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Using Objects to Divide: Division as
Repeated Subtraction (10 – 1)
When you divide, you subtract equal groups. Doris has 32 strawberries. She makes box lunches by putting 4 strawberries in each box lunch. How many box lunches can she make this way? What you think: Doris will put 4 strawberries in each lunch box. How many lunch boxes can she make? What you show: Repeated subtraction 32 – 4 = 28 16 – 4 = 12 28 – 4 = 24 12 – 4 = 8 24 – 4 = 20 8 – 4 = 4 20 – 4 = 16 4 – 4 = 0 You can subtract 4 from 32 eight times. What you write: 32 ÷ 4 = 8 32 is the dividend, the number that is being divided. 4 is the divisor, the number the dividend is being divided by. 8 is the quotient, or the answer to the division problem. Draw pictures to solve each problem.
1. You have 15 marbles. You put 5 marbles into each group. How many groups can you make? 2. You have 20 ice cubes. You put 4 ice cubes into each glass. How many glasses can you put ice cubes into?
Division as Repeated Subtraction (10 – 2)
For City Clean-Up Day, 18 people volunteered to clean up the city park. The volunteers worked in groups with 3 people each. How many groups of volunteers cleaned up the city park? Use repeated subtraction to find the number of groups. 18 – 3 = 15 15 – 3 = 12 12 – 3 = 9 9 – 3 = 6 6 – 3 = 3 3 – 3 = 0 There are 6 groups of volunteers. Use repeated subtraction to divide. Use a number line to help.
1. Mark is placing 12 model cars into equal groups. Each group has 4 model cars. How many groups of model cars will he make? 2. There are 24 students in gym class. They divided into teams of 6 for a volleyball game. How many teams were there? 3. Each necklace Cara makes has 5 beads. How many necklaces can Cara make with 20 beads? 4. Amy has 12 dolls in her collection. She places 6 dolls on each shelf. How many shelves does she need? 5. Charlie has 16 chores to do. He can complete 4 chores in one day. How many days will Charlie take to complete his chores? 6. The pet store has 9 parakeets. If 3 parakeets are in each cage, how many cages are there? 7. Shawn needs to learn how to play 15 songs for his band’s concert. If he learns 3 songs each week, how many weeks will it take him to learn all of the songs? 8. At Rosa Elementary School, 27 teachers signed up to carpool. If 3 teachers ride together in each car, how many cars are needed for all of the teachers?
Dividing 2-Digit by 1 - Digit Numbers (10 – 4)
You can find 2 - digit quotients by breaking apart the problem and dividing tens, then ones. Find 85 ÷ 5. Estimate: 100 ÷ 5 = 20. − −
Check: 17 × 5 = 85. The answer checks. Find 55 ÷ 3. Estimate: 60 ÷ 3 = 20. − −
18 R
Check: 18 × 3 = 54. 54 + 1 = 55 The answer checks. Find 83 ÷ 7. Estimate: 84 ÷ 7 = 12. − −
11R
Check: 11 × 7 = 77. 77 + 6 = 83 The answer checks. Find the missing values. 1. 2.
Dividing 3 - Digit by 1 - Digit Numbers (10 – 5)
You can find 3 - digit quotients by breaking apart the problem. Find 528 ÷ 4. Estimate 500 ÷ 4 = 125. − − −
Check 132 × 4 = 528 The answer checks. Find 575 ÷ 5. Estimate 600 ÷ 5 = 12 0. − − −
Check 115 × 5 = 575 The answer checks. Find 725 ÷ 3. Estimate 750 ÷ 3 = 250. − − −
241R
Check 241 × 3 = 723 723 + 2 = 725 The answer checks. Find the missing values.
1. 2.
Dividing 4-Digit by 1-Digit Numbers (10 – 7)
An estimate will help you decide where to place the first digit of the quotient. It will also help you check your answer. Divide 5,493 ÷ 6. Estimate first. You can use compatible numbers to divide mentally. 54 is a multiple of 6. 5,400 is close to 5,493 and 5, ÷ 6 will be easy to divide. 5,400 ÷ 6 = Divide to find the actual quotient. Compare: Is the estimate close to the quotient? estimate: quotient: If it is, then your answer is reasonable. Estimate. Then find each quotient. Use your estimate to check if your quotient is reasonable.
1. Divide 4,318 ÷ 7. Estimate: ÷ = 4,318 ÷ 7 = Is your answer reasonable? 3. Divide 4,377 ÷ 8. Estimate: ÷ = 4,377 ÷ 8 = Is your answer reasonable? 2. Divide 4,826 ÷ 5. Estimate: ÷ = 4,826 ÷ 5 = Is your answer reasonable? 4. Divide 7,192 ÷ 9. Estimate: ÷ = 7,192 ÷ 9 = Is your answer reasonable?
Problem Solving:
Multiple-Step Problems (10 – 8)
Solve Problems Step-by-Step Scott and Gina want to go see a movie after they eat dinner. They have brought $35 with them. Scott’s meal costs $9 and Gina’s meal costs $ 8. Movie tickets are $9 each. Will they have enough money left over after dinner to pay for 2 movie tickets? First Step Write down what you know:
- They have $35 to spend. - They are spending $9 and $ 8 on din- ner. Third Step Develop a problem-solving strategy: - Subtract $9 and $ 8 from $35. (Tip: Instead of subtracting these from $35 one at a time, combine them and then subtract from $35.) $ 9 $
- $ 8 then, −$ $17.00 $ Second Step Write down what you need to know: - How much money is left over? - Is it enough for 2 movie tickets? Fourth Step Finish the problem: - Is $18 enough for 2 movie tickets that cost $9 each? $9 × 2 = $ They have $18 left. Yes, they have enough for 2 movie tickets. Solve the problems below using the step-by-step process. 1. Nick and his friends are working on a project. They need to write 29 pages altogether. If his friend Kara writes 14 pages, and his friend Jared writes 12 pages, how many pages are left for Nick to write? 2. Ashlyn and Brooke went to the arcade with $1 8. They bought 4 bottles of water, which cost $ 2 each. They each bought a sticker book for $ 3 each. Ashlyn put $ 1 in a fundraiser jar. A game of pool cost $3 per game. Did they have enough money left to play? 3. Reasoning Cyndi and Jewel went shopping for school supplies. They had $1 4 to spend. They spent $4 on pencils, $3 on pens, and $6 on notebook paper. Cyndi thought she had enough money left over to buy a $2 pencil sharpener. Was she correct?
