Multiplication and
Division Fact Families
Objectives To review fact families and the Multiplication/Division
Facts Table; and to guide children as they practice multiplication
and division facts.
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Teaching the Lesson
Key Concepts and Skills
• Use Fact Triangles and the Facts Table
to generate multiplication and division
fact families. [Operations and Computation Goal 3]
• Look for patterns on the Facts Table. [Patterns, Functions, and Algebra Goal 1]
• Explore the inverse relationship between
multiplication and division fact families. [Patterns, Functions, and Algebra Goal 2]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Practicing with ×, ÷ Fact
Triangles
×, ÷ Fact Triangles
Children practice multiplication and
division with Fact Triangles.
Math Boxes 4 6
Math Journal 1, p. 90
Children practice and maintain skills
through Math Box problems.
Home Link 4 6
• Apply the turn-around rule
(Commutative Property of Multiplication). [Patterns, Functions, and Algebra Goal 4]
Math Masters, pp. 99–102
Children practice and maintain skills
through Home Link activities.
Key Activities
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Practicing Multiplication Facts
with a Calculator
Math Masters, p. 103
calculator
Children skip count with calculators.
ENRICHMENT
Examining a Pattern
Math Masters, p. 98 or Math Journal 1,
inside front cover
per partnership: half-sheet of paper,
highlighters (optional)
Children examine a pattern in the
Multiplication/Division Facts Table.
Children use the Multiplication/Division
Facts Table and Fact Triangles to find fact
families and to practice multiplication and
division facts.
Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message. [Patterns, Functions, and Algebra Goal 2]
Key Vocabulary
Multiplication/Division Facts Table
Materials
Math Journal 1, inside front cover
Math Journal 1, Activity Sheets 1 and 2;
Activity Sheets 3 and 4 (optional)
Student Reference Book, pp. 52 and 53
Home Link 45
Math Masters, p. 98 (optional); p. 421
transparencies of Math Masters, pp. 98 and
421 (optional) scissors slate paper envelope half-sheet of paper
Advance Preparation
When you send Home Link 46 home, copy and attach Math Masters, pages 101 and 102.
Teacher’s Reference Manual, Grades 1–3 pp. 16, 17
272
Unit 4
Multiplication and Division
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Getting Started
Mental Math and Reflexes
Math Message
Have children count chorally. They may use number
grids, number lines, or calculators as needed.
Write the +,- fact family for the numbers 2, 2,
and 4 on a half-sheet of paper.
Skip count forward and backward by 2s, 5s, and 10s.
Skip count forward and backward by 3s and 6s.
Skip count forward and backward by 4s and 8s.
Home Link 4 5 Follow-Up
Have partners discuss the multiplication-fact
shortcuts they like the best.
1 Teaching the Lesson
Math Message
•
12
WHOLE-CLASS
ACTIVITY
×, ÷
Follow-Up
4
Ask a volunteer to share the fact family for 2, 2, and 4. 2 + 2 = 4,
and 4 - 2 = 2. The fact family 2, 2, and 4 is a doubles fact family.
Mention that just like addition and subtraction fact families, there
are also multiplication and division fact families.
Ongoing Assessment:
Recognizing Student Achievement
Math
Message
3
3 × 4 = 12
12 ÷ 4 = 3
4 × 3 = 12
12 ÷ 3 = 4
Fact family for the numbers 4, 3, and 12
Use the Math Message to assess children’s progress toward using the +, -,
and = symbols. Children are making adequate progress if they are able to write
the fact family. Some children may notice that the same numbers (2, 2, and 4)
can be used to write a multiplication fact and a division fact using the ×, ÷, and
= symbols.
[Patterns, Functions, and Algebra Goal 2]
Teaching Aid Master
Name
Date
Time
Multiplication/Division Fact Triangle
Introducing Multiplication/
WHOLE-CLASS
ACTIVITY
Division Fact Families
(Math Masters, p. 421)
Use a transparency of a blank Fact Triangle (Math Masters,
page 421) or draw one on the board.
Write the three numbers from a multiplication fact—for example,
3, 4, and 12—in the corners of the triangle. Be sure the product is
at the top under the large dot.
⫻,⫼
Ask volunteers to name the fact family (the two multiplication
facts and two division facts) for those numbers. 3 × 4 = 12,
4 × 3 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3
Math Masters, p. 421
Lesson 4 6
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Write a few more triplets of numbers in the triangle. Children
write the fact families on their slates. A volunteer reads the
results as the others check their slates.
In the previous lesson, children used arrays to demonstrate a
turn-around rule for multiplication. Ask: Is there a turn-around
rule for the division facts in each fact family? No Have children
give examples to show that there is no turn-around rule for
division; for example, 6 divided by 3 gives a different answer than
3 divided by 6. Some children may recognize that division
problems, such as 3 ÷ 6, can be thought of as fractions: 3 ÷ 6 is
equivalent to _36 or _12 .
Finding Patterns in the
WHOLE-CLASS
DISCUSSION
Facts Table
(Math Journal 1, inside front cover; Math Masters, p. 98)
Algebraic Thinking Ask children to study the Multiplication/
Division Facts Table on the inside front cover of the journal.
You may also display a transparency of the table (Math Masters,
page 98). Give children a few minutes to examine the table. Have
them describe patterns they find. Examples:
Going across the second row and down the second column, the
numbers increase by 1. In the third row and third column, the
numbers increase by 2, and so on.
In the 10-column and the 10-row, all of the numbers end in 0.
In the 5-column and the 5-row, all of the numbers end in 0 or 5.
In the 2-column and the 2-row, all of the numbers end in an
even number.
In the diagonal, moving from upper left to lower right, the
numbers increase by 3, 5, 7, 9, and so on.
Teaching Master
Name
Date
Time
Page Title
Multiplication/Division
Facts Table
LESSON
40 06
䉬
Using the Facts Table and
Multiplication/Division Facts Table
⫻,⫼
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
WHOLE-CLASS
ACTIVITY
Fact Families
(Student Reference Book, pp. 52 and 53)
Model how to use the table to find products.
Example: 5 × 7 = ? and 7 × 5 = ?
●
Find the 5-row. Go across the 5-row to the 7-column. That
number is 35. This shows that 5 × 7 = 35.
●
Find the 7-row. Go across the 7-row to the 5-column. That
number is 35. This shows that 7 × 5 = 35.
Have children practice other multiplication examples, including
8 × 1 = ? and 1 × 4 = ?. Use the Multiplication/Division Facts
Table to highlight the special property of 1 in multiplication. If a
number is multiplied by 1, the number is not changed. 8 × 1 = 8;
1 × 4 = 4.
Math Masters, p. 98
274
Unit 4 Multiplication and Division
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Next, demonstrate how to use the Multiplication/Division Facts
Table to find quotients.
Example: 28 ÷ 4 = ?
Find the 4-row. Go across the 4-row until you find 28. Go up
that column to the heading, which is 7. This also shows that
28 ÷ 4 = 7.
Multiplication/Division Facts Table
Find the 4-column. Go down the column until you find 28. Go
across the row to the heading, which is 7. This also shows that
28 ÷ 4 = 7.
Have children practice other division examples including 6 ÷ 1 = ?
and 7 ÷ 7 = ?. Use the Multiplication/Division Facts Table to
highlight the special property of 1 in division. If a number is
divided by 1, the number is not changed. If a number is divided by
itself, the result is 1. For example, 6 ÷ 1 = 6 and 7 ÷ 7 = 1.
3 ,4
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
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7
8
9
10
2
2
4
6
8
10
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18
20
3
3
6
9
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21
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27
30
4
4
8
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24
28
32
36
40
5
5
10
15
20
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30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
Call out multiplication facts. Ask children to highlight the facts
with a sheet of paper as shown in the margin. Then children state
the corresponding division facts. Alternately, children highlight
division facts on the table as you call them out. They then state
the corresponding multiplication facts.
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
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18
20
3
3
6
9
12
15
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21
24
27
30
4
4
8
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28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
PARTNER
ACTIVITY
(Math Journal 1, Activity Sheets 1 and 2)
Student Page
Date
Time
LESSON
Multiplication/Division Fact Triangles 1
46
4
2
Links to the Future
6
⫻,
⫼
These Fact Triangles present the “easier” facts. In Unit 7, children will use the
harder Fact Triangles (Activity Sheets 3 and 4). Do not expect all children to
master all of the easier facts at this time. Children will have more opportunities to
practice the facts in later units.
4
NOTE Have children store their Fact Triangles in their tool kits in envelopes.
Some teachers have children write the fact families on the backs of the Fact
Triangles. This should be an ongoing project, done a few at a time.
⫻,
⫼
Review the procedure for practicing the facts with Fact Triangles.
While one child covers a number on a Fact Triangle, the partner
tells the multiplication or division fact for the exposed numbers.
The guide may be positioned either way to show
4 × 7 = 28, 7 × 4 = 28; or 28 ÷ 4 = 7 and
28 ÷ 7 = 4.
2
2
⫻,⫼
2
3
3
4
2
3
Have children cut out the Multiplication/Division Fact Triangles
from Activity Sheets 1 and 2 at the back of their journals.
8
Practicing with Fact Triangles
Multiplication/Division Facts Table
3 ,4
⫻,⫼
V I S U A L
⫻,
3
9
5
20
15
⫼
⫻,
⫼
12
T A C T I L E
16
10
K I N E S T H E T I C
⫻,
4
A U D I T O R Y
5
Have children practice with the Fact Triangles on Activity Sheets 3 and 4
as appropriate.
⫼
⫻,
⫼
Adjusting the Activity
4
3
5
4
⫻,⫼
Activity Sheet 1
Math Journal 1, Activity Sheet 1
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Lesson 4 6
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Student Page
Date
Time
4 6
䉬
Write ⬍, ⬎, or ⫽.
1.
3⫻2
4⫻1
5⫻3
9⫻0
⫽
⬎
⬍
⫽
5 ⫻ 9 ⫽ 45
9 ⫻ 5 ⫽ 45
45 ⫼ 5 ⫽ 9
45 ⫼ 9 ⫽ 5
8⫻0
5⫻4
0⫻7
yd
Rule
⫻3
Write the fact family.
2.
2⫻3
Complete.
3.
13 56
yd
ft
2
5
6
15
3
10
30
45
⫻, ⫼
9
5
55
Use the dots to show a
7-by-6 array.
4.
9
What is the number model?
Answers vary.
ft t
7
52
203 204
Lengths (in.) of 13 cats, including
the tails:
5.
2 Ongoing Learning & Practice
Math Boxes
LESSON
⫻
6
⫽
42
Fill in the empty
frames.
6.
Rule
⫹1,000
30, 29, 28, 24, 29, 35, 16, 27, 29,
36, 28, 31, 32
What is the maximum length? Fill
in the oval for the best answer.
36 inches
16 inches
29 inches
30 inches
64 65
1,107
2,107
3,107
6,107
5,107
4,107
7,107
79
200 201
Practicing with ×, ÷ Fact
PARTNER
ACTIVITY
Triangles
Have partners use their Fact Triangles to practice basic
multiplication and division facts. At first, children should limit
themselves to finding products. That is, one partner covers the
number below the large dot, and the other gives the product of the
uncovered factors. When children are well on their way to learning
products, they can cover one of the other two numbers to practice
finding missing factors.
Math Boxes 4 6
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 90)
90
Math Journal 1, p. 90
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 4-9. The skill in Problem 6
previews Unit 5 content.
Writing/Reasoning Have children answer the following
question: When a number is multiplied by 1, the number
does not change. What can you say about dividing a
number by 1? Sample answer: When a number is divided by 1, the
number does not change.
Home Link 4 6
INDEPENDENT
ACTIVITY
(Math Masters, pp. 99–102)
Home Link Master
Name
Date
HOME LINK
40 06
䉬
Page
Title
PageTriangles
Title
ⴛ,
ⴜ Fact
Home Connection Children review multiplication and
division fact families. Send home copies of Math Masters,
pages 101 and 102, which contain Fact Triangles.
Time
continued
Tell someone at home about multiplication/division fact families.
1. The numbers 2, 5, and 10 form the following facts:
10 2 5
10 5 2
Knowing 6 2 12 and 2 6 12
helps me know 12 2 6 and 12 6 2.
25
52
2.
10
10
3 Differentiation Options
3. The numbers 2, 7, and 14 form this multiplication/division fact family:
2 7 14
7 2 14
14 2 7
14 7 2
READINESS
Practicing Multiplication Facts
Write the fact family for each , Fact Triangle.
4.
5.
6.
16
, 2
60
20
2 8 16
8 2 16
16 2 8
16 8 2
5
4
5 4 20
4 5 20
20 5 4
20 4 5
10
15–30 Min
with a Calculator
, , 8
INDEPENDENT
ACTIVITY
6
10 6 60
6 10 60
60 10 6
60 6 10
(Math Masters, p. 103)
To provide experience skip counting on a calculator, have children
use their calculators to complete the tables on Math Masters, page
103. Review the steps for counting by 1s on the calculator.
Children can program the calculator using the following steps:
Math Masters, p. 100
276
Unit 4 Multiplication and Division
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Teaching Master
Name
TI
LESSON
46
䉬
1. Press
ON/C
. This clears your calculator.
3. Press
. This tells the calculator to count up.
One 3
Two 3s
Three 3s
Four 3s
Five 3s
Six 3s
Seven 3s
Eight 3s
Nine 3s
Ten 3s
3
6
9
12
15
18
21
24
27
30
2. Use your calculator to count by 4s. Complete the table below.
4. Press 1. This tells the calculator to count by 1s.
One 4
Two 4s
Three 4s
Four 4s
Five 4s
Six 4s
Seven 4s
Eight 4s
Nine 4s
Ten 4s
4
8
12
16
20
24
28
32
36
40
3. Use your calculator to count by 6s. Complete the table below.
Casio
1. Press
Time
1. Use your calculator to count by 3s. Complete the table below.
2. Press 0. This is the starting number.
+
Date
Multiplication Facts & Calculator Counts
. This clears your calculator.
Two 6s
Three 6s
Four 6s
Five 6s
Six 6s
Seven 6s
Eight 6s
Nine 6s
Ten 6s
6
12
18
24
30
36
42
48
54
60
4. How can counting on your calculator help you learn your
2. Press 1. This tells the calculator to count by 1.
3. Press
One 6
multiplication facts?
Sample answer: If I can count by 3s, I know
the products to the ⫻3 facts. If I can count by
any number, then I know which numbers are
the products to that number’s multiplication
facts.
. This tells the calculator to count up.
4. Press 0. This is the starting number.
Now the calculator is ready to count by 1s. Without clearing their
=
=
key. Press the
key
calculators, have children press the
repeatedly as the class counts together by 1s. Once they recall this
routine, have them work on Math Masters, page 103. When
children have completed the page, discuss how calculator counting
might help them learn their facts. Have children read aloud the
counts they have recorded on the master.
ENRICHMENT
Examining a Pattern
Math Masters, p. 103
PARTNER
ACTIVITY
1
2
3
15–30 Min
2
4
6
3
6
9
(Math Masters, p. 98; or Math Journal 1, inside front cover)
To further explore the Multiplication/Division Facts
Table, have children examine a pattern in the table.
Together, they circle a number on the table. Then, they
circle the number in the square above, to the right, below, and to
the left of the chosen number. Next, they add the starting number
plus the four circled numbers.
Children record their starting number and the sum of the five
circled numbers on a half-sheet of paper as shown. They repeat
this several times and look for a pattern in the recorded numbers.
The product of the starting number and 5 is always equal to the
sum of the five numbers. Ask: How does this pattern work? Sample
answer for the example: “I made the 6s into 4s and added the
leftovers to the 2s to make them into 4s. So I had five 4s.”
Starting
Number
4
Sum of
5 Numbers
4 + 2 + 6 + 6 +2 = 20
Sample recording sheet
Lesson 4 6
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