s - NJCTL

Transcription

s - NJCTL

Slide 1 / 176
Slide 2 / 176
4th Grade
Multiplication &
Division of Multi-Digit Numbers
2015-03-19
www.njctl.org
Slide 3 / 176
Table of Contents
• Multiply by Multiples of 10, 100 and 1,000
Click on a topic
to go to that section.
• Use Rounding to Estimate Products
• Multiplying Whole Numbers up to 4 Digits by One-Digit
• Multiplication by Two Digit Numbers
• Basics of Division & Estimating Quotients
• Division with and without Remainders
• Find Whole Number Quotients and Remainders with
up to Four-Digit Dividends and One-Digit Divisors
• Quotients with Zeros
Slide 4 / 176
Links to PARCC sample questions
Performance Based Assessment
Non-Calculator 3
Non-Calculator 11
Non-Calculator 8
Non-Calculator 17
End of Year
Non-Calculator 2
Non-Calculator 14
Non-Calculator 4
Non-Calculator 16
Non-Calculator 6
Non-Calculator 21
Non-Calculator 7
Non-Calculator 24
Non-Calculator 11
Slide 5 / 176
Multiplication by
Multiples of 10, 100, 1000
Click to return to the
table of contents
Multiplication Review
Multiplication is repeated addition of same-sized groups.
For example, 4 x 5 could be shown in the following ways:
Use the set model.
Use skip counting.
(Make 4 groups of 5)
(Count by 5, 4 times.)
5 + 5 + 5 + 5 = 20
= 20
s
Slide 6 / 176
Slide 7 / 176
Multiplication Review
Use an array.
(4 groups of 5
= 20
Use the area model.
s)
(a 4 x 5 graph)
s
= 20
s
Slide 8 / 176
Multiplying by 10
Teacher Notes
Let's multiply 7 x 10 using the area model. On the graph below,
draw a rectangle that is 7 units by 10 units. Shade in your rectangle.
Count the number of squares that are shaded.
You're counting 7 groups of 10, so 7 x 10 = ______.
When you find the area of any rectangle, you multiply the length (l)
by the width (w). The formula looks like this: A = l x w
Multiplying by 10
Use the area model to find each product.
10 x 3 = _____
14 x 10 = _____
What do you notice about each of these problems?
Can you come up with a "rule" or a short-cut to find the
product of any number and 10?
Slide 9 / 176
Slide 10 / 176
Patterns of Zeros
When you multiply by 10, 100, 1000, there is a pattern you can
use. You just discovered that multiplying a whole number by 10
adds one zero to the end. Based on that, what do you think will
happen if you multiply a number by 100 or by 1000?
Try These:
230 x 10
click
2,300
______
42 x 100
click
7 x 1000
click
7,000
______
4,200
______
501 x 100
click
50,100
______
100 x 10
1,000
______
click
330 x 1000
click
330,000
______
Slide 11 / 176
1 Find the product.
673 x 10 =
Slide 11 (Answer) / 176
1 Find the product.
Answer
673 x 10 =
6,730
[This object is a pull tab]
Slide 12 / 176
2 Find the product.
673 x 100 =
2 Find the product.
Answer
673 x 100 =
67,300
3 Find the product.
7103
x
10
Slide 13 / 176
3 Find the product.
7103
10
Answer
x
71,030
Slide 14 / 176
4 Find the product.
5421 x 100 =
Answer
4 Find the product.
5421 x 100 =
542,100
Slide 15 / 176
5 Find the product.
1,000 x 59 =
Answer
5 Find the product.
1,000 x 59 =
59,000
6 Find the product.
50 x 100,000 =
Slide 16 / 176
Answer
6 Find the product.
50 x 100,000 =
5,000,000
7 A football field is 100 yards long and 50 yards wide.
What is the area of the field?
Answer
7 A football field is 100 yards long and 50 yards wide.
What is the area of the field?
5,000 yards
Slide 17 / 176
8 Each student in 4th grade is planning on reading 60
books this school year. There are 100 students in the
4th grade. How many books will they read?
Answer
8 Each student in 4th grade is planning on reading 60
books this school year. There are 100 students in the
4th grade. How many books will they read?
Slide 18 / 176
6,000 books
9 There are 10 boys on the basketball team. If each boy
sells $219.00 worth of candy for the candy sale, how
much money will the team raise?
Slide 19 / 176
Answer
9 There are 10 boys on the basketball team. If each boy
sells $219.00 worth of candy for the candy sale, how
much money will the team raise?
$2,190.00
10 There are 4 wheels on each training wheel bike.
There are 5 kids in each group and there are 10
groups. How many wheels are there in all?
Answer
10 There are 4 wheels on each training wheel bike.
There are 5 kids in each group and there are 10
groups. How many wheels are there in all?
200 wheels
Slide 20 / 176
11 The number 234 is multiplied by 10. Select the
correct word from each group.
Slide 21 / 176
The numberal 2 in the resulting product is in the
_____ place, and the value of this digit is _____.
A ones
E 2
B tens
F 20
C hundreds
G 200
D thousands
H 2,000
From PARCC sample test
11 The number 234 is multiplied by 10. Select the
correct word from each group.
The numberal 2 in the resulting product is in the
_____ place, and the value of this digit is _____.
Answer
A ones
B tens
A thousands
H 2,000
C hundreds
D thousands
E 2
F 20
G 200
H 2,000
12 Mr. Soto's bicycle weighs 30 pounds. His car weighs
90 times as much as his bicycle. What is the weight,
in pounds, of Mr. Soto's car?
Slide 22 / 176
Answer
12 Mr. Soto's bicycle weighs 30 pounds. His car weighs
90 times as much as his bicycle. What is the weight,
in pounds, of Mr. Soto's car?
2,700 pounds
Slide 23 / 176
Use Rounding to
Estimate Products
table of contents
Use Rounding to Estimate Products
Why do we estimate?
Estimating (rounding) numbers helps us to see if the product makes
number sense.
It is an important skill to develop good judgment about how precise an
estimate is or whether your answer is possible or reasonable in various
circumstances.
This skill can be helpful if you don't need to find the exact answer.
Slide 24 / 176
00
Use Rounding to Estimate Products
Slide 25 / 176
How to Round Numbers:
Decide which is the last digit to keep (the place you are rounding to).
Leave it the same if the next digit is less than 5 (this is called rounding
down).
Increase it by 1 if the next digit is 5 or more (this is called rounding up).
Estimate Products
Slide 26 / 176
Round each number to the nearest ten.
77
1. Round each number to the nearest ten.
x 28
2. Multiply the whole numbers.
3. Count the number of zeros in the
estimation and add the same number of
zeros to the product.
77
80
x 28
x 30
click
2400
Estimate Products
Round each factor to its greatest place.
14 X 189 (It's helpful to write the problem vertically.)
189
X 14
Let's try one more!
click
189
rounds to
200
14 rounds to x 10
click
227 X 1,068
1,068 rounds to 1,000
227 rounds to x 200
Slide 27 / 176
Slide 28 / 176
13 Estimate the product of 47 x 430.
A 20,000
B 2,000
C 16,000
13 Estimate the product of 47 x 430.
B 2,000
C 16,000
Answer
A 20,000
C
14 You want to buy a video game system that costs
$399.95. If you save $40.00 per month, it will take you
ten months to purchase the X-Box.
True
False
Slide 29 / 176
14 You want to buy a video game system that costs
$399.95. If you save $40.00 per month, it will take you
ten months to purchase the X-Box.
False
Answer
True
True
15 A hospital ordered 79 boxes of cotton swabs. There
are 42 cotton swabs in each box. About how many
swabs were ordered in all?
Slide 30 / 176
A 40
B 400
C 4000
15 A hospital ordered 79 boxes of cotton swabs. There
are 42 cotton swabs in each box. About how many
swabs were ordered in all?
B 400
C 4000
Answer
A 40
C
Slide 31 / 176
16 Estimate the product.
527 x 62
Answer
527 x 62
500 x 60 = 30,000
452 x 81
Students type their answers here
Slide 32 / 176
Answer
452 x 81
500 x 80 = 4,000
Slide 33 / 176
Multiplying Whole Numbers
up to 4 Digits by One-Digit
table of contents
Teacher Notes
StudentsWhole
can use this
link
Multiplying
Numbers
to practice computation.
up to 4http://mrnussbaum.com/
Digits by One-Digit
draggablemain/index3
table of contents
Slide 34 / 176
Repeated Addition
Multiply 12 x 5 by using Repeated Addition
Starting with zero, add 12 five times .
0+12=12
12+12=24
Slide
24+12=36
Slide
36+12=48
Slide
Counting Multiples
48+12=60
Slide
Slide 35 / 176
List the first 8 multiples of 15.
Using your list, find 15 x 3.
Now find 15 x 7.
Counting Multiples
List the first 8 multiples
of 15.
Skip count
by 15's. The
Answer
product of 15 and 3 is the 3rd
multiple. The product of 15
and 7 is the 7th multiple.
Using your list, find 15 x 3.
Solution
15, 30, 45, 60, 75, 90, 105, 120
Now find 15 15
x 7.x 3 = 45
15 X 7 = 105
Multiplying Using a Model (Array)
Slide 36 / 176
Find 3 x 15
Arrange of 3 rows of 15 stars .
Using stars to represent ones, how many stars do you count?
This number is a multiple of 3.
Slide 37 / 176
Multiply Using the Area Model
You can use the area model to multiply numbers. To multiply 9 x 3,
draw a rectangle with a side length of 9 and a width of 3.
9
9 x 3 = __ squares
3
When you know your multiplication facts, there is no need to count
squares. You can just multiply the length and the width to find the
area (product).
7
Let's multiply 7 x 6.
7 x 6 = ____
6
Multiply Using the Area Model
You can also use the area model to multiply a larger (2, 3, 4+ digit)
number by a one-digit number. Here's an example...
78 x 5
When you first look at this problem, it may seem
difficult. But, don't worry! You can break it down into
smaller parts that are easy to multiply!
70
8
Bre
a
into k dow
70 + n 78
8!
5
Now, multiply each part! To find the total area, find the sum of the
two smaller parts.
click to reveal
5
70
70 x 5 = 350
8
5x8
= 40
350
+ 40
390
So, 78 x 5 = 390
Slide 38 / 176
Area Model
Slide 39 / 176
Let's try a few more problems!
37 x 9
click to reveal
9
30
7
30 x 9 = 270
7x9=
63
270 + 63 = 333
So, 37 x 9 = 333
Area Model
Slide 40 / 176
124 x 6
click to reveal
100
20
100 x 6 = 600
6
4
20 x 6 = 4 x 6 = 600 + 120 + 24 = 744
120
24
So, 124 x 6 = 744
Area Model
124 x 6
Hint
Rewrite 124 as
100 + 20 + 4
click to reveal
6
100
100 x 6 = 600
20
4
20 x 6 = 4 x 6 = 600 + 120 + 24 = 744
120
24
So, 124 x 6 = 744
18 Use the area model to find the product of 42 x 3.
Answer
Slide 41 / 176
126
19 Using the area model, find the product of 88 x 5.
Slide 42 / 176
Answer
19 Using the area model, find the product of 88 x 5.
440
20 Use the area model to multiply 263 x 4.
Answer
20 Use the area model to multiply 263 x 4.
1,052
Slide 43 / 176
Slide 44 / 176
21 Find the product.
509 x 8 =
Answer
509 x 8 =
4,072
Multiplication Strategies
We just reviewed the following strategies...
1. Repeated Addition
2. Counting Multiples
3. Drawing an Array
4. Using the Area Model.
These are all very good ways to help you understand the
meaning of multiplication. But now, you will learn to multiply
using the Standard Algorithm.
Slide 45 / 176
Multiplication Using the Standard Algorithm
Slide 46 / 176
Find 24 x 2
1. Write the numbers in columns.
Ones
2
4
x
2. Multiply the ones' digit by 2.
3. Multiply the tens' digit by 2.
2
Answer
Tens
Multiplication Using the Standard Algorithm
Slide 47 / 176
Let's try a few more examples...
21 x 4
Ones
x
Tens
413 x 2
Ones
x
Hundreds
Tens
Ones
x
Answer
32 x 3
Tens
Slide 48 / 176
Standard Algorithm
Now let's multiply 16 x 4.
Tens
Ones
1
6
4
x
4
+2
Tens
Ones
1
6
4
x
6
4
1. Multiply the ones.
a. When you multiply 4 x 6, you will not get a
one-digit number.
b. 4 x 6 = 24
c. 24 = 2 tens + 4 ones.
d. Write 4 in the ones' column and carry the
2 to the tens' column. This is called
"regrouping".
2. Multiply 4 to the number in the tens column and
then add the 2 tens you regrouped.
(4 x 1 + 2 = 6)
Answer
2
Slide 49 / 176
Standard Algorithm
Let's try another problem 87 x 6.
1. Multiply 6 x 7.
Tens
Ones
8
7
2. 6 x 7 = 42 (4 tens + 2 ones)
6
3. Write the 2 in the ones' column
and regroup the 4 to the tens'
column.
x
Answer
Hundreds
4. Multiply 6 x 8 and then add the 4.
6 x 8 + 4 = 52
5. Write the 5 in the hundreds'
column and the 2 in the tens' column.
Slide 50 / 176
Standard Algorithm
Do you remember the steps?
Thousands Hundreds
458 x 3
Tens
Ones
x
Thousands Hundreds
Tens
Answer
47 x 4
Ones
x
Slide 51 / 176
Standard Algorithm
4219 x 3
Ten-Thousands
Thousands
Hundreds
Tens
Don
't
Ones
forg
x
et to
re-g
5290 x 8
Ten-Thousands
x
Thousands
Hundreds
Tens
Ones
rou
p!
Answer
Here are two REALLY tricky problems!
Slide 52 / 176
Products
Can find these products without using a table?
47 x 3
265 x 2
1367 x 4
Products
Can find these products without using a table?
265 x 2
Answer
47 x 3
1367 x 4
47 x 3 = 141
265 x 2 = 530
1367 x 4 = 5468
22 When you multiply 561 x 9, there is nothing to
regroup from the ones column to the tens column.
True
False
Slide 53 / 176
False
Answer
True
True
Slide 54 / 176
True
False
False
Answer
True
False
24 Which shows the correct product for 99 x 9?
Slide 55 / 176
A 811
B 891
C 881
24 Which shows the correct product for 99 x 9?
B 891
C 881
Answer
A 811
B
25 The Cold Cow ice cream shop has a special on cones
with three scoops. If they sell 72 cones in one night,
how many scoops of ice cream did they serve?
Slide 56 / 176
Answer
25 The Cold Cow ice cream shop has a special on cones
with three scoops. If they sell 72 cones in one night,
how many scoops of ice cream did they serve?
216 scoops
Slide 57 / 176
616 x 7 =
Answer
616 x 7 =
4,312
Slide 58 / 176
2572 x 5 =
Answer
2572 x 5 =
12,860
28 Find the product of 7 x 9344.
Slide 59 / 176
Answer
28 Find the product of 7 x 9344.
65,408
Slide 60 / 176
29 Enter your answer in the box.
3,649 x 6 =
Answer
3,649 x 6 =
21,894
30 On a Friday night, 417 tickets were sold at the movie
theater. Each ticket cost $9. How much money did the
theater collect through ticket sales?
Slide 61 / 176
Answer
30 On a Friday night, 417 tickets were sold at the movie
theater. Each ticket cost $9. How much money did the
theater collect through ticket sales?
$3,753
31 A movie theater has two rooms. Room A has 9 rows
of seats with 21 seats in each row. Room B has
three times as many seats as Room A. How many
seats are there in both rooms?
Slide 62 / 176
Answer
31 A movie theater has two rooms. Room A has 9 rows
of seats with 21 seats in each row. Room B has
three times as many seats as Room A. How many
seats are there in both rooms?
9 x 21 = 189
189 x 3 = 567
567 seats
32 The middle school art teacher has 9 cases of crayons
with 52 boxes in each case. The elementary school art
teacher has 6 cases of crayons with 104 boxes in each
case. How many total boxes of crayons do both
teachers have?
Slide 63 / 176
Answer
32 The middle school art teacher has 9 cases of crayons
with 52 boxes in each case. The elementary school art
teacher has 6 cases of crayons with 104 boxes in each
case. How many total boxes of crayons do both
9 x 52 = 468
teachers have?
6 x 104 = 624
468 + 624 = 1,092 boxes
33 A family flies 1,765 miles to their favorite vacation
destination three times per year. How many round
trip miles do they travel per year?
Answer
33 A family flies 1,765 miles to their favorite vacation
destination three times per year. How many round
trip miles do they travel per year?
Slide 64 / 176
1765 x 2 = 3530
3530 x 3 = 10,590 miles
34 The Science Academy School has 1,204 students. If
849 of them buy school lunch five days each week,
how many lunches are purchased each week?
Slide 65 / 176
Answer
34 The Science Academy School has 1,204 students. If
849 of them buy school lunch five days each week,
how many lunches are purchased each week?
849 x 5 = 4245 lunches
35 A garden contains only bean plants and tomato
plants. There are 5 rows of bean plants and 6 rows of
tomato plants. Each row of bean plants has 13 plants.
Each row of tomato plants has 16 plants.
Slide 66 / 176
What is the total number of plants in the garden?
35 A garden contains only bean plants and tomato
plants. There are 5 rows of bean plants and 6 rows of
tomato plants. Each row of bean plants has 13 plants.
Each row of tomato plants has 16 plants.
Answer
What is the total number
13 x of
5 =plants
65 in the garden?
16 x 6 = 96
65 + 96 = 161 plants
36 The table shows the number of yards Ed ran in each
of the first three football games of the season.
Slide 67 / 176
After the first three games of the season, Rico had
exactly 3 times the total number of running yards
that Ed had.
How many more total running yards did Rico have
than Ed after the first three games of the season?
Show your work using equations.
36 The table shows the number of yards Ed ran in each
of the first three football games of the season.
Answer
157 + 309 + 172 = 638
638 x 3 = 1914
1914 - 638 = 1276
Rico had 1276 more yards
After the first three games of the season, Rico had
than Ed.
exactly 3 times the total number of running yards
that Ed had.
How many more total running yards did Rico have
than Ed after the first three games of the season?
Show your work using equations.
Slide 68 / 176
Multiplication by
2 Digit Numbers
table of contents
Teacher Notes
Multiplication by
Students can use this link
to practice
computation.
2 Digit
Numbers
http://mrnussbaum.com/
table of contents
2 Digit Numbers - Area Model
Slide 69 / 176
We are now ready to move onto multiplying larger numbers.
Let's use the area model to find the product of 20 x 57.
Because one of the factors is a multiple of 10, which is an easy
number to multiply, we only need to break up "57".
What is 20 x 50?
50
What is 20 x 7?
7
20
The sum of your products is equal to 20 x 57.
So, the product of 20 x 57 = ?
We are now ready to move onto multiplying larger numbers.
Let's use the area model to find the product of 20 x 57.
Answer
Because one of the factors is a multiple of 10, which is an easy
20 x 50 = 1000
number to multiply, we only need to break up "57".
What is 20 x 50?
50
20
20 x 7 = 140
What
1000is+20
140x =7?
1140
7
The sum of your products is equal to 20 x 57.
So, the product of 20 x 57 = ?
Slide 70 / 176
Most problems will not have factors that are so easy to
multiply! You will have to break upboth factors!
Let's use the area model to multiply 15 x 24. We'll need to
break up both the "15" and the "24". How do you think
these factors should be broken up to make solving this
problem as easy as possible?
Most problems will not have factors that are so easy to
multiply! You will have to break upboth factors!
Answer
Let's use the area model to multiply 15 x 24. We'll need to
break up both the "15" and the "24". How do you think
= 15 +solving
5
these factors should be broken up to15make
this
problem as easy as possible?
24 = 20 + 4
The model we'll make for this problem will look a little
different. We'll need two sections on each side since both
factors were broken up.
20
4
10
5
Multiply the factors in each of the four sections and
then find the sum. This will be the product of 15 x 24.
Slide 71 / 176
10
Answer
The model we'll make for this problem will look a little
different. We'll need two sections on each side since both
factors were broken up.
20
10
5
20
4
4
10 x 20 =
200
10 x 4 =
40
5 x 20 =
100
5x4=
20
200 + 40 + 100 + 20 = 360
5
Multiply the factors in each of the four sections and
then find the sum. This will be the product of 15 x 24.
Slide 72 / 176
Let's try another example...
26 x 13
How will you set up this problem? Think about it carefully
and use the model below to find the product.
Let's try another example...
26 x 13
How will you set up this problem? Think about it carefully
and use the model below to find the product.
Answer
10
20
6
20 x 10 =
200
3
20 x 3
= 60
6x3=
6 x 10 =
18
60
200 + 60 + 60 + 18 = 338
37 Use the area model to find the product.
29 x 19 =
37 Use the area model to find the product.
29 x 19 =
Answer
10
20
9
20 x 10 = 200
Slide 73 / 176
9
20 x 9
= 180
9 x 10 = 90
9x9
= 81
200 + [This
180object
+ 90
+ 81 = 551
is a pull tab]
Write your answer in standard form.
Slide 74 / 176
Write your answer in standard form.
Answer
50
70
70 x 50 = 3500
4
4 x 50 = 200
6
70 x 6
= 420
4 x 6 = 24
3500 + 420
+ 200 + 24 = 4144
Slide 75 / 176
39 The classroom has 27 boxes of crayons with 24
crayons in each box. What is the total amount of
crayons in the classroom? Use an area model to
solve the problem, and write your answer in standard
form.
Answer
39 The classroom has 27 boxes of crayons with 24
crayons in each box. What is the total amount of
crayons in the classroom? Use an area model to
solve the problem, and write your answer in standard
4
20
form.
20
7
20 x 20 = 400
7 x 20 = 140
20 x 4
= 80
7x4
= 28
400 +[This
80object
+ 140
+ 28 = 648
is a pull tab]
Slide 76 / 176
Click for Interactive Web Site
National Library of Virtual Manipulatives
Move to
Select
change
Common
numbers.
Standard Algorithm
Slide 77 / 176
Now, let's multiply 54 x 23 using the Standard Algorithm.
1
54
x 23
54
x
3
162
54
54
x 23
x 20
1080
1. First, we have to multiply 54
by 3 ones.
54 x 3 = 162
2. Next, we have to multiply
54 by 2 tens.
54 x 20 = 1080
1
54
the
hat
e
is w
s lik
This
look
rd
m
le
nda
ta
prob
eS
.
g th
m
in
h
s
it
u
r
Algo
x 23
162
+ 1080
1242
3. The last step is to add the
two products.
162 + 1080 = 1242
Standard Algorithm
Now, let's multiply 124 x 32 using the Standard Algorithm.
1
124
x 43
124
x
3
372
1. First, we have to multiply 124
by 3 ones.
124 x 3 = 372
1
124
124
x 43
x 40
4960
124
x 43
372
+ 4960
5332
2. Next, we have to multiply
124 by 4 tens.
124 x 40 = 4960
3. The last step is to add the
two products.
372 + 4960 = 5332
Slide 78 / 176
Slide 79 / 176
Can you find the product of 138 x 23?
Think about the steps we used in the examples. Don't forget to
regroup and place zeros as needed.
138
x
23
Can you find the product of 138 x 23?
Think about the steps we used in the examples. Don't forget to
regroup and place zeros as needed.
1
138
x
23
Answer
1 2
138
x
23
414
2760
3174
Slide 80 / 176
Let's try one more problem...
422 x 18
Let's try one more problem...
422 x 18
1 1
Answer
422
x
18
3376
+ 4220
7596
Slide 81 / 176
243
x 12
Answer
243
x 12
2,916
Slide 82 / 176
723
x 47
Answer
723
x 47
33,981
64 x 48 =
Slide 83 / 176
Answer
64 x 48 =
3,072
Slide 84 / 176
501 x 13 =
Answer
501 x 13 =
6,513
44 Mr. Kowolski ordered 35 boxes of granola bars. Each
box contained 24 granola bars.
Slide 85 / 176
What is the total number of granola bars Mr. Kowolski
ordered?
44 Mr. Kowolski ordered 35 boxes of granola bars. Each
box contained 24 granola bars.
Answer
What is the total number of granola bars Mr. Kowolski
ordered?
840 granola bars
45 The store ordered small posters and large posters to
promote their opening. Twelve times as many small
posters were ordered as large posters. If there were
48 large posters, how many more small posters were
ordered than large posters?
Slide 86 / 176
Answer
45 The store ordered small posters and large posters to
promote their opening. Twelve times as many small
posters were ordered as large posters. If there were
48 large posters, how many more small posters were
ordered than large posters?
12 x 48 = 576 small posters
576 - 48 = 528 more small
posters were ordered than
large posters
46 Thirty four people each did one hundred forty-nine sit
ups. What is their combined total number of sit ups?
Answer
46 Thirty four people each did one hundred forty-nine sit
ups. What is their combined total number of sit ups?
34 x 149 = 5,066 sit ups
Slide 87 / 176
47 On Saturday, Mike did one hundred twenty-six push
ups in five minutes. How many push-ups would he do
in one hour?
Answer
47 On Saturday, Mike did one hundred twenty-six push
ups in five minutes. How many push-ups would he do
in one hour?
Slide 88 / 176
60/5 = 12
126 x 12 = 1,512 push-ups
Slide 89 / 176
Basics of Division and
Estimating Quotients
table of contents
Slide 90 / 176
Division...the Basics!
There are three parts to a division problem.
This is the Quotient...
the answer to a division problem.
This is the Divisor...
the number you are dividing by.
215
3
645
This is the Dividend...
the number to be divided.
Slide 91 / 176
What does it mean if two numbers are divisible?
Let's come up with a list of numbers that are divisible...
Answer
What does it mean if two numbers are divisible?
Numbers are divisible if
they divide evenly.
Let's come up with a list of numbers that are divisible...
When you divide, it helps to know Rules of Divisibility.
Slide 92 / 176
How do you know that a number is divisible by 10?
click
The number ends with zero.
_____________________________________
click
The number ends with zero or five.
_____________________________________
click
The number ends with 0,2,4,6,or 8 (even #).
_____________________________________
Now that we've reviewed some of the simple rules, let's try a tricky one!
Slide 93 / 176
Think about this...
The following numbers are all divisible by 3:
9
1002
183
204
150
70,000,002
What do you notice about these numbers? Can you describe a
rule that can be used to determine if a number is divisible by 3?
Now that we've reviewed some of the simple rules, let's try a tricky one!
Think about this...
9
1002
Answer
The following numbers are all divisible by 3:
183
150
The sum 204
of the digits is a
multiple of 3.
70,000,002
What do you notice about these numbers? Can you describe a
rule that can be used to determine if a number is divisible by 3?
Use what you
learned about the
Rules of Divisibility
to place each
number into the
Venn Diagram.
Slide 94 / 176
Divisible by 2
152
250
81
54
316
105
Divisible by 10
Divisible by 3
4623
Use what you
learned about the
Rules of Divisibility
to place each
number into the
Venn Diagram.
247
170
126
83
15210
360
Divisible by 2
Divisible by 2
Answer
316
126
54
4623
83
152
247
170
360
250
15210
105
81
Divisible by 3
152
250
81
Divisible by 3
54
105
Divisible by 10
316
4623
126
Divisible by 10
170
247
83
15210
360
Estimating Quotients
When estimating quotients, it's helpful to use numbers that are divisible.
Let's estimate the quotient of 46 ÷ 6.
Ask yourself...how could I rewrite this problem using numbers that
are divisible?
click to reveal
Change the problem to 48 ÷ 6. The quotient is 8!
Numbers that are divisible are called Compatible Numbers because they
"get along" very well!
Slide 95 / 176
Let's rewrite each of the following problems using compatible numbers.
52 ÷ 5
50 ÷ 5
31 ÷ 6
103 ÷ 4
click
30 ÷ 6
100 ÷ 4
Slide 96 / 176
73 ÷ 8
72 ÷ 8
click
Consider the problem 147 ÷ 13. Do you think there is more than
one way to use compatible numbers to estimate the quotient?
Explain your answer.
Let's rewrite each of the following problems using compatible numbers.
52 ÷ 5
103 ÷ 4
click
30 ÷ 6
Answer
50 ÷ 5
31 ÷ 6
100 ÷ 4
73 ÷ 8
72 ÷ 8
click
Yes, there is more than one
Consider the problem 147 ÷ 13. Do you think there is more than
way.
You could
usethe
150quotient?
÷ 15
one way to use compatible
numbers
to estimate
Explain your answer.
or 140 ÷ 14.
Slide 97 / 176
Now, let's try a few word problems...
Molly has $21 and wants to buy a new nail polish that is $4 per
bottle. About how many bottles can she buy?
Scott wants to save $52. If he charges $5 for each lawn
he rakes, about how many lawns does he need to rake?
Now, let's try a few word problems...
Answer
Molly has $21 and wants to buy a new nail polish that is $4 per
bottle. About how many
20 ÷ 4bottles
= 5 can she buy?
Molly can buy about 5
bottles of nail polish.
50 ÷ 5 = 10
Scott wants to save $52. If he charges $5 for each lawn
he rakes,
about
how many
lawns
does he
Scott
needs
to rake
about
10need to rake?
lawns.
48 Tickets for the rides at the boardwalk cost $3 per ride.
About how many rides can you go on if you have $32
to spend on tickets?
Slide 98 / 176
48 Tickets for the rides at the boardwalk cost $3 per ride.
About how many rides can you go on if you have $32
to spend on tickets?
Answer
30 ÷ 3 = 10
About 10 rides
49 Nine friends want to share 38 slices of pizza. About
how many slices will each person get?
Slide 99 / 176
49 Nine friends want to share 38 slices of pizza. About
how many slices will each person get?
Answer
36 ÷ 9 = 4
Each person will get about 4
slices of pizza.
50 Mrs. Ruffle can make 7 fancy bows in an hour. If she
needs to make 68, about how many hours will it take?
Slide 100 / 176
50 Mrs. Ruffle can make 7 fancy bows in an hour. If she
needs to make 68, about how many hours will it take?
Answer
63 ÷ 7 = 9
It will take about 9 hours.
51 The art teacher needs 5 inches of string for each
project. If she has 39 inches of string, about how
many projects can be made?
Slide 101 / 176
51 The art teacher needs 5 inches of string for each
project. If she has 39 inches of string, about how
many projects can be made?
Answer
40 ÷ 5 = 8
About 8 projects can be
made.
52 Mr. Sugar, the pastry chef, can decorate 4 cakes in
one hour. If 42 cakes need to be decorated, about
how many hours will it take?
Slide 102 / 176
52 Mr. Sugar, the pastry chef, can decorate 4 cakes in
one hour. If 42 cakes need to be decorated, about
how many hours will it take?
Answer
40 ÷ 4 = 10
It will take about 10 hours.
Slide 103 / 176
Division with and
without Remainders
table of contents
Teacher Notes
Division with and
without
Remainders
to practice
computation.
table of contents
Now that we've learned how to estimate quotients, it's time to
find exact answers!
Slide 104 / 176
When you divide, you are breaking a number apart into equal
groups.
The problem 15 ÷ 3 means that you are making 3 equal groups
out of 15 total items.
Each equal group contains 5 items, so 15 ÷ 3 = 5
Slide 105 / 176
How will knowing your multiplication facts really well
help you to divide numbers?
click to reveal
Multiplying is the opposite (inverse) of dividing, so you're just
multiplying backwards!
Find each quotient. (You may want to draw a picture and circle
equal groups!)
16 ÷ 4
click
4
24 ÷ 8
click
3
30 ÷ 6
click
5
63 ÷ 9
click
7
You will not be able to solve every division problem mentally.
A problem like 56 ÷ 4 is more difficult to solve, but knowing your
multiplication facts will help you to find this quotient, too!
Slide 106 / 176
To make this problem easier to solve, we can use the same
Area Model that we used for multiplication.
How can you divide 56 into two numbers that are each
divisible by 4? ( ? + ? = 56)
4
?
?
56
You will not be able to solve every division problem mentally.
A problem like 56 ÷ 4 is more difficult to solve, but knowing your
multiplication facts will help you to find this quotient, too!
Answer
To make this problem easier to solve, we can use the same
Area Model that we used for multiplication.
40 + 16 = 56
How can you divide 56 into two numbers that are each
divisible by 4? ( ? + ? = 56)
4
?
?
56
You can break 56 into 40 + 16 and then divide each part by 4.
4
?
?
40
16
56
Ask yourself... What is 40 ÷ 4?
(or 4 x n = 40?)
What is 16 ÷ 4?
(or 4 x n = 16?)
The quotient of 56 ÷ 4 is equal to the sum of the two partial quotients.
Slide 107 / 176
You can break 56 into 40 + 16 and then divide each part by 4.
?
?
40
Answer
4
4
Ask yourself... What is 40 ÷ 4?
(or 4 x n = 40?)
16
56
10
4
40
16
What is 16 ÷ 4?
(or 4 x n = 16?)
10 + 4 = 14, so 56 ÷ 4 = 14
a pull tab]
The quotient of 56 ÷ 4 is equal to the sum[This
ofobject
theistwo
partial quotients.
Let's try another example. Use the area model to find the
quotient of 78 ÷ 3.
Slide 108 / 176
How can you break up 78?
Remember... you want the numbers to be divisible by 3.
3
Let's try another example. Use the area model to find the
quotient of 78 ÷ 3.
Answer
Remember... you want the numbers
20 to be divisible 6by 3.
3
3
60
18
20 + 6 = 26, so 78 ÷ 3 = 26
Slide 109 / 176
53 Use the area model to find the quotient.
96 ÷ 8 =
Answer
96 ÷ 8 =
8
10
2
80
16
10 + 2 = 12, so 96 ÷ 8 = 12
69 ÷ 3 =
Slide 110 / 176
Answer
69 ÷ 3 =
3
20
3
60
9
20 + 3 = 23, so 69 ÷ 3 = 23
Slide 111 / 176
98 ÷ 7 =
Answer
98 ÷ 7 =
7
10
4
70
28
10 + 4 = 14, so 98 ÷ 7 = 14
Sometimes, you'll have a problem with numbers that do not
divide evenly. The leftover number is called the remainder.
Slide 112 / 176
For example, 17 ÷ 6. This means we are making groups of 6
out of 17 total items. Here's how that would look...
There are not enough flowers to make another equal group of 6.
Since there are 2 complete groups and 5 remaining (extra)
items, we say the quotient of 17 ÷ 6 is "2 with a remainder of 5".
This is how we write the quotient: 17 ÷ 6 = 2 R5
Slide 113 / 176
Use basic multiplication facts to find each quotient. Be sure to
include the remainder!
Ask yourself...what is the largest number that will go in
evenly? (It may not go over!) How many do I have left?
24 ÷ 5
5x
click
4 = 20
19 ÷ 3
3 x 6 = 18
click
4 left
1 left
4 R4
6 R1
70 ÷ 8
8 x 8 = 64
click
52 ÷ 7
7 x 7 = 49
click
6 left
3 left
8 R6
7 R3
Here's what a problem with a remainder would look like using
the Area Model.
65 ÷ 9
9
65
Think about the 9 times tables. What is the largest multiple of 9
that will go in to 65? How many extras will you have?
7
9 x 7 = 63
65 - 63 = 2
9
2E
63
xtra
!
2
65
63 is the largest multiple of 9 that will fit into 65 and there will be
2 extra. So, 65 ÷ 9 = 7 R2
Slide 114 / 176
56 Find the quotient. Be sure to include the remainder.
Slide 115 / 176
48 ÷ 5
48 ÷ 5
Answer
9 R3
45 ÷ 7 =
Slide 116 / 176
45 ÷ 7 =
Answer
6 R3
Slide 117 / 176
68 ÷ 8 =
68 ÷ 8 =
Answer
8 R4
Slide 118 / 176
Interpreting the Remainder
When solving word problems, it is important to think about what
the remainder means so you can answer the question correctly!
Here's an example.
Kara has 38 strawberries. If she and her 3 friends share them,
how many strawberries will each girl receive?
38 ÷ 4 =
Interpreting the Remainder
When solving word problems, it is important to think about what
the remainder means so you can answer the question correctly!
Answer
Here's an example.
38 ÷ 4 = 9 R2
This
means
girl
Kara has 38 strawberries.
If she
and that
her 3each
friends
share them,
strawberries
how many strawberrieswill
will receive
each girl 9receive?
and there will be 2 extra.
38 ÷ 4 =
Let's look another word problem.
Manny is packing away some baseballs. He has 41
baseballs and can fit 6 into each box. How many boxes does
he need?
How does the remainder effect your answer?
41 ÷ 6
Slide 119 / 176
Let's look another word problem.
Manny is packing away some baseballs. He has 41
baseballs and can fit 6 into each box. How many boxes does
he need?
Answer
41 ÷ 6 = 6 R5
This means that Manny
How does the remainder
yourbecause
answer? he
needs 7effect
boxes
needs an extra box for the
remaining 5 baseballs.
41 ÷ 6
59 A class is taking a trip to the middle school to see a
play. They are going to travel by van. Each van will
hold 6 students. If 26 students are going on the trip,
how many vans will they need?
Slide 120 / 176
A 6
B 5
C 4
D 2
A 6
B 5
C 4
D 2
Answer
59 A class is taking a trip to the middle school to see a
play. They are going to travel by van. Each van will
hold 6 students. If 26 students are going on the trip,
how many vans will they need?
B
26 ÷ 6 = 4 R2
They will need 5 vans.
60 Justine wants to share her pretzels with her friends.
She has 38 pretzels to share among 5 people
(including herself). How many pretzels will each
person receive?
Slide 121 / 176
A 5
B 6
C 7
D 8
60 Justine wants to share her pretzels with her friends.
She has 38 pretzels to share among 5 people
(including herself). How many pretzels will each
person receive?
C
B 6
C 7
D 8
Answer
A 5
38 ÷ 5 = 7 R3
Each person will get 7
pretzels.
61 Ramel is cutting yarn for a project. Each piece needs
to be 7 inches long and he has 50 inches of yarn.
How many 7-inch pieces will he have?
A 9
B 8
C 7
D 6
Slide 122 / 176
A 9
B 8
Answer
61 Ramel is cutting yarn for a project. Each piece needs
to be 7 inches long and he has 50 inches of yarn.
How many 7-inch pieces will he have?
C
50 ÷ 7 = 7 R1
He will have 7, 7-inch
pieces.
C 7
D 6
62 Mr. Bullock wants new shelves in his classroom. He
has 68 books and wants to put 9 on each shelf. How
many shelves will he need?
Slide 123 / 176
Answer
62 Mr. Bullock wants new shelves in his classroom. He
has 68 books and wants to put 9 on each shelf. How
many shelves will he need?
68 ÷ 9 = 7 R5
He needs 8 shelves.
63 The Parent's Club raised money and bought 33 new
balls for the classes to use at recess. If there are 8
classes, how many balls will each class get?
Slide 124 / 176
Answer
63 The Parent's Club raised money and bought 33 new
balls for the classes to use at recess. If there are 8
classes, how many balls will each class get?
33 ÷ 8 = 7 R5
Each teacher will get 7 balls.
64 The art teacher needs to buy new boxes to store the
markers in. Each box will bold 8 markers and there are
78 markers. How many boxes does the art teacher
need to buy?
Slide 125 / 176
64 The art teacher needs to buy new boxes to store the
markers in. Each box will bold 8 markers and there are
78 markers. How many boxes does the art teacher
need to buy?
Answer
78 ÷ 8 = 9 R6
The art teacher needs 10
boxes.
Slide 126 / 176
Find Whole Number Quotients and Remainders
with up to Four-Digit
Dividends and
One-Digit Divisors
table of contents
Teacher Notes
Find Whole Number Quotients and Remainders
practice
computation.
with toup
to Four-Digit
Dividends
and
One-Digit Divisors
table of contents
Slide 127 / 176
Let's try a problem with larger numbers! How about 136 ÷ 4?
Even though the dividend is a three-digit number, the steps are
the same!
Remember... you want the numbers to be divisible by 4.
Fill in the area model below. You may break 136 up into
two or more parts.
4
Let's look at some of your possible area models for 136 ÷ 4.
You could have broken 136 up in many different ways!
Slide 128 / 176
How could you have broken 136 into two numbers?
How could you have broken 136 into three or more numbers?
Let's look at some of your possible area models for 136 ÷ 4.
You could have broken 136 up in many different ways!
Possible combinations:
100 + 36
Answer
How could you have broken 136 into two numbers?
50 + 56
100 + 20 + 16
80 + 40 + 16
60 + 60 + 16
etc.
How could you have broken 136 into
three or more numbers?
Slide 129 / 176
Here's another example. Let's find the quotient of 216 ÷ 3.
As we discussed before, knowing your multiplication facts will make
dividing numbers much easier! Keep your basic facts in mind when
breaking apart larger numbers.
Here's another example. Let's find the quotient of 216 ÷ 3.
As we discussed before, knowing your multiplication facts will make
dividing numbers much easier! Keep your basic facts in mind when
2
70numbers.
breaking apart larger
Answer
3
210
6
70 + 2 = 72, so 216 ÷ 3 = 72
Or any other way that would
work to break 216 apart.
Do you think you can try one on your own?
Use the area model to find the quotient of 485 ÷ 5.
Remember, there is more than one way to break up 485,
so use numbers that are easy for you to divide! And, you
may break 485 into as many parts as you want!
Slide 130 / 176
Do you think you can try one on your own?
Use the area model to find the quotient of 485 ÷ 5.
Possible Combinations:
Answer
100is+more
100 +than
100one
+ 100
+ 5 up 485,
Remember, there
way+to80
break
so use numbers that are
for+you
200easy
+ 200
80 to
+ 5divide! And, you
may break 485 into as many parts as you want!
400 + 80 + 5
485
÷ 5 = 97
Slide 131 / 176
65 Use an area model to solve.
358 ÷ 2 =
Answer
358 ÷ 2 =
2
150
25
4
300
50
8
150 + 25 + 4 = 179
358 ÷ 2 = 179
Slide 132 / 176
792 ÷ 6 =
Answer
792 ÷ 6 =
6
100
30
2
600
180
12
100 + 30 + 2 = 132
792 ÷ 6 = 132
Slide 133 / 176
The Standard Algorithm
You can also solve division problems using the standard
algorithm. Let's go step-by-step to find the quotient of 42 ÷ 3.
1. Set up your problem.
42 ÷ 3
Dividend
Place inside
the division
symbol.
3 42
Divisor
Place outside
the division
symbol.
Slide 134 / 176
2. Check to see if the divisor goes
into the first digit of the dividend.
3 42
"Does 3 go into 4?" Yes!
"How many times?" One time!
3. Since 3 goes into 4 one time, place a 1
in the quotient directly above the 4.
4. Multiply 1 x 3 and place it under the 4.
5. Subtract and then bring down the next
digit.
6. Now divide 12 by 3.
"How many times does 3 go into 12?"
4 times!
7. Since 3 goes into 12 four times,
place a 4 in the quotient above the 2.
8. Multiply 4 by 3 and then subtract.
42 ÷ 3 = 14
1
3 42
1
3 42
-3
12
1
3 42
-3
12
14
3 42
-3
12
14
42
3
-3
12
-12
0
Let's try another example. Find the quotient of 108 ÷ 3.
1. Set up the problem.
3 108
2. Check to see if 3 goes into
the first digit of the dividend.
"Does 3 go into 1?" No!
3. Since 3 does not go into 1, place
a zero in the quotient above the 1.
Slide 135 / 176
0
3 108
Slide 136 / 176
4. Now see how many times 3 goes
into the first two digits of the dividend.
"How many times does 3 go into 10?"
5. Since 3 goes into 10 three times, place
a 3 in the quotient above the zero and
then multiply 3 x 3.
6. Subtract and bring down the next digit.
Slide 137 / 176
0
3 108
03
3 108
9
03
3 108
-9
18
036
3 108
-9
18
-18
0
108 ÷ 3 = 36
7. Now divide 18 by 3. Since 3 goes into
18 six times, place a 6 in the quotient
above the 8.
8. Multiply 6 x 3 and subtract.
Both of these examples worked out perfectly! We ended up
with zero both times. Sometimes, that will not happen and
you will have a remainder!
Slide 138 / 176
Here's an example. Divide 57 by 4.
4 57
click
14
4 57
-4
17
-16
1
This is
the re
maind
er!
57 ÷ 4 = 14 R1
Slide 139 / 176
There are SO many steps to remember when dividing.
How will I remember all of them??
Here's a quick list of steps to use when dividing:
1. Divide
2. Multiply
3. Subtract
4. Bring Down
Use the steps you've learned to find the quotient of 640 ÷ 5.
click
128
5 640
-5
14
-10
40
-40
0
Slide 140 / 176
1. Divide
2. Multiply
3. Subtract
4. Bring Down
Slide 141 / 176
How about this one??
216 ÷ 3
... the steps!
1. Divide
2. Multiply
3. Subtract
4. Bring Down
How about this one??
Answer
216 ÷ 3
... the steps!
1. Divide
072
2. 3Multiply
216
-21
3. Subtract
06
- 6 Down
4. Bring
0
Slide 142 / 176
67 Find the quotient.
588 ÷ 7 =
Answer
588 ÷ 7 =
084
7 588
-56
28
-28
0
384 ÷ 4 =
Slide 143 / 176
Answer
384 ÷ 4 =
096
4 384
-36
24
-24
0
Slide 144 / 176
711 ÷ 9 =
Answer
711 ÷ 9 =
079
9 711
-63
81
-81
0
Slide 145 / 176
522 ÷ 9 =
Answer
522 ÷ 9 =
58
71 The toy store just received 426 new remote control
planes. They are very popular, so the store manager
wants to put all of them out. If there are 6 shelves,
how many planes will go on each shelf?
Slide 146 / 176
Answer
71 The toy store just received 426 new remote control
planes. They are very popular, so the store manager
wants to put all of them out. If there are 6 shelves,
how many planes will go on each shelf?
426 ÷ 6 = 71 planes
72 For field day, students will be organized into teams of
8. If there are 224 students participating in field day,
how many teams can be made?
Slide 147 / 176
Answer
72 For field day, students will be organized into teams of
8. If there are 224 students participating in field day,
how many teams can be made?
224 ÷ 8 = 28 teams
73 A basketball team scored a total of 747 points for the
season. This was 9 times the number of points
scored in the first game. How many points were
scored suring the first game?
Slide 148 / 176
A 73
B 75
C 82
D 83
A 73
B 75
Answer
73 A basketball team scored a total of 747 points for the
season. This was 9 times the number of points
scored in the first game. How many points were
scored suring the first game?
D
747 ÷ 9 = 83
C 82
D 83
74 New uniforms for the nine members of the basketball
team will cost $315. How much is one uniform?
Slide 149 / 176
74 New uniforms for the nine members of the basketball
team will cost $315. How much is one uniform?
Answer
315 ÷ 9 = $35
Slide 150 / 176
Be sure to read this problem carefully!
There's a lot of information and more than one step!
Jon has $120 in the bank. He puts in another $58. He
spends $45 on new sneakers and wants to spend the rest
on t-shirts. If each t-shirt cost $9, how many can he buy?
Be sure to read this problem carefully!
There's a lot of information and more than one step!
120 + 58 = 178
Answer
Jon has $120 in the bank. He puts in another $58. He
spends $45 on new sneakers and178
wants
- 45to=spend
133 the rest
on t-shirts. If each t-shirt cost $9, how many can he buy?
133 ÷ 9 = 14 R7
He can buy 14 t-shirts.
Slide 151 / 176
75 Hayley has 272 beads. She buys 38 more beads. She
will use 89 beads to make bracelets and the rest to
make necklaces. She will use 9 beads for each
necklace.
What is the greatest number of necklaces Hayley can
make?
75 Hayley has 272 beads. She buys 38 more beads. She
will use 89 beads to make bracelets and the rest to
make necklaces. She will use 9 beads for each
necklace.
Answer
What is the greatest number
of =
necklaces
Hayley can
272 + 38
310 beads
make?
310 - 89 = 221 left
221 ÷ 9 = 24 R5
She can make 24 necklaces.
76 Uniforms are sold in packages of 8. The store’s 119
employees will each be given 3 uniforms. How many
packages will the store need to order?
Slide 152 / 176
76 Uniforms are sold in packages of 8. The store’s 119
employees will each be given 3 uniforms. How many
packages will the store need to order?
Answer
119 x 3 = 357
357 ÷ 8 = 44 R5
They need to order 45
packages.
Oh no... This problem looks scary!!
Slide 153 / 176
Don't worry about solving division problems with larger dividends.
It may take a little longer, but just follow the steps!
7 3703
Oh no... This problem looks scary!!
7 3703
Answer
Don't worry about solving division problems with larger dividends.
It may take a little longer, but just follow the 0529
steps!
7 3703
-35
20
-14
63
-63
0
Slide 154 / 176
Let's try another one! Find the quotient of 7430 ÷ 5.
Answer
Let's try another one! Find the quotient of 7430 ÷ 5.
1486
5 7430
-5
24
-20
43
-40
30
-30
0
Slide 155 / 176
Let's try one more problem. Find the quotient of 3749 ÷ 5.
5 3749
Let's try one more problem. Find the quotient of 3749 ÷ 5.
Answer
5 3749
0749 R4
5 3749
-35
24
-20
49
-45
4
Slide 156 / 176
77 Solve.
1746 ÷ 3 =
Answer
77 Solve.
1746 ÷ 3 =
582
Slide 157 / 176
78 Solve.
1944 ÷ 9 =
Answer
78 Solve.
1944 ÷ 9 =
216
79 Solve.
6259Students
÷5=
type their answers here
Slide 158 / 176
Answer
79 Solve.
6259Students
÷5=
type their answers here
1251 R4
80 The circus made $5607 from ticket sales during the
first week in August. Each ticket cost $9. How many
tickets were sold?
Slide 159 / 176
80 The circus made $5607 from ticket sales during the
first week in August. Each ticket cost $9. How many
tickets were sold?
Answer
623 tickets
81 The circus also made $1004 from selling balloons for
$4 each. How many balloons were sold?
Slide 160 / 176
81 The circus also made $1004 from selling balloons for
$4 each. How many balloons were sold?
Answer
251 balloons
82 The circus also made $1443 from selling popcorn. If
each bag of popcorn costs $3, how many bags were
sold?
Slide 161 / 176
82 The circus also made $1443 from selling popcorn. If
each bag of popcorn costs $3, how many bags were
sold?
Answer
481 bags of popcorn
83 Ms. Hershey has 1,478 M & Ms to divide among 9
students. Will each student receive the same amount?
Explain.
Slide 162 / 176
83 Ms. Hershey has 1,478 M & Ms to divide among 9
students. Will each student receive the same amount?
Explain.
Answer
No
Each student will get 164
and there will be 2 left over.
Slide 163 / 176
84 Four teachers offer an after-school chess club. The
table shows the number of students who joined.
of Students
Third
12
Fourth
36
Fifth
9
Part A
Answer
Grade
The teachers will divide the total group of students
who joined into teams of no more than 6 students.
What is the least number of teams that will include all
of the students?
Slide 164 / 176
85 Part B
The chess club started with 18 chess sets. The
teachers ordered 3 cases of 15 chess sets. They will
divide the total number of chess sets so that each
teacher receives an equal number. Then they will
give any extra sets to the school library. What is the
greatest number of chess sets each of the 4
teachers should get?
85 Part B
Answer
The chess club started with 18 chess sets. The
teachers ordered 3 cases of 15 chess sets. They will
divide the total number of chess sets so that each
teacher receives an equal number. Then they will
3 x 15 =library.
45
give any extra sets to the school
What is the
+ 18
= 63of the 4
greatest number of chess45
sets
each
teachers should get? 63 ÷ 4 = 15 R3
They will each get 15 chess
sets.
86 The number of science fair projects entered for each
grade in a city-wide science fair is shown.
Slide 165 / 176
Part A
The science fair projects are set up on tables. There
are 99 long tables used. Each long table holds 7
projects. The rest of the projects are set up on short
tables. Each short table can hold 4 projects. What is
the fewest number of short tables that will be needed
for the rest of the projects?
A 202
C 354
B 203
D 355
Answer
86 The number of science fair projects entered for each
grade in a city-wide science fair is shown.
462 + 759 + 891 = 2112
Part A
99 x 7 = 693
The science fair projects are set up on tables. There
2112
- 693Each
= 1419
are 99 long tables
used.
long table holds 7
projects. The rest
of
the
projects
1419 ÷ 4 = 354 R3 are set up on short
tables. Each short table can hold 4 projects. What is
the fewest number of short tables that will be needed
for the rest of the projects?
D 355
A 202
C 354
B 203
D 355
87 Part B (Continued from previous slide.)
The science fair judges will be science teachers and
volunteers. Each judge will only have time to view 5
science fair projects. There are 133 science teachers.
What is the fewest number of volunteers needed to
have enough judges for all of the projects?
A 290
B 396
C 422
D 423
Slide 166 / 176
Answer
The science fair judges will be science teachers and
volunteers. Each judge will only have time to view 5
+ 759 There
+ 891 =are
2112
science fair462
projects.
133 science teachers.
What is the fewest
of volunteers needed to
133number
x 5 = 665
have enough judges for all of the projects?
2112 - 665 = 1447
A 290
B 396
C 422
1447 ÷ 5 = 289 R2
A 290
D 423
88 Jian's family sells honey from beehives. They
collected 3,311 ounces from the beehives this season.
They will use the honey to completely fill 4-ounce jars
or 6-ounce jars.
Slide 167 / 176
Jian's family will sell 4-ounce jars for $5 each or 6ounce jars for $8.
Jian says if they use only 4-ounce jars, they could
make $4,140 because 3,311 ÷ 4 = 827 R 3. That rounds
up to 828, and 828 multiplied by $5 is $4,140.
Part A
Explain the error that Jian made when finding the
amount of money his family could make if they use
only 4-ounce jars. Show your explanation.
Answer
88 Jian's family sells honey from beehives. They
collected 3,311 ounces from the beehives this season.
They will use the honey to completely fill 4-ounce jars
or 6-ounce jars.
3311 ÷ 4 does equal 827 R3,
Jian's family
sell
4-ounce
butwill
that
means
theyjars
canfor $5 each or 6ounce jars foronly
$8. make 827 jars.
Jian says if they use only 4-ounce jars, they could
make $4,140 because 3,311 ÷ 4 = 827 R 3. That rounds
827 x 5 = $4135
up to 828, and 828 multiplied by $5 is $4,140.
Part A
Explain the error that Jian made when finding the
amount of money his family could make if they use
only 4-ounce jars. Show your explanation.
Slide 168 / 176
Explain how to determine the money Jian's family
could make if they use only 6-ounce jars. Include the
total amount of money and the total number of 6ounce jars in your explanation.
Answer
Explain how to determine the money Jian's family
could make if they use
only
jars. Include the
3311
÷ 66-ounce
= 551 R5
total amount of money and the total number of 6They
can make 551 6-ounce
ounce jars in your
explanation.
jars.
551 x $8 = $4408
They will make $4408.
Slide 169 / 176
Quotients with Zeros
table of contents
Slide 170 / 176
Look closely at this problem.
Find the quotient of 3549 ÷ 7.
0507
7 3549
-35
04
-0
49
-49
0
You'll have to start out by placing a zero in the
quotient because 7 does not go into 3.
When you bring down the 4, you will need to
place another zero in the quotient because 7
does not go into 4. This zero serves as a
place-holder. When you bring the 9 down,
you'll be able to divide and finish the problem!
3549 ÷ 7 = 507
Slide 171 / 176
90 Solve.
2721 ÷ 3 =
Answer
90 Solve.
2721 ÷ 3 =
907
Slide 172 / 176
91 Solve.
2832 ÷ 4 =
Answer
91 Solve.
2832 ÷ 4 =
708
92 For vacation, the Tatum family wants to drive 1224
miles. If the driving is split evenly between 3 days,
how many miles will be driven each day?
Slide 173 / 176
Answer
92 For vacation, the Tatum family wants to drive 1224
miles. If the driving is split evenly between 3 days,
how many miles will be driven each day?
408 miles
93 While on vacation, the Tatum family will pay $1040 for
4-day passes to an amusement park for five people.
What is the cost per person?
Slide 174 / 176
93 While on vacation, the Tatum family will pay $1040 for
4-day passes to an amusement park for five people.
What is the cost per person?
Answer
$260
94 The Tatum family has budgeted $1540 for food for five
days. How much money can they spend on food each
day?
Slide 175 / 176
94 The Tatum family has budgeted $1540 for food for five
days. How much money can they spend on food each
day?
Answer
$308 per day
95 A team runs a race. There are 4 people on the team,
and each person runs the same distance. The team
runs a total distance of 5,280 feet. What is the
distance, in feet, that each person runs?
Slide 176 / 176
Answer
95 A team runs a race. There are 4 people on the team,
and each person runs the same distance. The team
runs a total distance of 5,280 feet. What is the
distance, in feet, that each person runs?
1,320 feet

s - NJCTL

Transcription

Similar documents

Family Fun June 18, 2016 • 5th Annual VintageTractor Pull MODEL

Career Connections Online Profile Setup Guide

Allscripts Basic Navigation for Residents and Providers Once you

File - El Paso High School Dual Language Magnet

1 Humbucker, 4 Conductor, Push Pull Volume Pot wiring for phase

Replacing LCD Inverter on a Dell Inspiron 8600 to

Monster Jobs - by Carpe Data

CISM 2201 - SIMnet Project Hints - Access In Access NEVER click

Jessica Kenney - BDCHS Office of Student Services

Computer Settings For NAUTIKOS