Multiplication Fact
Power and Shortcuts
Objectives To discuss multiplication facts and the importance
of
o fact power; and to review fact shortcuts.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Practice multiplication facts. [Operations and Computation Goal 3]
• Identify patterns in skip counting by 2s,
5s, and 10s. [Patterns, Functions, and Algebra Goal 1]
• Use arrays to represent turn-around
multiplication facts. [Patterns, Functions, and Algebra Goal 4]
• Use the Commutative Property of
Multiplication (the turn-around rule), the
Multiplicative Identity, and the Zero
Property of Multiplication to generate
multiplication facts. [Patterns, Functions, and Algebra Goal 4]
Key Activities
Children discuss multiplication facts and the
importance of fact power. They also review
multiplication shortcuts and play Beat the
Calculator (Multiplication).
Family
Letters
Assessment
Management
Ongoing Learning & Practice
Solving Multidigit Subtraction
Problems
Math Journal 1, p. 88
number grid (optional) base-10
blocks (optional)
Children solve multidigit subtraction
problems.
Math Boxes 4 5
Math Journal 1, p. 89
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 5. [Measurement and Reference Frames
Goal 2]
Home Link 4 5
Math Masters, p. 96
Children practice and maintain skills
through Home Link activities.
Key Vocabulary
factor product fact power turn-around
shortcut square numbers
Materials
Math Journal 1, p. 156
Student Reference Book, p. 279
Home Link 44
Math Masters, p. 95; p. 446 (optional)
transparency of Math Masters, p. 95
(optional) calculator slate per group of
3 children: calculator
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 pp. 195–198, 199
266
Unit 4
Multiplication and Division
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Building Facts on a Geoboard
Math Masters, p. 97
geoboard rubber bands
Children use an array model to find products
for basic facts.
ENRICHMENT
Creating Fact Shortcuts
paper
Children create and explain their own
fact shortcuts.
Mathematical Practices
SMP2, SMP4, SMP5, SMP6, SMP7, SMP8
Getting Started
Content Standards
3.OA.5, 3.OA.7, 3.OA.9, 3.NBT.2
Mental Math and Reflexes
Math Message
Children count from 1 to 30, clapping at the intervals
described below.
7 × 4 = 28 is a multiplication fact. Write 5 other
multiplication facts.
every 5th number 1, 2, 3, 4, 5 (clap), 6, 7, 8, 9, 10 (clap),
11, 12, 13, 14, 15 (clap), and so on to 30
every 3rd number 1, 2, 3 (clap), 4, 5, 6 (clap), 7, 8, 9
(clap), and so on to 30
every 4th number 1, 2, 3, 4 (clap), 5, 6, 7, 8 (clap), 9, 10,
11, 12 (clap), and so on to 30
Home Link 4 4 Follow-Up
Have partners describe to each other how they
solved one of the problems.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
ELL
Multiplication facts are products of two 1-digit numbers. Have
children call out multiplication facts, with or without the products,
while you write them on the board. Use both horizontal formats
(with the product to the left and the right) and vertical formats.
Tell children that the symbols * and • are sometimes used to show
multiplication.
The numbers being multiplied are factors. The result of
multiplication is the product. To support English language
learners, label some of the facts written on the board with the
words factor and product. Encourage children to use this
vocabulary, but do not insist on it.
Reviewing the Importance
2×3=6
18 = 9 * 2
5 • 4 = 20
3
×8
24
Different multiplication formats
WHOLE-CLASS
DISCUSSION
of Fact Power
Ask children to name some good and some bad habits. A habit is
an automatic behavior that comes from doing something over and
over again. Developing basic number-fact reflexes is developing a
good habit. In Everyday Mathematics, fact habits are referred to as
fact power. Stress to children that they need to learn the
multiplication and division facts so that they can solve multidigit
multiplication and division problems.
Reviewing Shortcuts for
WHOLE-CLASS
ACTIVITY
Multiplication Facts
(Math Masters, p. 95)
Algebraic Thinking Tell children they will review shortcuts that
will help them develop a good habit—knowing the multiplication
facts by heart.
Lesson 4 5
267
The Turn-around Shortcut
Illustrate the turn-around shortcut (Commutative Property
of Multiplication) by writing several fact phrases for small
numbers, such as 4 × 3, on the board. Pair each fact with its
turn around, or commutative partner—4 × 3 and 3 × 4. The
order of the factors does not change the product, so if you know
3 × 4 = 12, you also know 4 × 3 = 12.
Include square numbers, such as 3 × 3 and 5 × 5, and point
out that the turn-around fact for a square number is the same
as the original fact.
4 × 3 = 12 and 3 × 4 = 12
Then have children use Math Masters, page 95 to make arrays
for the facts you suggest.
Children write number models under each array.
NOTE It is not expected that children
use formal terms for the properties of
multiplication. It is important for them to
know, however, that order does not matter
when multiplying factors, that multiplying any
number by 1 results in a product that is that
number, and that multiplying any number by
0 results in a product of 0.
The arrays that children draw represent the multiplication
turn-around facts, similar in principle to the addition turn-around
facts. You may wish to use an overhead of the master to model
building arrays.
Ask: What number models made square arrays? Sample
answers: 3 × 3 = 9 and 5 × 5 = 25
Ask: What is the pattern of these number models? The factors
are the same.
Ask: How can you know if a number model will make a square
array? If the number model has two identical factors, it will
make a square array.
The Multiplication by 1 Shortcut
If 1 is multiplied by any number, or any number is multiplied by
1, the product is that number (Multiplicative Identity).
Tell a few times 1 and 1 times number stories, and have
children tell some. For example:
Teaching Master
Name
LESSON
45
䉬
Date
Time
4 3 Grid
●
There are 8 flowers in a pot. You have 1 pot. How many flowers
do you have? 1 × 8 = 8; 8 × 1 = 8. You have 8 flowers.
●
There is 1 ring in each box. You have 6 boxes. How many rings
do you have? 1 × 6 = 6; 6 × 1 = 6. You have 6 rings.
Adjusting the Activity
ELL
As you review the number stories, record the number models on the
board so that children will be able to see the patterns for the shortcut.
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
The Multiplication by 0 Shortcut
If 0 is multiplied by any number, or any number is multiplied by
0, the product is 0 (Zero Property of Multiplication).
Tell a few times 0 and 0 times number stories, and have children
tell some, including some with larger numbers. For example:
Math Masters, p. 95
268
Unit 4 Multiplication and Division
●
There are 10 cookies in a box. You have 0 boxes. How many
cookies do you have? 0 × 10 = 0; 10 × 0 = 0. You have
0 cookies.
Student Page
●
There are 0 cookies per box. You have 10 boxes. How many
cookies do you have? 10 × 0 = 0; 0 × 10 = 0. You have
0 cookies.
The Familiar Facts Shortcut
Tell children that the 2s, 5s, and 10s facts are simply counts by
2s, 5s, and 10s—remind them of the Mental Math and Reflexes
exercise. Have the class recite in unison the 2s, 5s, and 10s facts
in order. Point out the following patterns:
The products of 2s and 10s facts are always even numbers.
(The products of 4s, 6s, and 8s facts are also always even.)
The products of 5s facts always end in 0 or 5.
Games
Games
Beat the Calculator (Multiplication)
Materials 䊐 number cards 1–10 (4 of each)
Beat 䊐the
Calculator (Multiplication)
1 calculator
Materials
Players
3 䊐 number cards 1–10 (4 of each)
䊐 1 calculator
Skill
Mental multiplication skills
Players
3
Object of the game To multiply numbers without a
Skill faster
Mental
calculator
thanmultiplication
a player usingskills
one.
Object of the game To multiply numbers without a
Directions
calculator faster than a player using one.
1. One player is the “Caller.” A second player is the
Directions
“Calculator.”
The third player is the “Brain.”
1. One the
player
is the
A second
player is
the
2. Shuffle
cards
and“Caller.”
place them
number-side
down
“Calculator.”
The third player is the “Brain.”
on the
table.
2. Shuffle
cards
and place
number-side
down
3. The
Caller the
draws
2 cards
from them
the number
deck and
onfor
thethe
table.
asks
product of the numbers.
3. The
Caller draws
cards
from the
deck and
4. The
Calculator
solves2the
problem
withnumber
a calculator.
forsolves
the product
of the
numbers. The Caller
Theasks
Brain
it without
a calculator.
decides
who got thesolves
answer
4. The Calculator
thefirst.
problem with a calculator.
Brain
solves it
a calculator.
The
Caller
5. TheThe
Caller
continues
to without
draw 2 cards
at a time
from
the
decides
who
gotask
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answer
first. of the numbers.
number
deck
and
the product
5. The Caller
draw
2 cards
6. Players
trade continues
roles everyto10
turns
or so.at a time from the
number deck and ask for the product of the numbers.
The products of 10s facts always end in 0.
Additional Strategies with Familiar Facts
4 times any number can always be decomposed into 2 equal
addends. 4 × 7 can be thought of as 2 × 7 = 14 and 2 × 7 =
14. To find the product of 4 × 7, the two products can be added
together. 14 + 14 = 28, so 4 × 7 = 28.
6. Players
trade roles
every
turns
so.Caller
The Caller
draws
a 1010
and
a 7. or
The
says, “10 times 7.” The Brain and the Calculator
10
each solve
problem.
Caller
decides
got
7
Thethe
Caller
drawsThe
a 10
and a
7. Thewho
Caller
thesays,
answer
“10first.
times 7.” The Brain and the Calculator
10
each solve the problem. The Caller decides who got
the answer first
7
Student Reference Book, p. 279
Break one factor into easy addends. For example, 6 × 7 can be
thought of as 6 × 5 = 30 and 6 × 2 = 12. The two products,
30 and 12, can be added together to find the product of 6 × 7.
30 + 12 = 42, so 6 × 7 = 42.
Taking the Fact
Adjusting the Activity
WHOLE-CLASS
ACTIVITY
Power Challenge
Divide the class into two groups. Pose a multiplication fact problem.
Children in one group use calculators to find the product. Children
in the other group find the product without using calculators.
Use the minute hand on the clock
face to practice the 5s facts. When the
minute hand is on the 8, the time is 40
minutes past the hour: 5 × 8 = 40. When
the minute hand is on the 2, the time is 10
minutes past the hour: 2 × 5 = 10. Pose
other clock facts.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Repeat the activity with other multiplication facts. Mix easy and
hard facts, so that children in each group can get the product first
some of the time. Children are generally surprised to find that fact
power can indeed beat the calculator.
NOTE This activity makes the point that for many easy problems, mental
calculation is quicker than using a calculator. Over time, children should develop
good judgment about when to estimate and when to use calculators, calculate
mentally, or use paper and pencil.
Playing Beat the Calculator
SMALL-GROUP
ACTIVITY
(Multiplication)
(Student Reference Book, p. 279;
Math Journal 1, p. 156; Math Masters, p. 446)
Have children examine the Fact Power Table on journal page 156.
The unshaded facts include the 0s, 1s, and 10s facts as well as
the facts from Activity Sheets 1 and 2. The shaded facts are from
Activity Sheets 3 and 4.
Lesson 4 5
269
Student Page
Date
Time
LESSON
Subtraction Strategies
4 5
䉬
Make a ballpark estimate. Write a number model to
show your estimate. Choose at least two problems to
solve using the counting-up method. You may choose
any method you wish to solve the other problems.
63 192
Estimates vary.
1. Ballpark estimate:
2.
3. Ballpark estimate:
Ballpark estimate:
226
134
93
47
92
46
487
129
Explain to children that they will use the Fact Power Table during
Beat the Calculator games to record the facts they get correct
while playing the role of the Brain. When children have earned
3 check marks for a fact, they write the product in the table. The
page will become a cumulative record of their progress toward
multiplication fact power.
Divide the class into groups of three to play Beat the Calculator.
If necessary, review the directions on page 279 in the Student
Reference Book.
358
Have children follow the steps below to record their wins on their
Fact Power Table.
5. Ballpark estimate:
4. Ballpark estimate:
6. Ballpark estimate:
361
248
724
396
515
367
113
328
148
1. The Caller selects a problem at random from the Fact Power
Table on journal page 156. 2. The Brain finds the product without a calculator. The
Calculator finds the product using a calculator.
3. The Caller determines whether the Brain or the Calculator got
the product first. Math Journal 1, p. 88
4. If the Brain beats the Calculator and announces the correct
product, the Caller makes a check mark in the box for that fact
on the Brain’s Fact Power Table. Once a fact has three check
marks, the Brain writes the product in that box to indicate
that the fact has been mastered. 5. You might wish to pass out Beat the Calculator triangles (Math
Masters, page 446) to assist with assigning roles to players.
NOTE Playing this game frequently will help develop children’s automaticity with
multiplication facts. Remind children to use their copy of the Fact Power Table on
journal page 156 as a record sheet during Beat the Calculator games.
Student Page
Date
Math Boxes
4 5
䉬
1.
2 Ongoing Learning & Practice
Time
LESSON
Use the dots to show a 3 6
array.
2.
Game Points
Maximum number
of points scored:
30
25
Minimum number
of points scored:
What is the number model?
3
6
18
10
5
0
A
Solve. Fill in the oval for the best
answer.
C
D
79
86 87
4. Fill in the number grid.
2,957
2,967
10 chairs
12 chairs
24 chairs
20 chairs
2,976
2,986
2,996
3,006
66 67
Draw a 2 4 rectangle.
6.
Area:
8
2
square units
4
8
Unit 4 Multiplication and Division
(Math Journal 1, p. 88)
$3.45
$0.34 or $0.09? $0.34
$14.50 or $14.55? $14.55
$30.15 or $31.05? $31.05
Math Journal 1, p. 89
Problems
Math Boxes 4 5
Which is more?
154–156
INDEPENDENT
ACTIVITY
7–9
$3.45 or $3.09?
Number model:
Solving Multidigit Subtraction
Children use counting-up, trade-first, or other methods of their
choice to solve multidigit subtraction problems. Encourage
children to use the number grid, base-10 blocks, or other
manipulatives as needed.
2,946
How many chairs in all?
270
B
Players
20 points
6 chairs in each row
5.
15
Range of points scored:
4 rows of chairs
夹
20
5 points
64 65
3.
Points
25 points
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 89)
36
89
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 4-7. The skill in Problem 6
previews Unit 5 content.
Home Link Master
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 5
Use Math Boxes, Problem 5 to assess children’s progress toward finding the
area of rectangular shapes. Children are making adequate progress if they are
able to draw the rectangle and find the area. Some children might be able to
write the number model for the area.
[Measurement and Reference Frames Goal 2]
Name
Date
HOME LINK
Multiplication-Fact Shortcuts
45
䉬
Family
Note
Your child is learning the basic multiplication facts. Listen to your child explain multiplicationfact shortcuts as he or she works the problems. Review some 1s, 2s, 5s, and 10s
multiplication facts (facts like 1 3 ?, ? 2 4, 5 5 ?, and 10 4 ?).
Tell someone at home about multiplication-fact shortcuts.
The turn-around rule: 3 4 12 helps me know 4 3 12.
10
1. 2 5 15
10
and 5 2 15
5 3 and
20
3. 10 2 56
Please return this Home Link to school tomorrow.
2.
Home Link 4 5
Time
35
20
and 2 10 If 1 is multiplied by any number, the product is that number.
The same is true if any number is multiplied by 1.
INDEPENDENT
ACTIVITY
(Math Masters, p. 96)
9
4.
90
365
6. 365 1 Home Connection Children tell someone at home about
the multiplication fact shortcuts for turn-around facts and
for the 0s, 1s, 2s, 5s, and 10s facts.
9
1 9 and
5. 1 90 91
and 90 1 and 1 365 90
365
If 0 is multiplied by any number, the product is 0.
The same is true if any number is multiplied by 0.
0
0
7. 0 12 8. 99 0 0
9.
0
0
and 12 0 and 0 99 9,365 0 and
0
0 9,365
Think about counting by 2s, 5s, and 10s.
10.
10
2
5
4
11.
20
3 Differentiation Options
READINESS
Building Facts
20
12.
9
2
13.
18
2
7
14.
14
5
3
15.
15
10
5
50
Math Masters, p. 96
INDEPENDENT
ACTIVITY
5–15 Min
on a Geoboard
(Math Masters, p. 97)
To provide experience with multiplication facts using a
concrete model, have children use rubber bands on a
geoboard to find products for basic facts. Children record
their work on Math Masters, page 97. When they have finished,
briefly review which of the facts might be easiest to remember.
Teaching Master
Name
ENRICHMENT
Creating Fact
PARTNER
ACTIVITY
15–30 Min
Shortcuts
To further explore fact shortcuts, have children write
their own fact shortcut for facts they already know. They
explain their shortcut on paper and include an example.
Possible shortcuts:
If I know 2 times a number, adding one more of that number
would be 3 times the number.
LESSON
45
䉬
Date
Time
Building Facts on a Geoboard
For each problem:
Example
Use a rubber band to make each
rectangle on a geoboard.
24
8
pins
Draw the rectangle onto this record
sheet.
Record the number of pins inside the
rubber band as the answer to the
problem.
1. 3 3 9
pins
2. 4 3 12
pins
3. 3 2 6
pins
4. 4 4 16
pins
If I know 2 times a number, doubling the answer would be 4
times the number.
If I know 10 times a number, I can subtract the number once
and have 9 times the number.
The children’s shortcuts make a wonderful classroom resource.
Consider binding them into a class book.
Make up problems of your own.
5.
pins
Answers
vary.
6.
pins
Answers
vary.
97
Math Masters, p. 97
Lesson 4 5
271