Download 31 • Word Problems About Comparing

LESSON
Name
31
page 192
• Word Problems About
Comparing
New Concept
• To compare two numbers
Formula
Larger
− Smaller
Difference
Subtract.
Problem
43 apples
− 19 apples
24 apples
Always put the BIGGER
number on top!
• Watch for these words:
more
fewer
less than
greater than
Lesson Practice
a. How much greater?
b. How many fewer?
c. How many more?
42 Mary
43
−
−
fewer
−
Cesar
more
© 2008 Saxon
greater
Frank
95 Juanita
Saxon Math Intermediate 4
199
Adaptations Lesson 31
page 195
Written Practice
43 in the flock
1.
−
flew away
150
2.
3.
−
75 apples
−
greater
still in flock
fewer
4. It is morning. What time will it be 3 hours from now?
11
10
time now:
12
1
2
9
Count forward 3 hours.
3
4
8
7
5. 412
6
5
6.
expanded form:
© 2008 Saxon
words:
Use work area.
Saxon Math Intermediate 4
200
Adaptations Lesson 31
Written Practice, continued
7.
page 196
8. a. 2 × 5 =
4 cm
2 cm
b. 5 × 7 =
c. 2 × 7 =
a. perimeter
d. 4 × 11 =
b. area (area = length × width)
a.
b.
Use work area.
9.
50
30
20
+
+
−
−
Use work area.
10. down 8 degrees
10
5
© 2008 Saxon
0
–5
–10
C
Saxon Math Intermediate 4
201
Adaptations Lesson 31
Written Practice, continued
page 196
12. a. 5 × 8 =
11. How much less?
A
75
B
100
b. 2 × 8 =
125
150
c. 5 × 9 =
Find the pattern
B
A
110
−
less
Use work area.
quarters
b. 1 quarter =
c. 3 quarters =
14. Three hundred nine is less than three
hundred ninety.
of a dollar
of a dollar
Use work area.
15.
Use work area.
16.
390
$4.22
− $2.95
© 2008 Saxon
13. a. $1 =
less
Saxon Math Intermediate 4
202
Adaptations Lesson 31
page 197
Written Practice, continued
17.
909
− 27
20.
$4.86
+ $2.95
18.
21.
19.
$422
− $144
22.
370
− 209
703
− 471
23.
22
+ n
37
76
− c
28
c=
n=
__
24. What multiplication fact is illustrated
by this square?
25. a. √ 9 =
×
=9
___
b. √ 25 =
×
= 25
a.
×
b.
=
26. Which of these does not equal 9?
27. a. 1 × 1 =
___
A 3 squared
© 2008 Saxon
___
C √ 18
B √81
___
b. 5 × 5 =
___
D √25 + √16
c. 8 × 8 =
d. 9 × 9 =
Use work area.
Saxon Math Intermediate 4
203
Adaptations Lesson 31
Written Practice, continued
28. Compare.
page 197
29. compatible numbers
Look at the hundreds.
Look at the tens.
Look at the ones.
a. 510
501
b. 722
976
c. 234
238
318 is close to
is close to
and 473
.
+
=
Use work area.
b.
r
p
a
l
c.
d.
p
o
l
a
© 2008 Saxon
30. a.
s
Use work area.
Saxon Math Intermediate 4
204
Adaptations Lesson 31
LESSON
Name
32
Teacher Note:
page 199
• Refer students to the Multiplication
Table on page 5 in the Student
Reference Guide.
• Multiplication Facts:
9s, 10s, 11s, 12s
New Concept
• In 9s multiplication facts:
The first digit of the product is one less than the factor.
The two digits of the product always add up to 9.
Magic of 9s
9 × 2 = 18
1+8=9
9 × 3 = 27
2+7=9
9 × 4 = 36
3+6=9
9 × 5 = 45
4+5=9
9 × 6 = 54
5+4=9
9 × 7 = 63
6+3=9
9 × 8 = 72
7+2=9
9 × 9 = 81
8+1=9
9 × 10 = 90
9+0=9
Lesson Practice
© 2008 Saxon
Find the product for each multiplication fact. Remember, the first digit is one less
than the number multiplied, and the two digits add up to nine.
6
8
d.
b.
c.
a.
5
9
× 9
× 9
× 3
× 9
e.
9
× 4
Saxon Math Intermediate 4
f.
7
× 9
g.
9
× 2
205
h.
9
× 9
Adaptations Lesson 32
Lesson Practice, continued
Use the Multiplication Table on page 5 in the Student Reference Guide to find each
product.
i.
10
× 5
j.
10
× 7
k.
10
× 3
l.
10
× 9
m.
11
× 6
n.
11
× 4
o.
11
× 7
p.
11
× 9
q.
12
× 3
r.
12
× 5
s.
12
× 2
t.
12
× 4
page 202
Written Practice
1.
215 in book
2. greater than 800.
Kande has read
left to read
even
3. Four hundred eighty-five is less than six hundred ninety.
Use work area.
4. square numbers
1, 4, 9, 16,
,
,
© 2008 Saxon
See page 5 in the Student Reference Guide.
,…
1 is the square of
. 4 is the square of
sequence, 5 × 5 =
,6×6=
. To finish the
, and 7 × 7 =
.
Use work area.
Saxon Math Intermediate 4
206
Adaptations Lesson 32
page 202
Written Practice, continued
5. evening
11
10
6. 729
12
expanded form:
1
2
9
3
words:
4
8
7
6
5
Use work area.
7. 6 + 6 + 6 + 6 + 6 + 6 + 6
8. 3 nickels
¢
¢
2 dimes
Is the total even or odd?
×
9. a. nearest ten
66
=
10.
centimeters
b. nearest dollar $6.60
c. nearest 25¢
$6.60
a. each side
© 2008 Saxon
b. perimeter
a.
Saxon Math Intermediate 4
b.
a.
c.
b.
207
Adaptations Lesson 32
Written Practice, continued
11. Perpendicular looks like this:
page 203
12.
62
– w
38
w=
and
14. Draw an array of Xs to show 5 × 5.
13.
Use work area.
16. a. 9 × 6 =
15. How much greater?
A
0
b. 9 × 8 =
B
100
200
c. 9 × 4 =
d. 9 × 10 =
Find the pattern.
B
−
© 2008 Saxon
A
greater
Use work area.
Saxon Math Intermediate 4
208
Adaptations Lesson 32
Written Practice, continued
page 203
17. a. 6 × 6 =
18. a. 2 × 11 =
b. 4 × 4 =
b. 8 × 11 =
c. 7 × 7 =
c. 5 × 11 =
d. 10 × 10 =
d. 3 × 11 =
Use work area.
Use work area.
___
20. √ 81
19. a. What multiplication fact is shown
here?
×
= 81
___
b. √ 25
a.
×
=
b.
21.
$3.60
− $1.37
23.
413
− 380
875
− 218
25. 8 × 8 =
12 + 48
© 2008 Saxon
24. 24 + 36
22.
Use work area.
Saxon Math Intermediate 4
209
Adaptations Lesson 32
page 204
Written Practice, continued
26.
A 3
B 7
27. 4 × 6 = 24
28.
6 × 4 = 24
C 12
D 15
batters
batters
Property of
Multiplication
Use work area.
29. compatible numbers
620 East China Sea
121
Yellow Sea
difference
121 is close to
=
© 2008 Saxon
620 –
.
30. a. 11, 22, 33, 44, 55,
b. 12, 24, 36, 48, 60,
Use work area.
Saxon Math Intermediate 4
210
Adaptations Lesson 32
LESSON
Name
33
Teacher Notes:
page 205
• Writing Numbers Through
Hundred Thousands
• Introduce Hint #20 “Writing
Numbers” and Hint #21 “Place
Value (Digit Lines).”
• Review “Spelling Numbers” and
“Place Value” on pages 12 and 13
in the Student Reference Guide.
• Review reference chart “Spelling
Numbers.”
New Concept
• Place a comma after the word thousand:
4,507
34,507
234,507
four thousand, five hundred seven
thirty-four thousand, five hundred seven
two hundred thirty-four thousand, five hundred
seven
• Counting from the right, place a comma every three digits.
• Four-digit whole numbers are often written without a
comma.
• Picture the numbers in groups of three.
Each group is a family (units family, thousands family).
The comma tells us the family name.
Each family has three members: ones, tens, and hundreds.
Example
Write 75,634 in expanded form.
70,000 + 5000 + 600 + 30 + 4
Example
© 2008 Saxon
Compare: 510,000
501,000
Start at the greatest place value, then compare place by place.
510,000 > 501,000
Saxon Math Intermediate 4
211
Adaptations Lesson 33
Lesson Practice
Read the following numbers to your teacher:
a. 125 ,000
b. 435 ,000
c. 12 , 500
d. 25 , 375
e. 4 , 875
f. 250 , 625
Use words to write these numbers:
g. 2 , 750
h. 14 , 518
i.
500 ,000
Use digits to write each number.
j.
twenty thousand
,
k. twelve thousand, three hundred fifty
l.
,
one hundred twenty thousand, five hundred
,
Write in expanded form:
m. 5280
+
+
+
n. 2040
o. Which digit in 284,359 is in the ten-thousands place?
p. Compare: 760,000
670,000
Start at the greatest place value.
© 2008 Saxon
q. Arrange these dates in order from earliest to latest:
Start at the greatest place value.
1969
1903
,
Saxon Math Intermediate 4
1957
,
1927
,
212
Adaptations Lesson 33
page 209
Written Practice
1.
2. 3425
272 K’Neesha
Marcos
expanded form:
more
words:
Use work area.
3. Draw 2 parallel lines (horizontal).
Cross with right-angle line (vertical).
See page 16 in the Student Reference Guide.
Use work area.
4. 4 × 4 =
×
42
= 49
___
√49
−
5.
6. Put in commas. Circle groups.
250000
words:
© 2008 Saxon
a. perimeter
b. area (Area = length × width)
a.
b.
Saxon Math Intermediate 4
Use work area.
213
Adaptations Lesson 33
page 209
Written Practice, continued
7.
…, 230, 240, 250, 260,
,
,
,
,…
Use work area.
9. 9 × 4
8. ten-thousands place
___
√36
123,456
Use work area.
10. It is evening. What time will it be 2 hours and 25 minutes from now?
time now:
11
12
1
10
Count forward 2 hours.
2
9
Count forward 25 minutes.
3
4
8
6
5
© 2008 Saxon
7
11.
2000
2100
2200
2300
Find the pattern.
Saxon Math Intermediate 4
214
Adaptations Lesson 33
page 210
Written Practice, continued
12. a. 5 × 8 =
c. 8 × 8 =
b. 4 × 4 =
13. a. 9 × 3 =
d. 12 × 12 =
c. 9 × 5 =
b. 9 × 4 =
d. 9 × 10 =
a.
b.
a.
b.
c.
d.
c.
d.
14.
100
40
60
+
+
−
−
Use work area.
15. 20 + 20 + 20 + 20 + 20
16.
$7.37
− $2.68
×
17.
921
− 58
18.
464
+ 247
19.
329
+
z
547
© 2008 Saxon
z=
20.
$4.88
+ $2.69
21.
555
−
c
222
22. Which month?
5/27/98
c=
Saxon Math Intermediate 4
215
Adaptations Lesson 33
page 211
Written Practice, continued
23.
24.
1 inch
25.
4
8
12
16
14
28
+ 37
5
8
7
14
6
21
+ 15
The diameter of a circle is equal
to
radii.
27. Which number is not in the sequence?
26. 25,000
1, 4, 9, 16, 25, 36, …
250,000
Start at the greatest place value.
A 64
B 49
C 80
D 100
Use work area.
28.
189 Kentucky
176 Maryland
29. See page 1 in the Student Reference Guide.
12, 24, 36, 48,
,
,
altogether
© 2008 Saxon
,
30.
10, 20, 30,
Saxon Math Intermediate 4
,
,
216
,
,
,
Adaptations Lesson 33
LESSON
Name
34
Teacher Notes:
page 212
• Review Hint #21 “Place Value (Digit
Lines).”
• Review “Place Value” on page 13
in the Student Reference Guide.
• Writing Numbers Through
Hundred Millions
• For additional practice, students
may complete Targeted Practice 34.
New Concept
• Use digit lines.
• Three digit lines will always follow a comma.
,
hundreds
tens
ones
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
• Always put a comma after the words thousand and
million.
,
millions thousands
units
Example
Use words to write:
12345678
12,345,678
Circle the families.
© 2008 Saxon
Write the families.
Saxon Math Intermediate 4
12 , 345 , 678
Twelve million, three hundred forty-five
thousand, six hundred seventy-eight
217
Adaptations Lesson 34
Lesson Practice
Use words to write each number:
a. 121 , 340 , 000
b. 12 , 507 , 000
c. 5 , 075 , 000
Use digits to write each number:
d. twenty-five million
,
,
e. twelve million, five hundred thousand
,
,
f. two hundred eighty million
,
,
g. Start at the greatest place value.
Compare: 34 million
43 million
h. Start at the greatest place value.
Arrange in order from least to greatest:
,
Start at the greatest place value.
Arrange in order from least to greatest:
12,375
1,000,000
© 2008 Saxon
i.
,
987,000
,
Saxon Math Intermediate 4
,
218
Adaptations Lesson 34
Written Practice
page 215
465
1.
2.
420 Marcie
Kareem
fewer
greater
3. a. perimeter
4. 25,463
b. area
expanded form:
(area = length × width)
Use work area.
5.
Use work area.
6. It is afternoon. What time will it be in
1 hour and 35 minutes?
4 cm
© 2008 Saxon
Time now:
Count forward 1 hour:
Count forward 35 minutes:
Saxon Math Intermediate 4
219
Adaptations Lesson 34
page 216
Written Practice, continued
8. 12 + 12 + 12 + 12 + 12
7.
9. 76
59
×
10. a. 3
–4
b. two million
=
11. How much less?
200,000
A
200
210
B
220
230
Find the pattern.
B
–
A
less
Use work area.
12. a. 5 × 7 =
13. a. 3 × 9 =
b. 6 × 6 =
b. 9 × 7 =
b. 6 × 12 =
c. 9 × 9 =
c. 8 × 9 =
c. 8 × 11 =
d. 10 × 10 =
d. 9 × 1 =
d. 10 × 12 =
Use work area.
Use work area.
© 2008 Saxon
Use work area.
14. a. 11 × 11 =
15. a. Circle the families. 3,500,000
words:
b. seven hundred fifty thousand
digit lines digits:
Use work area.
Saxon Math Intermediate 4
220
Adaptations Lesson 34
Written Practice, continued
16.
535
– 268
19.
c
+ 329
715
17.
page 216
908
– 43
18.
20.
$471
– $346
c
– 127
398
c=
c=
22. Five squared is how much more than 5 + 5?
21. 12 in. = 1 ft
5×5
52
12 in.
5+5
more
d = 2r
24.
two odd
23.
one even
© 2008 Saxon
+
–
=9
×
= 16
__
fact family
+
×
√9
–
___
√16
+
Use work area.
Saxon Math Intermediate 4
221
Adaptations Lesson 34
page 217
Written Practice, continued
25. See page 15 in the Student Reference Guide.
26. thousands place
3,756,289
A 3
B 7
C 5
D 6
Use work area.
27. In order from greatest to least:
,
,
,
Use work area.
29. eighth term
28. twelfth term
,
,
,
,
,
$2.49
12, 24, 36, 48,
,
,
30. Caitlin needs
$
,
,
,
,
bags because 25 + 25 + 25 + 25 = 100.
© 2008 Saxon
11, 22, 33, 44,
per bag of 25
+$
+$
+$
=$
Use work area.
Saxon Math Intermediate 4
222
Adaptations Lesson 34
LESSON
Name
35
page 218
• Naming Mixed Numbers
and Money
New Concept
• Use the word “and” when naming mixed numbers.
two and one fourth
Math Language
â 2 14
A mixed number
is a whole number
and a fraction:
1
3__
2
• To write money amounts using digits:
There will always be two digits after the decimal point.
$0.04 = 4¢
40¢ = $0.40
• To write money amounts using words:
Use “and” in place of the decimal point.
thirty dollars and seventy-six cents
$30.76
Lesson Practice
What mixed numbers are pictured here?
a.
=
b.
=
Shade these circles to show the mixed numbers:
© 2008 Saxon
1
c. 1 __
4
Saxon Math Intermediate 4
3
d. 2 __
4
223
Adaptations Lesson 35
Lesson Practice, continued
Use words to write each mixed number:
3
e. 12 __
7
f. 2 ___
4
10
9
g. 6 ____
100
Write each amount with a cent sign instead of a dollar sign:
h. $0.17
i. $0.05
Write each amount with a dollar sign instead of a cent sign:
j. 8¢
k. 30¢
l. Write the value of two quarters, two dimes, and one nickel with a dollar sign.
Then use a cent sign to write this amount again.
$
.
¢
Use words to write:
m. $20.05 _______________________________________
n. Show how to write the dollars line on a check for $12.25.
100
Written Practice
72 in 1998
© 2008 Saxon
1.
page 222
in 1968
more
Saxon Math Intermediate 4
224
Adaptations Lesson 35
Written Practice, continued
2.
page 222
300 yd
100 yd
+
+
+
=
The distance around the block is the
.
Use work area.
97 first
3.
4. mixed number
5. four dollars and
sixty-five cents
second
third
in all
7. See page 15 in the Student Reference Guide.
6. Find the pattern.
A
B
C
D
9. It is evening. What time will it be 2
hours and 20 minutes from now?
8. The square root of 81 is how much
less than seven squared?
7×7=
© 2008 Saxon
______
×
______
time now:
= 81
Count forward 2 hours.
72
___
Count forward 20 minutes.
√81
Use work area.
Saxon Math Intermediate 4
225
Adaptations Lesson 35
Written Practice, continued
page 223
3
10. 2 ___
10
words:
Use work area.
B
11. Find the difference.
Find the pattern.
A
A
300
−
B
400
500
difference
600
12. $1.43
words:
Use work area.
14. a. 6 × 6 =
b. 4 × 9 =
b. 7 × 7 =
c. 3 × 9 =
c. 8 × 8 =
d. 10 × 9 =
d. 11 × 11 =
Use work area.
Saxon Math Intermediate 4
15.
×
= 25
×
= 16
___
√25
___
√16
−
Use work area.
226
Adaptations Lesson 35
© 2008 Saxon
13. a. 6 × 9 =
page 224
Written Practice, continued
2.
16. Shade __
17.
3
$6.05
− $2.53
18.
+
z=
Use work area.
19.
20.
$5.32
+ $3.44
489
z
766
c
+ 294
870
21.
22.
423
− 245
−
670
z
352
z=
c=
23. Write two hundred fifty million.
Use digit lines.
,
,
© 2008 Saxon
24.
25. a. 7 7
…, 3400, 3500, 3600, 3700,
,
,
b. $6. 82
,…
Use work area.
Saxon Math Intermediate 4
227
Use work area.
Adaptations Lesson 35
page 224
Written Practice, continued
26. If 7 + = 10, then which of the
following equals 7 − ?
A 3
B 4
C 7
27. a. thirty thousand 13,000
D 10
b. 74¢
$0.74
Use work area.
28. greatest to least
Start at the greatest place value.
,
,
Use work area.
29. twelfth term
30. Name a real-world
example of:
a. 11, 22, 33, 44,
,
,
a. parallel lines
,
,
,
Parallel looks like railroad tracks.
,
b. perpendicular lines
,
Perpendicular looks like this:
b. 12, 24, 36, 48,
,
,
,
,
© 2008 Saxon
,
,
,
Saxon Math Intermediate 4
a.
a.
b.
b.
228
Adaptations Lesson 35
LESSON
Name
36
page 226
• Fractions of a Dollar
New Concept
• Coins can be shown as fractions of a dollar.
• One penny is one hundredth of a dollar.
100 pennies = 1 dollar
3 of a dollar
3 pennies = ____
$0.03 =
3
____
100
100
of a dollar
• One fourth is also called “one quarter.”
4 quarters = 1 dollar
1 of a dollar
1 quarter = __
4
$0.25 =
1
__
4
of a dollar
• One dime is one tenth of a dollar.
10 dimes = 1 dollar
3 of a dollar
3 dimes = ___
10
$0.30 =
3
___
10
of a dollar
• One nickel is one twentieth of a dollar.
20 nickels = 1 dollar
7 of a dollar
7 nickels = ___
20
$0.35 =
7
___
20
of a dollar
© 2008 Saxon
Lesson Practice
a. three quarters
__
$ .
b. three nickels
__
$ .
Saxon Math Intermediate 4
229
Adaptations Lesson 36
Lesson Practice, continued
c. fifty pennies.
__
$ .
1 of a dollar
d. ___
_1_ of a dollar
4
10
¢
e.
¢
_1_ of a dollar
2
$0.25
¢
¢
f. List all of the different ways to pair two coins.
Act it out.
nickel, quarter
quarter,
nickel,
quarter,
nickel, half dollar
dime,
Written Practice
3.
70 in.
Dad
2.
$36.49 into the store
Quinh
spent
shorter
left the store
11 at school
4. mixed number
© 2008 Saxon
1.
page 230
homework
25 total
Saxon Math Intermediate 4
230
Adaptations Lesson 36
Written Practice, continued
page 230
5. Which letter below has NO right
angles?
T
H
E
6. 2,700,000
Circle the families.
words:
N
Use work area.
7. eighty−two thousand, five hundred
digit lines
,
Use work area.
8. It is morning. What time will it be 4 hours and 20 minutes from now?
11
10
time now:
12
1
2
9
Count forward 4 hours.
3
4
8
7
6
5
Count forward 20 minutes.
9. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4
10. a. nearest ten:
176
© 2008 Saxon
b. nearest dollar: $17.60
a.
b.
×
Saxon Math Intermediate 4
231
Adaptations Lesson 36
page 231
Written Practice, continued
11. How much less?
Find the pattern.
X
500
Y
600
Y
700
X
–
less
12. a. 2 × 8 =
13. a. 3 × 3 =
14. a. 9 × 7 =
b. 5 × 6 =
b. 5 × 5 =
b. 9 × 4 =
c. 4 × 5 =
c. 9 × 9 =
c. 9 × 8 =
d. 5 × 8 =
d. 10 × 10 =
d. 9 × 12 =
Use work area.
×
×
15.
= 36
= 49
Use work area.
16.
Use work area.
$7.32
– $3.45
___
√36
+
Saxon Math Intermediate 4
© 2008 Saxon
___
√49
232
Adaptations Lesson 36
page 231
Written Practice, continued
17.
$4.89
+ $2.57
18.
464
– 238
19.
548
+ 999
20.
487
+
z
721
21.
250
–
c
122
22.
c
– 338
238
z=
23.
c=
c=
24. ten−thousands place
87
– b
54
8,367,254
b=
25. Which does not equal one half of a
dollar?
5 in.
26.
4 in.
A 2 quarters
B 0.50¢
C $0.50
D 50¢
© 2008 Saxon
area = length × width
Saxon Math Intermediate 4
233
A 9 in.
B 18 in.
C 20 sq. in.
D 18 sq. in.
Adaptations Lesson 36
page 232
Written Practice, continued
27. a. –12
–21
28. tenth term
1 of a dollar
b. __
a. 12, 24, 36, 48, 60,
$0.25
4
,
¢
¢
,
,
,
,
b. 11, 22, 33, 44, 55,
,
,
,
a.
a.
b.
b.
29.
List all of the different ways to pair two bills.
Act it out.
$1,
$5,
$1,
$5,
$1,
$10,
Use work area.
Louisiana
30. 397
© 2008 Saxon
Oregon
296
combined
397 rounds to
+
and 296 rounds to
.
=
Use work area.
Saxon Math Intermediate 4
234
Adaptations Lesson 36
LESSON
Name
37
Teacher Note:
page 233
• For additional practice, students
may complete Targeted
Practice 37.
• Reading Fractions and
Mixed Numbers from a
Number Line
New Concept
• To name mixed numbers on a number line:
1. Count from the whole number to the arrow to find the
numerator (top number).
2. Count the segments between whole numbers to find
the denominator (bottom number).
3. Don’t forget the whole number.
Example
5
6
7
1. Two segments between 5 and arrow
The numerator is 2.
The denominator is 3.
2. Three segments between 5 and 6
3. The whole number is 5.
2.
The answer is 5 __
3
Lesson Practice
Name each fraction or mixed number marked by the arrows below:
© 2008 Saxon
a.
a.
c.
b.
b.
0
1
2
0
3
1
2
3
c.
d.
e.
d.
0
1
Saxon Math Intermediate 4
2
e.
3
235
Adaptations Lesson 37
Lesson Practice, continued
3, 26 __
1, and 27__
1.
f. Label 25 __
4
2
4
25
26
Written Practice
27
page 235
Pearl River
1.
Sabine
2.
+
San Juan River
longer
430 Wisconsin
longer
3. four hundred seventy-five thousand, three hundred forty-two
digit lines
Circle the digit in the ten-thousands place.
,
4. area = length × width
is a reasonable answer
because the tiles will be placed
×
Saxon Math Intermediate 4
down.
© 2008 Saxon
across and
=
236
Adaptations Lesson 37
page 235
Written Practice, continued
5. mixed number
6.
5 cm
3 cm
10
11
12
perimeter
Add all sides.
3
8. 12___
7.
10
words:
Use work area.
9. 7026
10. It is early morning. What time will it be
2 hours and 35 minutes from now?
expanded form:
11
10
12
1
2
9
3
4
8
7
6
5
words:
© 2008 Saxon
time now:
Count forward 2 hours.
Count forward 35 minutes.
Use work area.
Saxon Math Intermediate 4
237
Adaptations Lesson 37
Written Practice, continued
page 236
11. three quarters
12.
How many quarters in a dollar?
a. fraction
b. value
a.
b.
×
=
14. a. 10 × 10 =
13. a. 9 × 6 =
b. 9 × 5 =
b. 7 × 7 =
c. 9 × 0 =
c. 8 × 8 =
Use work area.
15. a. 5 × 7 =
Use work area.
×
×
16.
b. 6 × 5 =
= 81
= 49
___
√81
c. 2 × 8 =
___
√49
+
17.
$6.63
– $3.55
Saxon Math Intermediate 4
18.
238
© 2008 Saxon
Use work area.
$4.99
+ $2.88
Adaptations Lesson 37
page 236
Written Practice, continued
19.
a
– 247
321
20.
z
+ 296
531
z=
a=
21.
–
523
z
145
22.
28
46
48
64
32
+ 344
z=
23. a.
24.
…, 450, 460, 470, 480,
,
,
1 ft =
in.
1 ft
,…
d = 2r
b. Count by
.
Use work area.
1 of a dollar
25. a. __
4
1 of a dollar
__
2
26. One yard does not equal which of the
following?
See page 2 in the Student Reference Guide.
© 2008 Saxon
¢
b. 101,010
a.
Saxon Math Intermediate 4
A 36 in.
B 3 ft
C 1m
D 2 ft + 12 in.
¢
110,000
b.
239
Adaptations Lesson 37
Written Practice,
Practice, continued
page 237
27. In order from smallest to largest:
,
,
,
Use work area.
28. Twice the weight of a cheetah would be 130 +
which is
=
,
close to 170.
29. 23
30.
47° July
34° minimum
Saxon Math Intermediate 4
© 2008 Saxon
cooler
240
Adaptations Lesson 37
LESSON
Name
38
Teacher Note:
page 238
• Refer students to Multiplication
Table on page 5 in the Student
Reference Guide.
• Multiplication Facts
(Memory Group)
New Concept
• This is the memory group:
3 × 4 = 12
4 × 7 = 28
3 × 6 = 18
4 × 8 = 32
3 × 7 = 21
6 × 7 = 42
3 × 8 = 24
6 × 8 = 48
4 × 6 = 24
7 × 8 = 56
Lesson Practice
a. Complete Power Up F.
Find each product.
b.
c.
12
× 8
g.
12
× 12
d.
12
× 7
h.
12
× 9
e.
12
× 5
i.
×
12
6
12
× 11
© 2008 Saxon
f.
11
× 11
Saxon Math Intermediate 4
241
Adaptations Lesson 38
Written Practice
page 239
405 harbor
1.
river
more
2. five hundred seventy-five thousand, five hundred forty-two
digit lines.
,
3. 2503
expanded form:
words:
Use work area.
© 2008 Saxon
4.
a. perimeter
a.
b. area (area = length × width)
b.
Saxon Math Intermediate 4
242
Adaptations Lesson 38
Written Practice, continued
page 240
5.
6. Which street is parallel to Broad St.?
7
8
9
10
BROAD ST.
ELM ST.
MAIN ST.
7.
8. a. nearest ten
624
b. nearest dollar
$6.24
c. nearest 25 cents
$6.24
a.
b.
c.
9. It is morning. How long is it until 12:30 p.m?
11
10
time now:
12
1
2
9
3
4
© 2008 Saxon
8
7
Count forward hours: 7:25 − 12:25
6
5
Count forward minutes: 12:25 − 12:30
Saxon Math Intermediate 4
243
Adaptations Lesson 38
Written Practice, continued
page 241
11
11. 2 ____
10. fifty-cent coin
100
a. fraction
words:
b. value
a.
b.
12. 6 squared
×
=
Use work area.
13. a. 3 × 4 =
14. a. 4 × 6 =
b. 3 × 6 =
b. 4 × 7 =
c. 3 × 8 =
c. 4 × 8 =
a.
a.
b.
b.
c.
c.
1 of a dollar
16. ___
15. a. 6 × 7 =
10
1 of a dollar
__
2
b. 6 × 8 =
c. 7 × 8 =
¢
© 2008 Saxon
¢
a.
b.
c.
Saxon Math Intermediate 4
244
Adaptations Lesson 38
page 241
Written Practice, continued
17.
$7.23
− $2.54
$5.42
18.
19.
943
− 276
+
20. top missing
21.
Add.
z
− 581
222
z=
c
+ 843
960
22.
100 cm
c=
___
23. 28 + 36 + 78 + √ 49 =
×
×
24.
28
36
78
____
= 144
= 121
____
√144 − √121
+
–
© 2008 Saxon
1 of
25. Which of the following is not ___
10
a dollar?
=
26. Which digit in 457,326,180 is in the
hundred-thousands place?
See page 13 in the Student Reference Guide.
A dime
C $0.10
Saxon Math Intermediate 4
B 0.10¢
A 1
B 6
C 4
D 3
D 10¢
245
Adaptations Lesson 38
page 242
Written Practice, continued
27. a. A
s
angle has
corners.
b. An
angle is
than a right angle.
c. An
angle is
than a right angle.
Use work area.
28. 12, 24, 36, 48, …
a. rule: Count
by
b. Complete the sequence. Circle the eleventh term.
12, 24, 36, 48,
,
,
,
,
,
,
Use work area.
29. compatible numbers
$14.99
$18.95
$14.99 rounds to
+
and $18.95 rounds to
.
=
© 2008 Saxon
Use work area.
30. How much for six?
Number of Tickets
Cost
Saxon Math Intermediate 4
1
2
3
4
5
6
$11 $22 $33 $44
246
Adaptations Lesson 38
LESSON
Name
39
Teacher Notes:
page 243
• Introduce Hint #22 “Reading Inch
Rulers.”
• Use a tape measure to illustrate
concepts in this lesson.
• Reading an Inch Scale
to the Nearest Fourth
New Concept
• The long marks on this ruler are inch marks.
inch
mark
inch
mark
1
2
inch
1 inch
2 mark
3
4
1 inch
2 mark
1 -inch
• The marks halfway between the inch marks are __
2
marks.
• Each inch is divided into fourths.
inch
1
2
3
4
1 -inch marks.
The short tick marks are __
One quarter inch =
2 = __
1
__
4 2
© 2008 Saxon
Activity
1
__
4
4
inch
(Think: Two quarters equal half of a dollar.)
page 244
Make a Ruler and Measure
Use an inch ruler to measure the segments below.
a.
b.
c.
Saxon Math Intermediate 4
247
Adaptations Lesson 39
Lesson Practice
2 equals __
1.
a. Shade these circles to show that __
4
2
â
Name each point marked by an arrow on this inch scale.
Remember to write the whole number.
b
inch
b.
c
1
d
e
2
c.
3
4
d.
e.
f. Measure the length and width of this paper.
width:
length:
g. Find the distance from A to C.
A
B
C
h. If Pam stacks two of these blocks together, what are all the possible combined
heights she could make?
1
inch
11
2
inches
© 2008 Saxon
Act it out.
2
inches
,
Saxon Math Intermediate 4
248
,
Adaptations Lesson 39
Written Practice
1.
page 246
35 mother
Trinity
older
This is
l
problem because it
−
s
=
c
d
two numbers.
2. four hundred sixty-eight thousand, five hundred two
digit lines
,
3. 3905
4.
243 J’Maresh
Leilani
expanded form:
total
Odd or even?
words:
© 2008 Saxon
Use work area.
1
5. 100 ____
100
words:
Use work area.
Saxon Math Intermediate 4
249
Adaptations Lesson 39
Written Practice, continued
page 246
6. Negative nineteen is greater than
negative ninety.
7. Use a dollar sign and a decimal point
to write the value of two dollars, one
quarter, two dimes, and three nickels.
$ 2.00
$ .
$ .
$ .
Use work area.
8. It is morning. School begins at 8:15 a.m.
11
10
time now:
12
1
2
9
3
4
8
early or late?
7
6
5
how many minutes?
Use work area.
10. One kilometer is how many meters?
9. nine dimes
See page 1 in the Student Reference Guide.
a. fraction
b. value
a.
11.
Saxon Math Intermediate 4
12. Find the length to the nearest quarter
inch.
250
Adaptations Lesson 39
© 2008 Saxon
b.
page 247
Written Practice, continued
13. a. 4 × 3 =
14. a. 6 × 3 =
15. a. 7 × 3 =
b. 6 × 4 =
b. 7 × 4 =
c. 7 × 6 =
c. 8 × 6 =
d. 6 × 12 =
d. 8 × 12 =
b. 8 × 3 =
c. 8 × 4 =
d. 4 × 12 =
Use work area.
×
×
16.
= 64
= 36
Use work area.
17.
$4.86
Use work area.
18.
$4.86
− $2.47
21.
463
−
y
411
+
___
√64
___
√36
−
293
19.
20.
893
− 678
+
y=
22.
© 2008 Saxon
+
463
q
527
23.
8 squared
24. … , 470, 480, 490, 500,
,
,
,…
q=
Saxon Math Intermediate 4
×
=
251
Use work area.
Adaptations Lesson 39
page 248
Written Practice, continued
26. Which of these does not equal 9 + 9?
25. Draw a triangle that has three acute
angles.
See page 15 in the Student Reference Guide.
A 2×9
B 9×2
C 3×6
D nine squared
Use work area.
28. Anastacia’s estimate
27. In order from most
expensive to least
expensive:
reasonable because
350 – 200 =
which
,
close to 140.
Use work area.
Use work area.
30. How many inches
in 20 feet?
29. What are the perimeters?
feet × 12 = inches
4 in. 2 in.
© 2008 Saxon
6 in. 2 in.
6 in. 4 in.
Saxon Math Intermediate 4
252
Adaptations Lesson 39
LESSON
Name
40
Teacher Notes:
page 249
• Introduce Hint #24 “Measuring
Liquids and Capacities of
Containers.”
• Capacity
• Refer students to “Liquids” and
“Equivalence Table for Units” on
page 1 in the Student Reference
Guide.
• Display reference chart “Liquids.”
New Concept
Abbreviations for
U.S. Liquid Measures
fluid ounce
fl oz
cup
c
pint
pt
quart
qt
gallon
gal
Milk
1 cup
1 mL
1 oz
1 cup
Activity
Half
&
Half
1 pint 1 quart
1 liter 1 gallon
2
2 liters
1 gallon
page 251
Measuring Capacity
© 2008 Saxon
a. How many cups of liquid equal a pint?
b. How many pints of liquid equal a quart?
c. How many quarts of liquid equal a half gallon?
d. How many half gallons of liquid equal a gallon?
Saxon Math Intermediate 4
253
Adaptations Lesson 40
New Concept, continued
e. How many quarters equal a dollar?
f. How many quarts of liquid equal a gallon?
g.
U.S. Liquid Measure
8 fl oz â 1 c
c â 1 pt
pt â 1 qt
qt â 1 gal
h. Compare: 1 quart
1 liter
i. Compare: _1_ gallon
2 liters
2
j. How many liters will it take to fill a gallon container?
k. A full 2-liter bottle of liquid
contains how many milliliters of liquid?
Lesson Practice
a. Complete this table.
Gallons
1
2
Quarts
4
8
3
b. How many quarts in 12 gallons?
4
5
6
7
8
c. one pint = 2 cups
© 2008 Saxon
one cup = 8 ounces
How many ounces is one pint?
2×
=
d. About how many milliliters would it take to fill a 3 _1_ -liter container?
2
1000 + 1000 + 1000 + 500 =
Saxon Math Intermediate 4
254
Adaptations Lesson 40
page 253
Written Practice
1.
112
big
small
2.
36 in. one yard
12 in. one piece
other piece
3.
47
Mrs. Green
husband
son
fewer
in all
4. 7,500,000
Circle the families.
expanded form:
words:
Use work area.
5. thousands place
27,384,509
6.
$3.00
$ .
$ .
$ .
words:
© 2008 Saxon
Use work area.
7. 1 gal =
qt
8.
See page 1 in the Student Reference Guide.
Saxon Math Intermediate 4
255
Adaptations Lesson 40
page 253
Written Practice, continued
10. 1 gal = 3.78 L
9.
Use this information to compare:
1 gallon
3 liters
Use work area.
11. It is evening. How long until 12:00?
12. What type of angle is
formed by the hands of the
clock in problem 11?
time now:
Count forward minutes:
11
10
10:10
11:00
12
1
2
9
B right
C obtuse
D straight
3
4
8
7
5
6
Count forward hours:
11:00
A acute
12:00
13. a. −29
−32
14.
2 cm
b. $0.75
¢
3 of a dollar
__
4
¢
15. a. 6 × 6 =
b. 7 × 7 =
c. 8 × 8 =
d. 12 × 12 =
Use work area.
16. a. 7 × 9 =
b. 6 × 9 =
c. 9 × 9 =
d. 9 × 12 =
Use work area.
Saxon Math Intermediate 4
256
Adaptations Lesson 40
© 2008 Saxon
Use work area.
page 254
Written Practice, continued
b. 6 × 7 =
17. a. 7 × 8 =
c. 8 × 4 =
d. 12 × 7 =
Use work area.
18.
19.
$4.98
+ $ .
20.
m
− $6.70
$3.30
−
416
z
179
z=
m=
__
21.
22. √ 1
536
+ z
721
23. Draw an array of Xs to
show 3 × 7.
__
√4
__
√9
+
z=
Use work area.
1
24. 10 ___
25. two quarters
10
a. fraction
b. value
words:
a.
Use work area.
b.
© 2008 Saxon
26. A rectangle has an area of 24 square inches. Which of these could be the length
and width of the rectangle? Circle one.
Area = length × width
A 6 in. by 6 in.
B 12 in. by 12 in.
C 8 in. by 4 in.
D 8 in. by 3 in.
Use work area.
Saxon Math Intermediate 4
257
Adaptations Lesson 40
Written Practice, continued
page 255
27. Two quarters equal half of a dollar.
2=8
8 __
4
Use work area.
28.
+
24 ft.
12 ft.
+
+
=
12 ft.
24 ft.
The perimeter is
so the gardener should buy the
roll.
Use work area.
29. compatible numbers
$0.66
$0.66
$
$
$12.00
+ $12.00
The tax on each pair of gloves is about
more than $12 + $12 +
+
. The total cost is a little
=
.
Use work area.
30. How many different three-digit numbers can you make with 6, 2, and 0?
© 2008 Saxon
Label even or odd.
Saxon Math Intermediate 4
258
Adaptations Lesson 40
4A/B
I NVE S TIGATION
Name
Teacher Note:
• Student will need Lesson Activity
23 to complete Activity 2.
page 256
Focus on
• Tenths and Hundredths
• Relating Decimals and
Fractions
• The value of coins can be shown as a fraction of a dollar.
• We use decimal numbers when we write money amounts.
_1_
4
1
___
10
â$0.25
1
___
20
â$0.10
â$0.05
1
____
100
â$0.01
• The numbers after the decimal point show parts of a dollar.
decimal point
.
1s
place
© 2008 Saxon
Activity 1
1
10 s
1
s
100
place
place
page 256
Tenths and Hundredths
Show these amounts with your money manipulatives.
1. $345.23
2. $0.42
3. $5.20
4. $3.02
Write the amount shown in your textbook.
5.
Saxon Math Intermediate 4
6.
7.
259
Adaptations Investigation 4A/B
INVE STIGATION
4A/B
continued
Use money manipulatives to compare.
8.
9. $0.40
$0.07
Write the amounts shown in your textbook in order from greatest to
least for problems 10 and 11.
10.
$1.10 ,
,
11.
$1.20 ,
,
Use bills and coins to show these decimal numbers:
12. 3.42
three and forty-two hundredths
13. 0.24
twenty-four hundredths
14. 12.03
twelve and three hundredths
15. 1.3
one and three tenths
© 2008 Saxon
• The square is divided into 10 equal parts.
1 â 0.1 (Both say one tenth.)
10
• One part is shaded.
Saxon Math Intermediate 4
260
Adaptations Investigation 4A/B
INVE STIGATION
4A/B
continued
Use the pictures in your textbook for problems 16-19.
16. decimal:
fraction:
17. decimal:
fraction:
18. decimal:
fraction:
19. decimal:
fraction:
• The square is divided into 100 equal parts.
• One part is shaded.
© 2008 Saxon
1 â 0.01 (Both say one hundredth.)
100
Saxon Math Intermediate 4
261
Adaptations Investigation 4A/B
INVE STIGATION
4A/B
continued
Use the pictures in your textbook for problems 20-23.
20. decimal:
21. decimal:
fraction:
fraction:
22. decimal:
23. decimal:
fraction:
fraction:
• Look at problems 19 and 22. Half of each square is shaded.
5 = ____
50 and __
1 = ___
1 = 0.5 = 0.50
__
2 10 100
2
24. Which of the following numbers does not equal one half?
5
A ___
10
50
C ____
B 5
D 0.05
100
Complete each comparison.
25.
0.1
0.10
0.2
0.02
27. The pictures above show the decimal numbers 0.1, 0.2, 0.02.
Arrange the numbers in order from least to greatest.
Saxon Math Intermediate 4
262
Adaptations Investigation 4A/B
© 2008 Saxon
26.
INVE STIGATION
continued
4A/B
Activity 2
page 260
Using Unit Squares to Relate Fractions and Decimal Numbers
• Use your textbook to complete this activity.
• Fractions and decimals are two ways to describe parts of a whole.
• Decimals use place value to show the part of the whole.
0
whole number
.
.
2
tenth
5
hundredth
one decimal place
two decimal places
three decimal places
1
0.1 = ___
12
0.12 = ____
123
0.123 = _____
10
100
1000
Read each number aloud. Remember to say tenths, hundredths, or
thousandths.
75
33. a. ____
b. 0.75
7
____
100
b. 0.07
100
34. a.
3
35. a. ___
b. 0.3
2
36. a. ___
b. 0.2
10
© 2008 Saxon
10
Saxon Math Intermediate 4
263
Adaptations Investigation 4A/B
INVE STIGATION
4A/B
continued
• To name 12.25:
whole
number fraction
12
25
.
1. Name this part.
2. Say or write “and.”
3. Then name this part.
Read each number aloud. Then use words to write each number.
37. a. 10.75
b. 12.5
38. a. 6.42
b. 10.1
Use digits to write each of these decimal numbers:
39. one and three tenths _____
40. two and twenty-five hundredths _____
41. three and twelve hundredths _____
Activity 3
page 262
Using Decimal Numbers on Stopwatch Displays
• This activity is optional.
Saxon Math Intermediate 4
264
Adaptations Investigation 4A/B
© 2008 Saxon
42. four and five tenths _____