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
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Math Message Follow-Up

• 4 R1 is 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.
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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?
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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 persons 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
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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.

Lets do this problem together.
Three children wish to divide a set of 16 toy
cars equally. What is each childs 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.
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• 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.
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• 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.
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Partnership Work

• Math Journal page 148 and Math Journal page 149.

• REMEMBER
• What does the remainder represent?
• What should I do with the remainder?