LESSON
Name
51
page 326
• Adding Numbers with
More Than Three Digits
• Checking One-Digit
Division
New Concept
• Adding Numbers
with More Than
Three Digits
• When writing whole numbers in columns, carefully line up
digits starting with the ones digit in each number.
• Write whole numbers in columns to make adding easier.
• Line up digits starting with the ones digit in each number.
Example
+
1 1 1
$4 9 5
0
$
4
8
3
$
5
2
5
3
7
9
5
$
$5
• Checking
One-Digit Division
9
• Check division by multiplying.
Example
© 2008 Saxon
4
___
)
3 12
Saxon Math Intermediate 4
331
4
×3
12
Adaptations Lesson 51
Lesson Practice
Add:
a.
b.
4356
+ 5644
46,027
+ 39,682
c.
360,147
+ 96,894
Check with a calculator.
d.
e.
436
+
43,284
+
Divide. Check each answer by multiplying.
___
___
3×
___
h. 6 ) 48
g. 7 ) 42
f. 3 ) 21
= 21
Written Practice
7×
= 42
2. number in each group × number of groups
8 players on team
× 4 teams
×
players in all
pennies
stacks
total pennies
second lap
© 2008 Saxon
65.3 seconds
= 48
page 328
1. number in each group × number of groups
3.
6×
first lap
faster
Saxon Math Intermediate 4
332
Adaptations Lesson 51
Written Practice, continued
4.
page 329
42
6
7
×
_____
_____
)
×
)
Use work area.
5. 1 + 3 + 5 + 7 + 9
52
6. a. 3 6 7
b. 36 7
a.
b.
Use work area.
7. Shade 50% of this circle.
Use work area.
b.
c.
© 2008 Saxon
8. a.
a.
b.
c.
Saxon Math Intermediate 4
333
Adaptations Lesson 51
Written Practice, continued
4 ft
9.
page 329
a. length
b. width
c. perimeter
d. area
2 ft
10. 2.75 quarts
a.
b.
c.
d.
11. Round each area to the nearest
hundred.
words:
Estimate the difference.
710
488
–
Use work area.
12. Describe the order of
operations.
13.
63,285
+ 97,642
Solve.
15.24 + (19.6 – 1.1)
First
–
19.6
1.1
n
Saxon Math Intermediate 4
. Then
© 2008 Saxon
Order of operations:
.
n
+ 15.24
334
Adaptations Lesson 51
Written Practice, continued
14.
$5.00
– $4.81
15.
page 330
n
+ 39.8
61.4
16. Carry on your fingers.
85
× 5
n=
17.
18. in your head
37
× 7
×
19.
f
× 8
72
20.
–
40
8
47.8
c
20.3
f=
21.
+
462,586
39,728
c=
22.
z
– 4.78
2.63
© 2008 Saxon
z=
___
____
23. 2 ) 18
Check: 2 ×
Saxon Math Intermediate 4
24. 7 ) 21
= 18
Check: 7 ×
335
= 21
Adaptations Lesson 51
Written Practice, continued
page 330
56 =
25. ___
8
Check: 8 ×
= 56
–––
–––
–––
26. The length of AB is 7 cm. The length of AC is 12 cm. How long is BC?
A
B
27. 2_1 boys
+
%
boys
%
girls
C
28. 5n = 0
n=
100%
6n =
29.
30. What was the median age in 2000?
30
+
B 0.11
C 11%
D 11
when I added
and
the sum was
.
Saxon Math Intermediate 4
© 2008 Saxon
My answer is reasonable because
Which is not equal to the other choices?
100
increase
median in 2000
Which does not name the shaded
portion of the large square?
11
A ____
median in 1980
336
Use work area.
Adaptations Lesson 51
LESSON
Name
52
Teacher Notes:
page 331
• Introduce Hint #29 “Word Problem
Cues, Part 2.”
• Review Hint #3 “Finding Missing
Numbers.”
• Subtracting Numbers with
More Than Three Digits
• Word Problems About
Equal Groups, Part 2
• Review “Word Problem Keywords”
on page 6 in the Student Reference
Guide.
• For additional practice, students
may complete Targeted Practice 52.
New Concept
• Subtracting
Numbers with
More Than Three
Digits
• Write whole numbers in columns to make subtracting
easier.
• Line up digits starting with the ones digit in each number.
• Always start subtracting in the ones column. Then continue
subtracting as you move from right to left.
Example
2 15
4
3 6,11 5 12
− 9, 4 1 5
2 6, 7 3 7
• Word Problems
About Equal
Groups, Part 2
• Formula for equal groups problems
Number in each group
× Number of groups
Total
• When a factor is missing
© 2008 Saxon
3 tennis balls in each can
× n cans
21 tennis balls altogether
Saxon Math Intermediate 4
337
Divide.
missing factor
___
3 ) 21
divide
n=7
Adaptations Lesson 52
Lesson Practice
Subtract.
a.
b.
4783
− 2497
c.
4000
− 527
$20.00
− $12.25
d. There were 35 people.
There were 7 cars. The number of people in each car was the same.
How many people were in each car? missing factor
divide
n
people in each car
cars
35 total people
×7
____
7)3 5
people
e. Thirty students were arranged in rows.
Six students were in each row.
How many rows were there? missing factor
students in each row
× n rows
30 total students
divide
6
____
)3 0
rows
f. Mr. Tran wants to arrange his 29 students into 5 groups.
About how many students will be in each group?
Explain how you found your answer. missing factor
divide
n
students in each group
× 5 groups
29 total students
____
_____
5)2 9
5)
compatible numbers
is not compatible with 5.
with 5 and is close to 29, so I divided
answer was
Saxon Math Intermediate 4
3
is compatible
by 5 and the
students.
338
Adaptations Lesson 52
© 2008 Saxon
2
page 334
Written Practice
1. number in each group × number of groups
2.
60 students in each bus
× 8 buses
missing factor
total students
3.
10
____
missing factor
____
5.
Tanya
Hermelinda
will not win
sooner
7. 1 + 2 + 3 + 4
56
×
___
58.26 seconds
will win
6.
7
____
√100
8
___
)
© 2008 Saxon
)
divide
4)2 8
swimmers
×
divide
9)6 3
n players on each team
× 4 teams
28 total players
4.
9 students in each van
vans
63 total students
×n
Use work area.
Use work area.
8.
… , 6000, 7000, 8000,
,
,…
Use work area.
Saxon Math Intermediate 4
339
Adaptations Lesson 52
page 335
Written Practice, continued
9.
465
second
10.
8.4 9
11. 6n = 42
0.0 0
first
42
+ 0.0 0
6
n
fewer
n=
12.
47,586
+ 23,491
13.
$5.00
− $3.26
14.
n
+ 25.8
60.4
n=
15.
49
× 6
16.
84
× 5
17.
19.
400
−
n
256
20.
70
× 8
Did you carry on your
fingers?
35
× 9
$40.00
− $24.68
© 2008 Saxon
18.
n=
Saxon Math Intermediate 4
340
Adaptations Lesson 52
page 335
Written Practice, continued
21. a. 6 3 9
22. Which side of this
triangle appears to be
perpendicular to PR?
b. 6 3 9
23.
1
__
2
49%
P
%
R
%
Q
a.
b.
Use work area.
___
24. a. 3 ) 27
check
check
× 7
____
check
× 8
____
____
c. 8 ) 72
25. perimeter
27
14 m
___
b. 7 ) 28
× 3
____
17 m
16 m
18 m
Use work area.
27. If
= , which of these is not
necessarily true?
26. Round.
a. $24.10
A
b. 24.1
+2=
B 2×
© 2008 Saxon
C
=2×
−2=
D 2×
+2
=
−2
+2
a.
b.
Saxon Math Intermediate 4
341
Adaptations Lesson 52
page 336
Written Practice, continued
28.
a. fraction:
b. decimal:
c. percent:
Use work area.
29. Find a reasonable estimate of 33 ÷ 8.
3
The multiple of 8 that is the closest to 33 is
3
divided by 8 is
,
,
and
so
is a
reasonable estimate.
Use work area.
30. List the different amounts using 2 coins from least to greatest.
50¢
25¢
5¢
1¢
Write each amount with a dollar sign.
+
1¢
+
=
1¢
+
=
5¢
+
=
+
=
+
=
25¢
5¢
=
6¢
$0.06
© 2008 Saxon
1¢
Use work area.
Saxon Math Intermediate 4
342
Adaptations Lesson 52
LESSON
Name
53
Teacher Notes:
page 337
• Use color tiles to demonstrate
concepts in this lesson.
• One-Digit Division with a
Remainder
• For additional practice, students
may complete Targeted Practice 53.
New Concept
• We cannot divide 13 dots into equal groups of four.
There will be one dot too many.
â
13 dots
3 equal groups
Remainder
• There is one dot left over.
The amount left over is the remainder.
3 R1
___
4 )13
− 12
_____
1
We write the answer like this: 3 R 1
“R” means “remainder.”
• Any remainder must be smaller than the divisor.
Activity
page 339
Finding Equal Groups with Remainders
1. 25 students were divided into groups of 4.
How many groups?
© 2008 Saxon
Use counters.
Saxon Math Intermediate 4
343
Adaptations Lesson 53
New Concept, continued
I used my counters and made four equal groups of
students. There was
leftover. I added the leftover
to one group. Now there are
and
groups of 4 students
group of
students. Altogether there are
groups of students.
2. Use your textbook to complete problem 2.
Lesson Practice
a. Circle groups of dots below to show 14 ÷ 4.
Write the answer shown by your sketch.
R
Divide. Write each answer with a remainder.
___
b. 3 )17
R
e. 15 ÷2
___
c. 5 )12
____
) 15
R
R
___
d. 4 )23
____
) 20
f. 20 ÷ 6
h. About how many yards is 28 feet?
R
R
g. 25 ÷ 3
____
) 25
R
© 2008 Saxon
1 yard
formula: feet ÷ 3 = yards
Circle groups of 3.
yards
Saxon Math Intermediate 4
344
Adaptations Lesson 53
page 341
Written Practice
1.
8 beads in each bag
× n bags
56 total beads
missing factor
2.
divide
missing factor
___
) 42
4. See page 3 in the Student Reference Guide.
28
4
divide
___
8 ) 56
3.
n children in each car
× 7 cars
42 total children
7
×
×
_____
)
)
_____
Use work area.
5. … , 16,000, 17,000, 18,000,
a. To find the next term
Use work area.
,
a
,
,…
.
© 2008 Saxon
b. next term:
Use work area.
6. a. 47 2 8
7. a quarter after four in the afternoon
b. 472 8
Use work area.
Saxon Math Intermediate 4
345
Adaptations Lesson 53
page 342
Written Practice, continued
8. One side of a square is 4 feet long.
a. What is the perimeter of the square?
4 ft
b. What is the area?
Area = length × width
a.
b.
9.
First,
+
(42 ÷ 6) =
+
=
d
r
14.
×
by
of
$6.35
$0.00
$0.
11.
42
60
9
. Second, find the
.
12.
Then, add
$100.00
$
.
51,438
13.
−
.
15. Carry on your fingers.
×
Saxon Math Intermediate 4
and
s
© 2008 Saxon
___
10. √64
346
57
4
Adaptations Lesson 53
Written Practice, continued
16. Show 22 ÷ 5.
page 342
17. 25 ÷ 4
____
) 25
18.
____
6 ) 39
R
R
R
Use work area.
19.
____
7 ) 30
R
20.
46
× 8
21.
38
× 7
22.
z
– 16.5
40.2
z=
23.
6.75
.
.
24. seven million, two hundred sixty thousand
,
© 2008 Saxon
25. 1.89 L
,
26. Shakir said, “I am thinking of two
numbers. Their product is 6.” The two
numbers Shakir was thinking of could
not be
.
words:
A 1 and 6
B 2 and 3
C 3 and 2
D 6 and 0
Use work area.
Saxon Math Intermediate 4
347
Adaptations Lesson 53
page 343
Written Practice, continued
27. a. a quarter =
% of a dollar
b. a quart =
28.
a. fraction
b. decimal
% of a gallon
c. percent
See page 1 in the Student Reference Guide.
a.
a.
b.
b.
c.
29. ounces ÷ 8 = cups
_____
___
8 ) 67.6
8)
Use compatible numbers.
Look for a multiple of 8.
I used
c
numbers. For 67.6, I used the number
because it is a multiple of 8. Then I divided by 8. Brandon
bought about
cups of juice.
Use work area.
871 taller building
−
shorter building
© 2008 Saxon
30.
feet taller
I subtracted
feet from
feet.
Saxon Math Intermediate 4
feet and got
Use work area.
348
Adaptations Lesson 53
LESSON
Name
54
Teacher Note:
page 344
• The Calendar
• Rounding Numbers to the
Nearest Thousand
• Refer students to “Time” on page 2
and “Months of Year” on page 3 in
the Student Reference Guide.
New Concept
• The Calendar
Math Language
• This will help you remember how many days are in each
month:
Thirty days hath September,
A common year
is a year with 365
days.
April, June, and November.
A leap year is a
year with 366 days.
All the rest have thirty-one.
The extra day
is added to
February.
A leap year
happens every 4
years.
February has twenty-eight alone,
Excepting leap year,
That’s when February’s days are twenty-nine.
• To find the amount of time between two years
Formula
Later
− Earlier
Difference
A decade is 10
years.
A century is 100
years.
Subtract.
1776
− 1620
156
© 2008 Saxon
• Rounding Numbers • To round a number to the nearest thousand:
to the Nearest
1. Underline the thousands place.
Thousand
2. Circle the digit to its right.
3. Ask: Is the circled digit 5 or more? (5, 6, 7, 8, 9)
Yes
Add 1 to the underlined number.
No
The underlined number stays the same.
4. Replace the circled number and the numbers after it
with zero.
Example
6 2 46
Saxon Math Intermediate 4
349
6000
Adaptations Lesson 54
Lesson Practice
a. How many days are in a leap year?
b. According to this calendar, what is the date of the
fourth Friday of the month?
,
MAY 2014
S M T W T F S
04
11
18
25
05
12
19
26
06
13
20
27
07
14
21
28
1
08
15
22
29
02
09
16
23
30
03
10
17
24
31
c. How many years were there from 1918 to 1943?
1943
− 1918
d. A century is how many decades?
century × 10 = decades
10
× 1
decades
Round each number to the nearest thousand:
e. 6 7 46
f. 5 2 80
h. 21,694
i.
g. 12, 3 27
j. 27,462
9870
Round 6472 to the neartest thousand, to the nearest hundred, and to the nearest ten.
© 2008 Saxon
k. 6 4 72
64 7 2
647 2
Saxon Math Intermediate 4
350
Adaptations Lesson 54
Written Practice
1.
s
×4
24
page 348
students in each row
rows
total students
missing factor
____
)2 4
2. number in each group × number of groups
3. 1938
1921
students
×
divide
later
earlier
difference
projects
total projects
10
4.
×
years in a decade
5. What day of the week was December
25, 1957?
number of decades
DECEMBER 1957
© 2008 Saxon
total years
A 5 years
B 50 years
C 500 years
D 5000 years
S M T W T F S
01
08
15
22
29
02
09
16
23
30
03
10
17
24
31
04
11
18
25
05
12
19
26
06
13
20
27
07
14
21
28
6. 5 2 36
6 9 29
+
Saxon Math Intermediate 4
351
Adaptations Lesson 54
page 348
Written Practice, continued
7. a.
a. fraction
8.
mi
mi
b. percent
b. perimeter:
c. Area = length × width
a.
b.
Use work area.
9. Write the number two different ways.
mixed number:
–2
–1
0
1
2
decimal:
Use work area.
14.
$0.17
$ .
$ .
$ .
$20.00
− $18.47
11.
794,150
+ 9,863
12.
$51,786
+ $36,357
13.
87.6
4.0
31.7
5.5
1.1
+ 0.5
15.
41,315
− 29,418
16. Carry on your
17.
54
× 8
fingers.
© 2008 Saxon
10.
46
× 7
Saxon Math Intermediate 4
352
Adaptations Lesson 54
page 349
Written Practice, continued
18. Write the “carry number.”
19.
39
× 9
21. 4y = 32
22. 43 ÷ 7
missing factor
3.68
0.0 0
0. 00
20.
40
× 9
____
)4 3
divide
R
23.
____
9)6 4
R
___
)
y=
24. 2.54 cm
words:
Use work area.
25.
___
9 )52
____
Use compatible numbers.
9)
52 is not compatible with 9.
© 2008 Saxon
so I divided
estimate:
is compatible with 5 and is close to 52,
by 5, and the answer was
students.
26. a. name of segment showing diameter:
R
M
and
b.
S
intersect at point
T
.
Use work area.
Saxon Math Intermediate 4
353
Adaptations Lesson 54
Written Practice, continued
page 349
27. Round.
a. fraction
28.
a. $136.80
b. decimal
b. 136.8
c. percent
a.
a.
b.
b.
c.
29.
Number of $1 Bills
10
20
30
40
50
Number of $10 Bills
1
2
3
4
5
The number of $1 bills times
$
equals the number of
bills.
Use work area.
30.
$1
$5
$1
$1
© 2008 Saxon
$5
$10
Use work area.
Saxon Math Intermediate 4
354
Adaptations Lesson 54
LESSON
Name
55
Teacher Notes:
page 351
• Introduce Hint #30 “Multiples,”
and Hint #31 “Factors of Whole
Numbers.”
• Prime and Composite
Numbers
• Refer students to “Factors” and
“Multiples” on page 8 in the
Student Reference Guide.
• Review “Multiplication Table” on
page 5 in the Student Reference
Guide.
New Concept
• The multiples of 4 are the numbers we say
if we count by fours.
Math Language
Multiples of 4:
A prime number is a
counting number that
has exactly two factors
(itself and 1).
4, 8, 12, 16, 20, 24, …
• The factors of 8 are the numbers that can be multiplied to
get 8.
2, 3, 5, 7, 11, 13, 17, 19…
1×8=8
A composite number
is a number with more
than two factors.
2×4=8
1, 2, 4, and 8 are factors of 8.
4, 6, 8, 9, 10, 12, 14, 15…
Activity
page 353
Using Arrays to Find Factors
© 2008 Saxon
Use your textbook to complete this activity.
• To find the factors of a whole number:
1. Always start with the number 1.
2. Always end with the number given.
3. Find all the other factors of the given number.
Use the multiplication table.
4. Make sure the factors are listed in order.
Write each factor only once.
Example
List the factors of 12.
Remember to start with 1 and to end with 12.
1
Saxon Math Intermediate 4
,
2
,
355
3
,
4
,
6
,
12
Adaptations Lesson 55
Lesson Practice
a. List the first five multiples of 6.
6
,
,
b. multiples of 9:
,
,
,
c. multiples of 8:
,
,
,
,
,
,
,
,
,
d. What is the last digit of any multiple of 10?
e. What two digits appear as the last digit of the multiples of 5?
f. What five digits appear as the last digit of the multiples of 2?
last digit:
,
,
,
or
g. Ten is a multiple of which whole numbers?
,
,
,
factors of 10
h. Draw two different rectangles with an area of 8.
Use grid paper.
i.
The rectangle below shows one possible way to make a rectangle with an area of 10.
5
Draw all the other possible arrangements.
Find the factors of 10 first.
5ñ2
2
,
,
,
Use grid paper.
j.
List the factors of 5.
,
prime number
l.
,
,
,
True or False: If a counting number is greater than 1 and is not prime, then it is
composite.
prime = 2 factors
composite = more than 2 factors
Saxon Math Intermediate 4
356
Adaptations Lesson 55
© 2008 Saxon
k. Write all the prime numbers less than 10.
Written Practice
$1.85
1.
bought
page 356
2000
2.
entered
3.
−
$ .
more
will win
sold
will not win
4. More boys or girls?
60%
+
11,003
8484
4 cm
5.
boys
% girls
100%
a. perimeter:
b. area:
Use work area.
6. first 3 multiples of 4:
7. factors of 15
Use the Multiplication Table.
,
,
1
,
,
,
15
third multiple of 4
−2 =
© 2008 Saxon
Use work area.
Use work area.
It is afternoon. What time was it 30 minutes ago?
8.
12 1
11
10
2
9
3
4
8
7
6
5
Saxon Math Intermediate 4
Time now:
30 minutes ago:
357
Adaptations Lesson 55
page 356
Written Practice, continued
___
9.
1789
1776
later
earlier
10. What is the length of ST ?
R
S
T
difference
11.
4.00
− 2.22
12.
14.
$25.42
− $ 7.25
15.
89
× 4
18.
17.
20.
____
8 ) 15
R
3
4
5
6
7
8
70.5
− 42.3
13.
$45.87
+ $23.64
64
5
16.
70
× 6
63
× 7
19.
×
21.
2
63
___
7
4 . 68
.
.
____
)
9
R
22. Make groups to show
15 ÷ 6.
Use work area.
Saxon Math Intermediate 4
358
Adaptations Lesson 55
© 2008 Saxon
cm 1
page 357
Written Practice, continued
___
23. √ 64 ÷ (4 + 4)
÷
First,
24. $0.75 + $0.75 + $0.75 + $0.75
=
a
and
Second, find the
.
s
r
of
.
Then, divide
by
.
Use work area.
25. a. Which of these numbers can be
divided by 5 without leaving a
remainder?
×
26. Is 500 a reasonable estimate of
128 × 4?
Which is a multiple of 5?
A 32
B 35
C 37
D 41
compatible number
×
500
b. Whole numbers ending in
or
are multiples of 5,
© 2008 Saxon
r
know 128 is close to
and
,
×4=
.
.
Use work area.
Saxon Math Intermediate 4
a
reasonable estimate of 128 × 4. I
so they can be divided with
no
4
500
359
Use work area.
Adaptations Lesson 55
Written Practice, continued
page 357
27. Round.
a. $2. 5 4
b. 2. 5 4
a.
b.
28.
a. fraction:
b. decimal:
c. percent:
Use work area.
29. composite number = more than 2 factors
A 2
B 3
C 4
30. three-digit numbers using 8, 3, and 4
D 5
least to greatest
3
least
4
greatest
different numbers
Saxon Math Intermediate 4
360
Adaptations Lesson 55
© 2008 Saxon
8
LESSON
Name
56
Teacher Notes:
page 359
• Introduce Hint #32 “Comparing
Fractions.”
• Review Hint #27 “FractionDecimal-Percent Manipulatives.”
• Using Models and
Pictures to Compare
Fractions
• For additional practice, students
may complete Fraction Activity 56.
New Concept
Activity
page 360
Comparing Fractions
Use your textbook to complete problems 1– 6.
Write >, <, or =.
Use your fraction manipulatives.
3
7. __
4
1
9. __
4
6
__
3
___
8
1
8. __
4
10
1
__
5
2
10. __
3
6
___
10
11. Use your fraction manipulatives to model:
• three fifths
• four tenths
• one half
• two eighths
• three fourths
a. greatest to least using fractions
3
__
4
,
,
,
,
,
,
© 2008 Saxon
b. least to greatest using decimals
0.25 ,
,
3
2, __
1, __
c. __
2 8 5
greatest to least using decimals
,
Saxon Math Intermediate 4
,
361
0.25
Adaptations Lesson 56
New Concept, continued
• When we draw figures to compare fractions, the figures
must be congruent. Congruent figures have the SAME
shape and size.
1
2
1
3
• To compare fractions:
1. Cross multiply.
2. Compare the numbers on top.
3
1
__
1
__
2
8
3 > 2, so _1_ > _1_
2
3
2
Lesson Practice
Compare the fractions and shade the rectangles to show each comparison.
a.
1
__
2
__
2
3
b.
c. greatest to least:
1
__
1
__
2
4
,
,
,
,
,
,
Use your fraction manipulatives.
d. greatest to least:
© 2008 Saxon
Use your fraction manipulatives.
Saxon Math Intermediate 4
362
Adaptations Lesson 56
page 361
Written Practice
1. missing factor
2.
divide
7 rolls on each tray
× n trays
56 total rolls
3.78 liters
×
2 gallons
total liters
words:
_____
)5 6
Use work area.
3. $6.87
$5.92
4.
24
3
+
8
×
×
_____
)
)
_____
Use work area.
5. months with 31 days
6. multiples of 6:
See p. 3 in the Student Reference Guide.
,
,
,
,
,
,
,
__________ __________ __________
© 2008 Saxon
__________ __________ __________
8th multiple of 6
__________
Add one.
square root
Use work area.
Saxon Math Intermediate 4
363
Use work area.
Adaptations Lesson 56
page 362
Written Practice, continued
1
__
4
7.
1
__
6
8. Round.
4651
Shade the rectangles to show the
comparison.
4651
Use fraction pieces.
4651
Use work area.
9.
Use work area.
10.
7 mi
4 mi
a. perimeter
$10.00
– $ 5.46
b. area
a.
b.
11.
12.
36,024
– 15,539
14.
46
7
15.
84
× 6
16.
×
40
5
17.
_____
7)4
8
© 2008 Saxon
×
13. Carry on your fingers.
73
× 9
43,675
+ 52,059
Saxon Math Intermediate 4
364
Adaptations Lesson 56
page 362
Written Practice, continued
___ =
18. 63
19.
7
20.
3.75
.
.
42.25
–
.
22. one dime
21. a. Which of these numbers is a
multiple of 10?
a. fraction
A 35
B 40
C 45
b. percent
D 101
b. Multiples of 10 end with
.
a.
b.
Use work area.
24. factors of 16
23. $12,350,000
Use the Multiplication Table.
words:
1,
Use work area.
,
,
, 16
Use work area.
25. Is 16 a prime number? Why or why not?
© 2008 Saxon
Find the factors of 16.
,
,
16 has
,
,
factors. A prime number has only
Therefore 16
factors.
a prime number.
Use work area.
Saxon Math Intermediate 4
365
Adaptations Lesson 56
page 363
Written Practice, continued
___
26. a. Which segment appears to be parallel to AB?
b. Angle B is what type of angle?
D
A
C
B
a.
b.
27. Which of these numbers is a factor
of 12?
A 0
B 6
C 8
29. one penny
28. Which of these numbers is a multiple
of 12?
D 24
A 0
B 6
C 8
D 24
30. greatest to least
Use your fraction manipulatives.
a. fraction
3
__
4
,
,
,
,
b. value as a decimal
c. percent
© 2008 Saxon
0.09
a.
b.
c.
Saxon Math Intermediate 4
Use work area.
366
Adaptations Lesson 56
LESSON
Name
57
Teacher Notes:
page 364
• Introduce Hint #33 “Rate, Part 1.”
• Review “Proportion (Rate)
Problems” on page 10 in the
Student Reference Guide.
• Rate Word Problems
New Concept
Example
If a car goes 30 miles per hour, how far will it go in 4 hours?
1. Name the two things the problem is about:
miles
______
hours
2. Fill in what you know:
mi 30
___
hr 1
3. Fill in what you are looking for:
?
30 = __
mi ___
4
hr 1
4. Draw a loop around the numbers that are diagonally opposite.
The loop should never include the question mark.
?
mi 30
___ = __
4
hr 1
5. Multiply the numbers inside the loop:
4 × 30 = 120 mi
Lesson Practice
© 2008 Saxon
a. Angela drove 55 miles in one hour.
At that rate, how far can she drive in 6 hours?
miles
Multiply the loop.
?
55 = __
mi ___
6
hr 1
Saxon Math Intermediate 4
367
Adaptations Lesson 57
Lesson Practice, continued
b. Barak swims 20 laps every day.
How many laps will he swim in 1 week? (1 week = 7 days)
Multiply the loop.
laps 20
?
_____
___ = __
days 1
laps
Written Practice
page 387
2. Multiply the loop.
1. Multiply the loop.
times
minutes
miles
______
hours
42 = __
?
___
1
1
?
7 = __
__
1
___
3.
4. √ 36
72
8
9
×
___
×
_____
√64
_____
)
)
Use work area.
5. 50% = what fraction?
3
50%
5280
© 2008 Saxon
1
__
6. a. nearest thousand
b. nearest hundred
5280
Use work area.
Saxon Math Intermediate 4
368
a.
b.
Adaptations Lesson 57
page 367
Written Practice, continued
7. Use the multiplication table.
factors of 12:
,
,
3
,
4
,
,
Draw an array of 12 stars that shows two other factors of 12 (not 3 × 4).
Use work area.
8. multiples of 6:
,
,
multiples of 8:
,
,
th
4
multiple
_________
of 6
,
rd
3
multiple
_________
of 8
Use work area.
9.
10. 7 inches
later
+
a. perimeter
b. area
earlier
area = length × width
difference
a.
© 2008 Saxon
b.
11.
70,003
– 36,418
12.
n
– 4.32
2.57
13.
$861.34
+ $764.87
n=
Saxon Math Intermediate 4
369
Adaptations Lesson 57
page 368
Written Practice, continued
14. Carry on your fingers.
×
15.
93
5
17. in your head
18.
84
× 6
16.
×
56
=
8
77
7
19. 8 _____ R
7)6 5
80
× 8
Use work area.
20. 45÷6
21. 7n = 42
8_____ R
)4 5
1.7 5
22.
+
.
n=
23. a. Which segment in this figure is a diameter?
b. Segments MW and MX form an angle. What type of angle is it?
a
Segments MW and MX form an
than a right angle.
© 2008 Saxon
because it is
angle. It is
W
M
X
a.
Y
b.
Saxon Math Intermediate 4
370
Adaptations Lesson 57
Written Practice, continued
page 368
24. Shade the rectangles to show the comparison.
2
__
3
3
__
4
Use fraction pieces.
Use work area.
25.
X
4
5
6
7
mixed number: ________
decimal: ________
Use work area.
26.
2.54
2.54
+ 2.54
27. 2.54 + 2.54 + 2.54
×
28. three pennies
a. fraction
© 2008 Saxon
b. value as a decimal
c. percent
a.
b.
c.
Saxon Math Intermediate 4
371
Adaptations Lesson 57
Written Practice, continued
page 369
29. prime = 2 factors
A 6
B 7
C 8
D 9
30. sum of lengths
1 yard + 2 feet + 12 inches = 2 yards
Change 2 yards to feet.
yards × 3 = feet
2 yards
×3
feet
Change 2 yards to inches.
yards × 36 = inches
2 yards
× 36
inches
© 2008 Saxon
Use work area.
Saxon Math Intermediate 4
372
Adaptations Lesson 57
LESSON
Name
58
Teacher Note:
page 370
• For additional practice, students
may complete Targeted Practice 58.
• Multiplying Three-Digit
Numbers
New Concept
Multiply the
ones digit.
Multiply the
tens digit.
Multiply the
hundreds digit.
123
×
3
369
123
×
3
69
123
×
3
9
• If necessary, carry on your fingers.
Lesson Practice
Multiply. Remember to write the dollar sign in money problems.
a.
234
×
3
b.
c.
$340
×
4
$4.25
×
5
d. You may skip this problem.
$2.47
×
4
Use compatible numbers.
$2._ _
×
4
© 2008 Saxon
e.
Saxon Math Intermediate 4
373
Adaptations Lesson 58
Written Practice
page 373
1. Multiply the loop.
$
week
2. Multiply the loop.
apple _4_
= _?_
pints 1
= _?_
4
1
__
3. Get up time:
Count hours back.
4. quarts ÷ 4 = gallons
8 quarts ÷ 4 =
gallons
Hosni needs
quarts of paint, which is the same as
gallons. The
gallon can would be too much paint. Hosni could buy
quarts or
g
than
gallons. It would be cheaper to buy
because
g
are bigger
q
© 2008 Saxon
Use work area.
5. 8402
expanded form:
words:
Use work area.
Saxon Math Intermediate 4
374
Adaptations Lesson 58
page 374
Written Practice, continued
6. Multiples of 7:
,
,
,
Multiples of 6:
,
,
,
,
,
4th multiple of 7
6th multiple of 6
+
square root
Use work area.
7.
8. 5 + n = 23
SEPTEMBER 2042
S M T W T F S
7
14
21
28
n=
1 2 3 4 5 6
8 9 10 11 12 13
15 16 17 18 19 20
22 23 24 25 26 27
29 30
n – 5=
second Tuesday
,
9.
D
C
6 ft
6 ft
A
7 ft
7 ft
B
© 2008 Saxon
a. perimeter:
b. Describe each angle as acute, obtuse, or right.
Angle A:
Angle C:
Angle B:
Angle D:
Use work area.
Saxon Math Intermediate 4
375
Adaptations Lesson 58
page 374
Written Practice, continued
10. Shade to show the comparison.
1
__
2
__
2
4
11.
7
8
Use fraction pieces.
Use work area.
12. Name a segment that
appears parallel to AB.
E
F
A
0.47
13.
+
B
$
3.00
.
$
.00
.
+ $
.00
14.
H
G
D
C
Use work area.
15. 36.47 − (3.5 + 12.6) =
$20.00
$0.29
36.47
3.5
+
–
–
© 2008 Saxon
+
16. $20.00 − (29¢ + $7) =
Saxon Math Intermediate 4
376
Adaptations Lesson 58
page 375
Written Practice, continued
17.
41,059
– 36,275
18.
768
× 3
19.
$2.80
×
4
20.
436
–
z
252
z=
21.
____
5)3 6
22.
R
____
7)4 5
R
23.
____
4)3 5
24. To find the product of 4 × 100 using only mental math, multiply
Then add two
z
R
times 1.
at the end.
© 2008 Saxon
Use work area.
25. factors of 20:
1,
,
,
,
, 20
Use the multiplication table.
Use work area.
Saxon Math Intermediate 4
377
Adaptations Lesson 58
Written Practice, continued
page 375
27. If 4n = 24, then which of these
equations is not true?
26. a. 6781
b. 6781
24 = n
a. ___
4
___ = 4
b. 24
n
c. 2n = 12
d. 4n = 6
a.
b.
28. seven pennies
29. Which of these even numbers is a
prime number?
prime = 2 factors
a. fraction
A 2
B 4
C 6
D 8
b. value as a decimal
c. percent
a.
b.
c.
30. Kwan drives about 400 miles a day.
© 2008 Saxon
About how many miles will he drive in 5 days?
Multiply the loop.
400 = __
miles
?
_____ ____
1
days
Saxon Math Intermediate 4
378
Adaptations Lesson 58
LESSON
Name
59
page 376
• Estimating Arithmetic
Answers
New Concept
• Estimating is the same as rounding.
• Estimates help you see whether your answers make sense.
396
+ 512
400
+ 500
900
Don’t round the 1-digit number.
72
× 5
70
× 5
350
Round 43 to a multiple of 8.
8 ____
5
8)4 0
43÷8
Lesson Practice
Find each missing number. Check your answers.
a.
estimate
© 2008 Saxon
estimate
estimate
8
exact
_____
)
exact
8 ____
5)4 2
Saxon Math Intermediate 4
estimate
e.
estimate
estimate
8
exact
59
× 6
×
h.
exact
c.
607
+ 891
+
82
– 39
–
g.
b.
59
68
+ 81
+
d.
exact
____
)2 8
379
estimate
585
– 294
+
f.
estimate
×
exact
exact
397
×
4
exact
8 ____
7)2 9
Adaptations Lesson 59
Lesson Practice, continued
Dixie estimated the product of 5 and 5280 by multiplying 5 by 5000. Was Dixie’s
estimate more than, equal to, or less than the actual product? Why?
Dixie’s estimate was
than the actual product because she
rounded 5280 down to
j.
Estimate the cost.
Round up for sales tax.
before multiplying.
Item
Cost
Notebook computer
$845
Wireless mouse
$27.50
Accessory bag
$39.95
$845
$27.50
+
$39.95
A reasonable estimate is
$
. I rounded each number
because sales tax will
Written Practice
miles
1. ______
hours
3=?
__
__
1
i
page 379
2.
6 pears in each box missing factor
× n boxes
____
48 total pears
)4 8
3. 1 mile = about 1.61 km
divide
4. Estimate:
193
a. 1.61 km in words:
b. 1 mile
the cost.
© 2008 Saxon
i.
×5
1 km
Use work area.
Saxon Math Intermediate 4
380
Adaptations Lesson 59
Written Practice, continued
page 379
___
√16
5. 50% of 16
6. multiples of 6:
,
,
multiples of 4:
,
,
2nd multiple of 6
3rd multiple of 4
–
difference
Use work area.
7.
later
– 1587 earlier
difference
8. a. Which angle in this figure
appears to be a right angle?
A
b. Which segment in this figure
C
does not appear to be
–––
perpendicular to AB?
b.
a.
9. Shade to show comparison.
2
__
5
10.
B
packages
_________
hours
40 = __
?
___
1
1
__
4
Use work area.
11. fifteen million, two hundred ten
thousand
12. a. perimeter
© 2008 Saxon
b. area
,
,
3 mi
2 mi
Use work area.
Saxon Math Intermediate 4
381
a.
b.
Adaptations Lesson 59
page 380
Written Practice, continued
13.
$37.75
+ $45.95
16.
$50.00
– $42.87
17.
20.
207
×
8
21.
14.
43,793
+ 76,860
43,793
– 26,860
18.
R
22.
____
8)4 3
4 8.0
9.7
1 2.6
5.3
+ 2 3 6.2
15.
483
×
4
____
5)4 3
19.
R
23.
24. a. What was the temperature at 3 p.m. (shown here)?
360
×
4
____
7)4 3
R
10
b. From 3 p.m. to 6 p.m., the temperature rose 4 degrees.
0
Ľ10
Ľ20
C
a.
Saxon Math Intermediate 4
382
b.
Adaptations Lesson 59
© 2008 Saxon
What was the temperature at 6 p.m.?
Written Practice, continued
page 381
25. Draw a parallel segment that is 10 cm long.
4 in.
Use work area.
26. formula: quarts × 2 = pints
1
3 __
2
3.5
3.5 × 2
Write as addition.
+ 3.5
pints
27. Estimate perimeter.
58.5 ft
42.5 ft
58.5 + 58.5 + 42.5 + 42.5 =
© 2008 Saxon
+
+
+
=
58.5 rounds to
feet
and 42.5 rounds to
A reasonable estimate is about
.
feet.
Use work area.
Saxon Math Intermediate 4
383
Adaptations Lesson 59
page 381
Written Practice, continued
28.
Sum:
Difference:
larger
–
+
smaller
difference
Use work area.
29. a. composite = more than 2 factors
A 5
B 7
C 9
D 11
is a composite number and not a prime number because it has more
b.
than
factors. A prime number only has
factors.
Use work area.
30. Round to the nearest dollar.
skates = $59.95
accessories = $44.50
–
I rounded $59.95 to
I
s
The skates were
and $44.50 to
.
to find the difference in price.
$
more than the accessories.
Use work area.
Saxon Math Intermediate 4
384
Adaptations Lesson 59
© 2008 Saxon
difference
LESSON
Name
60
Teacher Notes:
page 382
• Introduce Hint #34 “Rate, Part 2.”
• Review “Proportion (Rate)
Problems” on page 10 in the
Student Reference Guide.
• Rate Problems with a
Given Total
New Concept
Example
Zariali can read 2 pages in 1 minute.
How long will it take him to read 18 pages?
1. Name the two things the problem is about:
pages
________
minutes
2. Fill in what you know:
pages
2
________ __
minutes 1
3. Fill in what you are looking for:
pages
2 = 18
________
__
___
minutes 1
?
4. Draw a loop around the numbers that are diagonally
opposite.
The loop should never include the question mark.
pages
2 = 18
________
__
___
minutes 1
?
5. Multiply the numbers inside the loop:
1 × 18 = 18 minutes
© 2008 Saxon
6. Divide this answer by the outside number:
___
2 )18
Saxon Math Intermediate 4
9
___
2 )18
385
9 minutes to read 18 pages
Adaptations Lesson 60
Lesson Practice
a. Javier can sharpen 5 pencils in a minute.
How long will it take Javier to sharpen 40 pencils?
Multiply the loop.
Divide by the outside number.
pencils
minutes
___
= 40
1
?
5
__
____
5)
minutes
b. The troop hiked 12 miles in 4 hours.
The troop’s average rate was how many miles per hour?
Multiply the loop.
Divide by the outside number.
miles
hours
?
= __
4
1
__
____
4)
miles per hour
c. Alexis was paid $48 for 6 hours of work.
How much money was Alexis paid for each hour of work?
Multiply the loop.
Divide by the outside number.
____
)
$
© 2008 Saxon
$
8 = __
?
__
1
hour 8
Saxon Math Intermediate 4
386
Adaptations Lesson 60
Written Practice
1.
page 384
2. Multiply the loop.
214 parrots
Divide by the outside number.
crows
blue jays
plants
______
bags
in all
3. signs
hours
5.
___
= 24
?
1
__
_____
)
4. 50% of one hour
0
__
?
= __
0
1
8363
+ 1314
+
I rounded 8363 to
feet and 1314 to
+
Then I added
The sum was
feet.
.
feet above sea level.
© 2008 Saxon
Use work area.
6. Which of these numbers is not a
multiple of 2?
A 23
B 24
Saxon Math Intermediate 4
C 32
7. quarter to seven in the morning
D 46
387
Adaptations Lesson 60
page 385
Written Practice, continued
8. 3n = 3 × 5
9. The product of 6 and 7 is how much
greater than the sum of 6 and 7?
product
–
sum
greater than
n=
10. What is the length of segment BC?
A
B
cm 1
2
11. (32 ÷ 8) ÷ 2
3
4
C
5
6
7
32 ÷ (8 ÷ 2)
8
12.
$6.49
$0.00
$0.00
$0. 00
Use work area.
6.5
0.0
00
+ 0.0
Saxon Math Intermediate 4
14.
12.56
–
15.
350
×
5
© 2008 Saxon
13.
.0
388
Adaptations Lesson 60
page 385
Written Practice, continued
16.
204
×
7
17.
463
×
6
18. 8 ___ R
4 )37
19. 8 ___ R
6 )39
20. 8 ___ R
3 )28
21. one nickel
22. factors of 25
1
__
2
23. 5%
Use the multiplication table.
a. fraction
b. percent
%
%
a.
b.
24.
,
A
B
,
25.
5 yd
4 yd
D
C
a. “Go around” tells us to find the perimeter.
b. “Cover” tells us to find the area.
© 2008 Saxon
a. What type of angle are angles
A and C?
b. What type of angle are angles
B and D?
Saxon Math Intermediate 4
a.
a.
b.
b.
389
Adaptations Lesson 60
page 386
Written Practice, continued
26. If n + 10 = 25, then which of these
equations is not true?
A n + 11 = 26
B n + 12 = 27
C n – 5 = 20
D n + 9 = 24
27. a. 8 ÷ (4 ÷ 2)
(8 ÷ 4) ÷ 2
b. Associative Property
order doesn’t
affect answer
Yes or no?
Use work area.
28. nineteen pennies
a. fraction
a.
b. percent
b.
c. value as a decimal
c.
29.
$7.95
$1.75
+ $3.95
30.
A
E
B
F
© 2008 Saxon
C
G
D
H
a. parallel to EF
a.
b. perpendicular to BF
b.
Saxon Math Intermediate 4
390
Adaptations Lesson 60
6
I NVE S TIGATION
Name
page 387
Focus on
• Displaying Data Using
Graphs
• Read all the words on the graph to get information.
• A legend, or key, tells what the symbols on a graph mean.
• Pictographs use pictures to display information.
• The pictograph below shows the results of a survey of some
students about their favorite lunches.
Favorite School Lunches
of Students in Room 12
Chicken
Tuna
Turkey
Pizza
represents the choice of 2 students
1. What is the title of the pictograph?
© 2008 Saxon
2. How many different types of lunches are shown?
3. How can you tell how many students chose a particular lunch
as their favorite lunch?
The
l
tells us that each whole picture
represents the favorite choice of
the pictures and multiply by
Saxon Math Intermediate 4
391
students. We count
to find the number.
Adaptations Investigation 6
6
INVE STIGATION
continued
4. How many students named chicken as their favorite?
How did you find your answer?
There are
whole pictures for chicken, and
×
=
.
5. How many students named tuna as their favorite?
How did you find your answer?
There are
whole pictures and
×2=
.
so I added
There is
half picture,
more and the sum was
.
6. The pictograph shows the favorite lunches of how many
students?
How did you find your answer?
There are
whole pictures and
×
=
.
There are
half
and
Saxon Math Intermediate 4
+
=
392
© 2008 Saxon
pictures that show the choices of two more students,
.
Adaptations Investigation 6
6
INVE STIGATION
continued
• The information in a pictograph can also be shown in a bar
graph.
Number of Students
Favorite School Lunches of Students in Room 12
10
8
6
4
2
Chicken
Turkey
Lunch
Pizza
7. What is the label along the vertical left side of the graph?
Math Language
The bars can be
vertical (up and
down) or horizontal
(sideways).
The labels along
the sides of the
graph tell us what
the numbers mean.
Tuna
Number of
8. Along the vertical left side of the graph are marks and numbers.
What does the number 8 stand for?
8
9. Which bar is the tallest, and what does that mean?
The tallest bar is the bar for
means that
.
That
is the favorite lunch of
more students in Room 12 than any other lunch on the graph.
© 2008 Saxon
10. How many more students named tuna than turkey?
How did you find the answer?
I
s
the number who named turkey from
the number who named tuna.
Saxon Math Intermediate 4
393
Adaptations Investigation 6
6
INVE STIGATION
continued
• Line graphs show information that changes over time.
This line graph shows Jamil’s height from his birth until he was
10 years old. There is a vertical scale and a horizontal scale.
The labels along these scales show the units (in parentheses)
for the numbers along the scales.
The change in Jamil’s height is shown by the segments
connecting the dots.
Jamil’s Height from Birth to Age Ten
Height (inches)
50
40
30
20
0
1
2
3
4
5 6 7
Age (years)
8
9
10
11. What does the 8 on the horizontal scale mean?
The 8 shows the day Jamil turned
.
12. How tall was Jamil on his fourth birthday?
How did you find your answer?
from the
v
on the age scale. I went
.
Then I looked left to the
scale and saw that the height
was
Saxon Math Intermediate 4
u
inches.
394
Adaptations Investigation 6
© 2008 Saxon
I found
INVE STIGATION
6
continued
13. During which year did Jamil become 45 inches tall?
How did you find the answer?
v
I found 45 inches on the
scale. I
went straight to the right to the graph. From there I
looked straight
d
to the age scale and saw
that Jamil was between his
and
birthdays.
14. The graph of Jamil’s height is steep during the first few years
and then becomes less steep. What does the change in
steepness mean about Jamil’s growth?
During Jamil’s
As he became
s
e
years he grew
o
,
f
.
his height changed more
.
• This circle graph shows how Vanessa usually spends a whole
school day.
Math Language
© 2008 Saxon
• A circle graph is
sometimes called
a pie graph.
It shows how a
whole is divided
into parts.
How Vanessa Spends a School Day
School
7 hr
The “scale” on the
circle graph is the
size of the slices.
hr
ew
r
om
V2h
H
T
g
n
hi
Watc
Soc Other 1 hr
cer
pra
ctic
e
121 h
r
g
tin
Ea
Sleeping
9 hr
k
or
2
1
12
hr
Saxon Math Intermediate 4
395
Adaptations Investigation 6
6
INVE STIGATION
continued
15. Which slice of this circle graph is the largest?
What does it mean that it is the largest?
It means that Vanessa spends
time
m
than on any other single activity.
16. Together, school and homework equal how many hours of
Vanessa’s day?
17. What is the total number of hours represented by the entire
circle graph?
18. According to the graph, Vanessa is awake about how many
hours each day?
How did you find the answer?
I
s
Activity
9 hours from
hours.
page 390
Displaying Information on Graphs
© 2008 Saxon
This activity is optional.
Saxon Math Intermediate 4
396
Adaptations Investigation 6