Lesson 6.4 Expressing and Interpreting Remainders

1. Lesson 6.4 Expressing and Interpreting Remainders • Math Message: • Three students share 13 sticks of gum. How many sticks of gum does each student get if they receive equal shares? students sticks students sticks 3 ? 13 13/3 =

2. Draw a picture of the problem. Math Message Follow-Up • 4 R1is a correct answer to the Math Message problem, but this will not satisfy the three students who want to know who gets the last piece of gum. • What do the quotient, 4, and remainder, 1, represent? Should you ignore the remainder? 1 left over piece of gum split between 3 people.

3. Mixed Number • Each student in the group will receive 4 1/3 sticks of gum. Or you can say, 4 1/3 sticks of gum per student. 4 1/3 is a mixed number - it has a whole number and a fraction. Can you think of other examples of mixed numbers?

4. Expressing Remainders as Fractions or Decimals • In division number stories, when there is a remainder, you have to decide: • What does the remainder represent? • What should I do with the remainder?

5. Draw a picture on your whiteboard to organize the information for the problem. Four brothers are given 35 fruit bars. They agree to share the bars equally. How many fruit bars will each boy get? What does the remainder represent? What should I do with the remainder? 3 fruit bars Split it between the brothers. Write as a mixed number - 8 3/4 fruit bars the remainder becomes the numerator (top part of fraction) and the divisor becomes the denominator (bottom part of fraction - think down)

6. Draw a picture on your whiteboard to organize the information for the problem. • Four people split the cost of a $15 present equally. What is each person’s share? 3 R3 What does the remainder represent? What should I do with the remainder? 3 left over dollars Split it between the people. the remainder becomes the numerator (top part of fraction) and the divisor becomes the denominator (bottom part of fraction - think down) $3 3/4, or $3.75

7. Sometimes you cannot turn a remainder into a fraction or a decimal • It is VERY important to identify what the remainder represents so you can decide if you should ignore it or round up to the next whole number.

8. It is VERY important to identify what the remainder represents so you can decide if you should ignore it or round up to the next whole number. Let’s do this problem together. Three children wish to divide a set of 16 toy cars equally. What is each child’s share? 5 R 1 Draw a picture on your whiteboard to organize the information for the problem. How is this different from splitting pieces of gum? The remainder, a toy car, cannot be divided up. It is a leftover amount - you must ignore it. The answer would be 5 cars.

9. It is VERY important to identify what the remainder represents so you can decide if you should • ignore it • or • round up to the next whole number. Ann has $18 to buy notebooks that cost $4 each. How many notebooks can she buy? 4 R 2 Draw a picture on your whiteboard to organize the information for the problem. Ann can buy four notebooks and have $2 leftover. Ann does not have enough money to purchase another notebook. Therefore, you must ignore the remainder. The answer would be 4 notebooks.

10. Jeffrey needs 4 5/6 pages to include all 29 photos. • It is VERY important to identify what the remainder represents so you can decide if you should • ignore it • or • round up to the next whole number. Jeffrey has 29 photographs. He can fit 6 photos on each page of his photo album. How many pages must he use to hold all 29 photos? 4 R5 Draw a picture on your whiteboard to organize the information for the problem. Four pages holds only 24 photos and are not enough. Jeffrey must use a fifth page to hold the last 5 photos. You must round up to the next whole number, from 4 pages to 5 pages to ensure all photos are included.

11. Partnership Work • Math Journal page 148 and Math Journal page 149. • REMEMBER: • What does the remainder represent? • What should I do with the remainder?