Multiplication Facts
Survey
Objective To guide children as they determine which
multiplication facts they still need to learn.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Identify square products. [Operations and Computation Goal 3]
• Describe patterns in factors and products. [Patterns, Functions, and Algebra Goal 1]
• Describe and apply the turn-around rule
(Commutative Property of Multiplication) to
generate multiplication facts. [Patterns, Functions, and Algebra Goal 4]
Key Activities
Children use a Multiplication/Division Facts
Table to identify the facts they know and the
facts they still need to learn. They take a
timed multiplication facts survey.
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Practicing Multiplication/Division
Facts with Fact Triangles
×, ÷ Fact Triangles
Children practice multiplication
basic facts using the second set
of Fact Triangles.
Math Boxes 7 2
Math Journal 2, p. 160
Children practice and maintain skills
through Math Box problems.
Home Link 7 2
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Exploring Turn-Around Facts
Math Masters, p. 210
scissors
Children identify turn-around facts on the
Multiplication/Division Facts Table.
ENRICHMENT
Finding Patterns in the 9s Facts
1 sheet of paper
Children identify and describe patterns
in the products for 9s facts.
Math Masters, pp. 209 and 431–434
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message. [Operations and Computation Goal 6]
Materials
Math Journal 2, p. 159
Math Journal 1, Activity Sheets 3 and 4
Math Masters, p. 438A; pp. 438B and 438C
(optional)
transparency of Math Masters, p. 206 half-sheets of paper colored pencil or
crayon scissors Place-Value Books envelopes
Advance Preparation
For Part 1, make one copy of Math Masters, page 438A for every 2 children. Math Masters, pages 431–434 are Fact
Triangles. Make copies of the Fact Triangles to send home with Home Link 72.
Teacher’s Reference Manual, Grades 1–3 pp. 196–198
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Unit 7
Multiplication and Division
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Getting Started
Mental Math and
Reflexes
Home Link 7 1
Follow-Up
Math
Message
Have children practice quick recall of basic
multiplication facts. Suggestions:
Ask children to demonstrate
different paths for escaping the labyrinth
on a transparency of Home Link 7-1.
Discuss which of the paths is the
shortest.
Each of the following products is a
square product. Complete the number
sentences on a half-sheet of paper.
Examples:
2 × 10 20 3 × 10 30 6 × 10 60 8 × 10 80
2 × 2 4 3 × 3 9 4 × 4 16 5 × 5 25
4 × 9 36 6 × 7 42 7 × 8 56 6 × 9 54
3×3=9
Sample answer:
5 × 5 = 25
7 × 7 = 49
9 × 9 = 81
Draw an array to show one of the
square products.
1 Teaching the Lesson
Math Message
WHOLE-CLASS
DISCUSSION
Follow-Up
PROBLEM
PRO
PR
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
VIN
IIN
NG
Briefly review the answers. Have children make observations
about the factors and the products. Point out that all the factors
and their products are odd numbers. Make a chart (see below) on
the board to record examples of factors and their products. Ask:
●
If both factors are odd numbers, is the product odd or even? odd
●
What is the result if both factors are even numbers? even
●
What is the result if one factor is even and the other odd? even
Products for even and odd factors
Ongoing Assessment:
Recognizing Student Achievement
Math
Message
Use the Math Message to assess children’s progress toward using arrays to
model multiplication. Children are making adequate progress if they are able to
draw an array to show one of the square products. Some children may be able
to draw an array for each of the square products and discuss their similarities.
[Operation and Computation Goal 6]
Lesson 7 2
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Student Page
Date
Identifying the Multiplication
Time
LESSON
Multiplication/Division Facts Table
72
×,÷
1
2
3
4
5
6
7
8
9
10
Facts to Be Learned
1
1
2
3
4
5
6
7
8
9
10
(Math Journal 2, p. 159)
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
By now, most children know the 1s, 2s, and 10s multiplication
facts. Most children should also know all of the facts on the first
set of Fact Triangles from Lesson 4-6. The purpose of the activity
on journal page 159 is to let children know that there are only a
few facts left to learn.
Ask children to use light-colored crayons or pencils to color all the
products above the square-number diagonal. Remind them that
the square-number diagonal divides the table into two parts:
Each product above the diagonal has a turn-around product
below the diagonal.
Math Journal 2, p. 159
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159
WHOLE-CLASS
ACTIVITY
2/12/10
10:14 AM
Next, children color the products for all remaining 1-facts, 2-facts,
and 10-facts. Finally, they shade the remaining products from the
first set of Fact Triangles, including those on the square-number
diagonal, even though they are pre-shaded. The pre-shading
indicates square products. The children’s shading indicates
products they already know.
Ask: How many products are left unshaded? 16 This shows that if
they know all the 1-, 2-, and 10-facts, all the facts from the first
set of Fact Triangles, and the turn-around rule, they need to learn
only 16 more facts. Have children examine the 16 products left
unshaded. Discuss patterns they notice with the
unshaded products.
NOTE To extend this activity
to include basic multiplication
facts through 12 × 12, go to
www.everydaymathonline.com.
Adjusting the Activity
Show children the 9s Facts-on-Fingers shortcut. Hold both hands open,
palms down. To multiply a number less than 10 by 9 (for example, 7 × 9), count
fingers, starting with the little finger of the left hand. If the factor is greater than 5,
continue counting on the right hand, starting with the thumb. Bend down the last
finger in your count. (For 7 × 9, the down finger is the right-hand index finger.)
The number of fingers to the left of the down finger represents the tens digit in
the product; the number of fingers to the right represents the ones digit (6 to the
left and 3 to the right).
Student Page
Date
Time
LESSON
×, ÷ Fact Triangles 3
36
9
6
×,
16
÷
×,
÷
45
72
6 tens
3 ones
6
5
×, ÷
8
9
4
3
8
2
×, ÷
×,
÷
×,
÷
4
9
÷
×,
÷
×,
27
18
24
3
32
36
8
40
7×9
The last finger in the count bends to separate the 10s and the 1s in the answer.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
9
2
×, ÷
5
8
Math Journal 1, Activity Sheet 3
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Unit 7 Multiplication and Division
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Teaching Aid Master
Administering a Facts Survey
INDEPENDENT
ACTIVITY
Name
LESSON
72
Date
Multiplication Facts Survey 1
(Math Masters, pp. 438A–438C)
6×6=
8×5=
Explain to children that they will find out for themselves how
many of the 16 facts they already know and how many they have
yet to learn.
Distribute the survey on Math Masters, page 438A. At your signal,
children have 90 seconds (approximately 5 seconds per problem) to
complete as many problems as possible. Adjust the amount of time
as you see fit, but remember that children should not be given
enough time to figure out the answers. The point is to know the
answers from memory.
8×8=
6×8=
4×8=
9×5=
7×8=
4×9=
72
6×6=
Once the surveys are corrected, consider having children write
the facts they still need to learn on the Notes page at the back of
Math Journal 2. They will be able to access these facts quickly for
continued practice.
4×9=
INDEPENDENT
ACTIVITY
(Math Journal 1, Activity Sheets 3 and 4)
8×8=
6×8=
4×8=
9×5=
7×8=
9×7=
9×9=
8×3=
7×7=
9×6=
9×8=
27
42
63
81
24
49
54
72
Time
36
40
64
48
32
45
56
36
9×3=
7×6=
9×7=
9×9=
8×3=
7×7=
9×6=
9×8=
27
42
63
81
24
49
54
72
Math Masters, p. 438A
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NOTE Have children write their initials on the
back of each Fact Triangle in case they
misplace them.
NOTE For additional Fact
Triangles for facts through
12 × 12, go to
www.everydaymathonline.com.
After children have cut out the Fact Triangles on the Activity
Sheet card stock pages, review how to use Fact Triangles to
generate fact families and to practice the multiplication and
division facts.
Teaching Aid Master
Name
Remind children that they need to learn the multiplication
and division facts so they can solve multiplication and division
problems with larger numbers. Provide children frequent
opportunities to practice their facts with the Fact Triangles. The
year-end goal for third grade is to demonstrate automaticity with
facts through 10 × 10.
7×6=
Multiplication Facts Survey 1
8×5=
Cutting Out Fact Triangles
9×3=
Date
Decide how you would like to have the surveys corrected. Children
may correct their own or you may correct them yourself. Note that
the reason for administering the survey is to help children to
identify the facts they still need to learn; it is not to give a grade.
Plan to assess children’s progress on the Facts Survey once every
couple of months. Math Masters, pages 438B and 438C are
alternate versions of the same 16 facts.
36
40
64
48
32
45
56
36
Name
LESSON
Time
LESSON
72
Date
Multiplication Facts Survey 2
8×8=
9×7=
9×9=
8×3=
9×5=
7×8=
7×6=
4×9=
64
63
81
24
45
56
42
36
Name
LESSON
72
Time
8×5=
6×8=
4×8=
6×6=
7×7=
9×3=
9×6=
9×8=
40
48
32
36
49
27
54
72
Date
Time
Multiplication Facts Survey 2
8×8=
9×7=
9×9=
8×3=
9×5=
7×8=
7×6=
4×9=
64
63
81
24
45
56
42
36
8×5=
6×8=
4×8=
6×6=
7×7=
9×3=
9×6=
9×8=
40
48
32
36
49
27
54
72
Math Masters, p. 438B
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Lesson 7 2
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Teaching Aid Master
Name
Date
Time
2 Ongoing Learning & Practice
Multiplication Facts Survey 3
LESSON
72
4×8=
9×7=
p
6×8=
g
8×5=
py g
9×9=
9×6=
7×8=
4×9=
32
63
48
40
81
54
56
36
8×3=
6×6=
8×8=
9×3=
7×7=
9×8=
7×6=
9×5=
Name
24
36
64
27
49
72
42
45
Date
Practicing Multiplication/Division
Facts with Fact Triangles
Partners practice basic facts using their Fact Triangles. Children
keep track of the facts they miss and direct their partners to focus
on those facts during a second round. Encourage children to store
their Fact Triangles in an envelope when they are not using them.
Time
Multiplication Facts Survey 3
LESSON
72
4×8=
p
9×7=
g
6×8=
py g
8×5=
9×9=
9×6=
7×8=
4×9=
32
63
48
40
81
54
56
36
8×3=
6×6=
8×8=
9×3=
7×7=
9×8=
7×6=
9×5=
PARTNER
ACTIVITY
24
36
64
27
49
72
42
45
Math Boxes 7 2
(Math Journal 2, p. 160)
Mixed Practice The Math Boxes in this lesson are paired
with the Math Boxes from Lesson 7-4. The skill in
Problem 6 previews Unit 8 content.
Math Masters, p. 438C
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INDEPENDENT
ACTIVITY
3/16/11 12:34 PM
Home Link 7 2
INDEPENDENT
ACTIVITY
(Math Masters, pp. 209 and 431–434)
Home Connection Children share with someone at home
their progress with the multiplication facts. Send home
Math Masters, pages 431–434 (which are the same Fact
Triangles as Activity Sheets 3 and 4) so children can practice
multiplication facts.
Student Page
Date
72
1.
3 Differentiation Options
Time
LESSON
Math Boxes
2.
Draw the lines of symmetry.
Draw a trapezoid. Then draw a line
segment that intersects the two
parallel sides.
READINESS
Sample answer:
There are
2
Solve.
99 109
4.
Unit
150
1,300 = 800 + 500
1,700 − 900 = 800
15,000 − 6,000 = 9,000
600 = 1,100 − 500
90 + 60 =
378
109
389
To provide experience with turn-around facts, have children
compare two halves of the Multiplication/Division Facts Table.
They cut out the Multiplication/Division Facts Table on Math
Masters, page 210 along the dotted lines and fold it diagonally
from right to left along the blank squares. Notice that equal
factors and products fold onto themselves. Ask children why this
happens. The same factors are used in order along the top row as
are used down the first column. The products of the turn-around
facts are the same.
Fill in the circle for the best answer.
A. trapezoid
B. kite
C. hexagon
Complete the number-grid puzzles.
98
(Math Masters, p. 210)
I have 3 vertices. All my sides are
different lengths. I have one right
angle. What am I?
D. right triangle
5.
100
5–15 Min
Turn-Around Facts
122 123
3.
Exploring
lines of symmetry.
SMALL-GROUP
ACTIVITY
6.
103 107
109
1
Shade _
3 of the rectangle.
Sample answer:
380
400
7 8
22 23
Math Journal 2, p. 160
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Unit 7 Multiplication and Division
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Home Link Master
Name
Have children find a few turn-around facts on the table. Next, have
children fill in the blank boxes along the diagonal fold line and
share their strategies. Ask children why these numbers are not
mirrored like the others. Both factors are the same number; they
are square products; the turn-around fact is exactly the same.
Date
72
Family
Note
Listen to your child explain what factors and products are before he or she writes the answers
in the table. Then listen as your child tells you what he or she knows about multiplying by 1,
multiplying by 0, and multiplying numbers that result in square products. Fact Triangles for
the remaining multiplication/division facts are included with this Home Link.
Please return this Home Link to school tomorrow.
1. Explain to someone at home what factors
and products are. Find the missing
products and factors in the table.
ENRICHMENT
Finding Patterns in the
SMALL-GROUP
ACTIVITY
●
The digits in the tens place (first column) of the products
column are in order starting at 0, 1, 2, ... 9 and repeat as the
factors get larger.
●
The digits in the ones place (second column) of the products
column are in backwards order starting at 9, 8, 7, ... 0 and
repeat as the factors get larger.
●
The sum of the digits of the products equals 9. (3 × 9 = 27,
2 + 7 = 9; 11 × 9 = 99, 9 + 9 = 18, 1 + 8 = 9)
●
For 1 × 9 through 9 × 9, the product of the first factor
multiplied by 10, minus that factor is the product of the
first factor multiplied by 9. For example, (4 × 10) - 4 = 36
and 4 × 9 = 36.
●
For 1 × 9 through 9 × 9, digits in the product are predictable.
The first factor minus 1 is the first digit in the product. The
second digit of the product is 9 minus the first digit in the
product. For example, 5 × 9: first digit of product is 4;
5 - 1 = 4. The second digit of product is 5; 9 - 4 = 5.
Thus, 5 × 9 = 45.
Have children describe the patterns they see using words
like factor, product, more, less, multiplied by, larger, smaller,
and so on.
Factor
3
5
15
7
2
14
40
64
when you multiply by 1.
The product is the same
as the other factor.
4
10
8
8
Product
9
5
45
864
1
864
when you multiply by 0.
10
10
100
The product is always 0.
0
999
00
1
48
48
243
0
0
3. Write what you know about the products
9s Facts
Possible 9s facts patterns:
Factor
2. Write what you know about the products
15–30 Min
4. Write what you know about facts with
square products.
The factors are always the same number.
g
Practice
Write these problems on the back of this page. Make a ballpark estimate for
each. Solve. Show your work.
5.
y g
To apply children’s understanding of patterns, have them
identify and describe patterns they see in the products
for 9s facts. First, children write the 9s facts on paper in
a column and look for patterns among the factors and products.
Then, they write a description of the patterns they find. Encourage
children to test their patterns by continuing to multiply 2-digit
numbers by 9. Consider making a class book of the
children’s work.
Time
Factors and Products
HOME LINK
6.
7,201
+6,988
Unit
3,623
- 457
3,166
14,189
ballpark estimate
ballpark estimate
14,000
3,100
Math Masters, p. 209
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Teaching Master
Name
Date
Time
Turn-Around
Facts
Page Title
LESSON
72
ⴛ,ⴜ
1
1
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
6
8
10
12
14
16
18
20
2
2
3
3
6
4
4
8
12
5
5
10
15
20
6
6
12
18
24
30
7
7
14
21
28
35
42
8
8
16
24
32
40
48
56
9
9
18
27
36
45
54
63
72
10
10
20
30
40
50
60
70
80
12
15
18
21
24
27
30
20
24
28
32
36
40
30
35
40
45
50
42
48
54
60
56
63
70
72
80
90
90
Math Masters, p. 210
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Name
LESSON
72
Copyright © Wright Group/McGraw-Hill
Date
Multiplication Facts Survey 1
6×6=
9×3=
8×5=
7×6=
8×8=
9×7=
6×8=
9×9=
4×8=
8×3=
9×5=
7×7=
7×8=
9×6=
4×9=
9×8=
Name
LESSON
72
Copyright © Wright Group/McGraw-Hill
Time
Date
Time
Multiplication Facts Survey 1
6×6=
9×3=
8×5=
7×6=
8×8=
9×7=
6×8=
9×9=
4×8=
8×3=
9×5=
7×7=
7×8=
9×6=
4×9=
9×8=
438A
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Name
LESSON
72
Date
Multiplication Facts Survey 2
8×5=
9×7=
6×8=
9×9=
4×8=
8×3=
6×6=
9×5=
7×7=
7×8=
9×3=
7×6=
9×6=
4×9=
9×8=
72
Date
Copyright © Wright Group/McGraw-Hill
8×8=
Name
LESSON
Time
Time
Multiplication Facts Survey 2
8×5=
9×7=
6×8=
9×9=
4×8=
8×3=
6×6=
9×5=
7×7=
7×8=
9×3=
7×6=
9×6=
4×9=
9×8=
Copyright © Wright Group/McGraw-Hill
8×8=
438B
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3/16/11 12:34 PM
Name
LESSON
72
Copyright © Wright Group/McGraw-Hill
Date
Multiplication Facts Survey 3
4×8=
8×3=
9×7=
6×6=
6×8=
8×8=
8×5=
9×3=
9×9=
7×7=
9×6=
9×8=
7×8=
7×6=
4×9=
9×5=
Name
LESSON
72
Copyright © Wright Group/McGraw-Hill
Time
Date
Time
Multiplication Facts Survey 3
4×8=
8×3=
9×7=
6×6=
6×8=
8×8=
8×5=
9×3=
9×9=
7×7=
9×6=
9×8=
7×8=
7×6=
4×9=
9×5=
438C
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