60 \) and \( 70 \) (closer to \( 70 \)).