Reteaching
Name
11
Lesson 11
• Word Problems About Combining
• “Some and some more” problems have an addition formula.
Formula
Some
+ Some more
Total
Problem
8 miles
+ 7 miles
15 miles
• Find a missing total by adding.
• Find a missing addend by subtracting.
• Remember to check your answer.
Practice:
Find the missing number and check the answer. Remember to write the dollar sign in
money problems.
1. Quentin wants to buy a new pair of shoes for the choir performance. Shoes cost
$43. Quentin has $28. How much money does he need to buy the shoes?
2. Nicolette’s mother asked her how many times she had watched her favorite
movie. Nicolette said she had watched it 18 times last month, but she had
watched 27 times in all. How many times, before last month, had Nicolette
watched the movie?
3. Write a word problem about combining for the equation to
the right. Then answer the question in your word problem.
12
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$38 + $54 = b
Saxon Math Intermediate 5
Reteaching
Name
12
Lesson 12
• Lines
• Number Lines
• Tally Marks
Lines
• A point, a line, a line segment, and a ray are shown below:
Point
Line
Line segment
Ray
• Lines, rays, and segments can be horizontal, vertical, or oblique.
Oblique lines
Vertical line
Horizontal line
Number Lines
• A number line represents numbers in order. Integers are separated by unit
intervals.
Unit interval
–5
–4
–3
–2
–1
1
0
2
3
4
5
Tally Marks
• Tally marks can be used to quickly record data of things we count by ones. We
then use a cross hatch to mark sets of five, so it’s easier to read large numbers
of tally marks.
Four
Five
Six
Practice:
1. Which of these represents a line segment?
A
B
C
2. Show the number 21 using tally marks.
3. Draw a pair of oblique line segments.
Saxon Math Intermediate 5
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13
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13
Lesson 13
• Multiplication as Repeated Addition
• Adding and Subtracting Dollars and Cents
Multiplication as Repeated Addition
• Multiplication is repeated addition of the same number.
5 × 6 = 5 + 5 + 5 + 5 + 5 + 5
Adding and Subtracting Dollars and Cents
• When adding or subtracting dollars and cents, line up the decimal points.
Example: $2.54 + $4.15 + $0.60 =
1
$ 2.5 4
$ 4.1 5
+ $ 0.6 0
$ 7.2 9
Practice:
Write a multiplication problem for each of these addition problems.
1. 4 + 4 + 4 + 4 + 4 =
2. 13 + 13 + 13 =
×
×
3. Write a multiplication problem that shows how to find the number of Xs.
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
×
Find each sum or difference. Remember to write the dollar sign.
14
4.
$8.91
+ $1.12
5.
$6.34
– $3.55
6.
$11.27
+ $10.96
7.
$5.60
– $3.74
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Saxon Math Intermediate 5
Reteaching
Name
14
Lesson 14
• Missing Numbers in Subtraction
• To find missing numbers in subtraction:
If the top number is missing, add.
a
Ľ4
9
7
à4
a â 11
If the bottom number is missing, subtract.
15
Ľn
9
15
Ľ9
n â6
• To check your work, put the number you found back into the original problem, and
perform the subtraction.
Practice:
Find each missing number. Check your answers.
1. Bottom number missing, subtract.
2. Top number missing, add.
14
Ľb
7
3.
16
Ľx
9
n
Ľ8
2
4.
n
Ľ5
13
5. Write a subtraction problem with the top number missing. Solve and show how
to check.
6. Write a subtraction problem with the bottom number missing. Solve and show
how to check.
Saxon Math Intermediate 5
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15
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15
Lesson 15
Making a Multiplication Table
• If you know one fact family, you know four facts.
3 × 4 = 12
4 × 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
• Factors are numbers that are multiplied together to get a product (the answer).
• The Commutative Property of Multiplication says that the order of the numbers
does not matter.
5 × 4 = 20
4 × 5 = 20
• The Property of Zero for Multiplication says any number times zero equals zero.
2 × 0 = 0
• The Identity Property of Multiplication says that any number times one equals
itself.
2 × 1 = 2
• Practice reciting the four facts for each triangle by covering one number in the
triangle at a time.
9
3
12
3
3
4
4
16
4
3
6
4
6
7
3
7
4
8
7
3
8
4
8
7
7
72
8
9
49
9
6
8
36
54
64
9
24
32
8
6
63
8
6
48
7
6
21
28
42
56
7
4
24
36
6
18
81
9
9
9
Practice:
Find each product.
1. 3 × 7 =
2. 8 × 4 =
3. 6 × 3 =
4. 10 × 0 =
5. 9 × 10 =
6. 4 × 6 =
7. The answer to a multiplication problem is called the
The numbers we multiply together are called
16
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
.
.
Saxon Math Intermediate 5
Reteaching
Name
16
Lesson 16
• Word Problems About Separating
• In word problems about separating, the missing number can be the top number,
the bottom number, or the difference.
• If the top number is missing, add.
Some
Some went away
What is left
m
Ľ$13
$20
$20
à$13
$33
• If the bottom number is missing, subtract.
Some
Some went away
What is left
$33
Ľm
$13
$33
Ľ$13
$20
• If the difference is missing, subtract as usual.
Some
Some went away
What is left
$33
Ľ$13
m
$33
Ľ$13
$20
Practice:
1. 600 students started a painting club for the city. In the sixth month there were
313 members. How many members dropped out of the club?
2. Edwin paid $65.00 for 5 tickets to the school play. He had $129.00 left.
How much did Edwin have before he bought the tickets?
3. An adventure team has 47 members. 18 of the members went camping, while
the others went rafting. How many members went rafting?
Saxon Math Intermediate 5
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17
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Name
17
Lesson 17
• Multiplying by One-Digit Numbers
• Learn to carry using mental math. If the “carry” number is more than 5, write it
down instead.
Example:
×4 3 3 × 5 = 15
× 05 Write 5 in the ones column.×
5 Carry the 1 mentally.
×4 3 4 × 5 = 20
× 05 Add the carried 1 to the product (20 + 1 = 21).
215 Write the 21.
• When multiplying money amounts that have decimals, show two decimal places in
the answer for “cents.”
Practice:
1.
4.
7.
18
×
38
5
2.
×
320
8
5.
×
$359
7
8.
40
× 8
3.
×
$6.92
4
6.
×
507
9
9.
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
×
$0.45
7
×
704
6
×
$2.83
3
Saxon Math Intermediate 5
Reteaching
Name
18
Lesson 18
• Three Factors and Missing Factors
• We can multiply factors in any order.
3 × 5 × 4
3 × 5 × 4
3 × 5 × 4
15 × 4 = 60
12 × 5 = 60
3 × 20 = 60
• To find missing factors, first recall any multiplication facts that might use the
same numbers.
Practice:
1. 5 × 8 × 3 =
2. 10 × 6 × 2 =
3. 2 × 3 × 4 =
4. 5 × 3 × 1 =
Find each missing factor.
5. m × 7 = 42
m =
7. 4 × 5 = n × 2
n =
Saxon Math Intermediate 5
6. 5 × b = 45
b =
8. 2 × 8 = p × 4
p =
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19
Reteaching
Name
19
Lesson 19
• Relationship between Multiplication and Division
• If you know one fact family, you know two multiplication facts and two division
facts:
7
× 5
35
35
5
7
5
× 7
35
7
___
5) 35
5
___
7) 35
Practice:
Find the missing number in each triangle (fact family).
___
___
1. 3) 18
2. 4) 20
18
4
3
___
20
___
3. 6) 36
4. 10) 40
36
40
6
10
___
5. 9) 63
___
6. 7)42
63
7
9
___
7. 8) 56
___
8. 5)55
56
8
20
42
55
5
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
Saxon Math Intermediate 5
Reteaching
Name
20
Lesson 20
• Three Ways to Show Division
• Below are three ways to show division:
__________
divisor)dividend
dividend ÷ divisor
dividend
_________
Box
Sign
Bar
divisor
• The answer to a division problem is called the quotient.
• Say the dividend first.
Practice:
1. Show “15 divided by 3” in three different forms:
___
)
_____
÷
2. Use three different division forms to show “32 divided by 8”.
___
)
_____
÷
Use words to show how each division problem is read.
___
3. 4) 24
divided by
.
4. 42 ÷ 6
divided by
.
27
5. ___
9
divided by
.
Rewrite each division problem with a division box.
6. 54 ÷ 6
)
___
40
7. ___
8
___
)
8. Identify the quotient, dividend, and divisor in this equation: 24 ÷ 3 = 8
quotient
dividend
divisor
Saxon Math Intermediate 5
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
21