Multiplication Facts
Objectives To review strategies for solving multiplication facts;
to
t help students maintain automaticity with multiplication facts;
and to introduce prime and composite numbers.
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EM Facts
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Teaching the Lesson
Key Concepts and Skills
• Find factors and multiples of numbers. [Number and Numeration Goal 3]
• Identify prime and composite numbers. [Number and Numeration Goal 3]
• Identify square numbers. [Number and Numeration Goal 4]
• Solve multiplication facts. [Operations and Computation Goal 3]
• Identify and use patterns in the
Multiplication/Division Facts Table. [Patterns, Functions, and Algebra Goal 1]
Key Activities
Students cut out Multiplication/Division Fact
Triangles. They discuss the Multiplication/
Division Facts Table, symbols, and
vocabulary for multiplication. Students
identify prime and composite numbers. They
use Fact Triangles to maintain automaticity
with multiplication facts.
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Student Reference Book, p. 254
Math Masters, p. 489
deck of number cards (the Everything
Math Deck, if available)
Students practice representing
numbers in different ways.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Masters, page 489. Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Making Rectangular Arrays
Math Masters, p. 76
centimeter cubes 4 each of number cards
1–10 (from the Everything Math Deck, if
available)
Students practice multiplication facts using
a concrete model.
EXTRA PRACTICE
[Number and Numeration Goal 4]
Playing Buzz and Bizz-Buzz
Math Boxes 3 2
Student Reference Book, p. 234
Students practice naming multiples.
Math Journal 1, p. 57
Students practice and maintain skills
through Math Box problems.
Study Link 3 2
Math Masters, p. 75
Students practice and maintain skills
through Study Link activities.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 140
Students add the term square numbers
to their Math Word Banks.
Key Vocabulary
multiplication facts factors products factor pair multiples square numbers turn-around facts prime number composite number
Materials
Math Journal 1, inside front cover; p. 56;
Activity Sheets 1–4 Student Reference
Book, pp. 8, 178A, and 178B Study Link 31 transparencies of Math Masters, pp. 408
and 409 (optional) paper clips envelopes
or resealable plastic bags scissors calculator counters (optional)
Advance Preparation
For Part 1, have plastic bags or envelopes available for storing the Fact Triangles. Think about how to pair
students for this activity so they will be at similar skill levels.
Teacher’s Reference Manual, Grades 4–6 pp. 16, 79, 80, 267–269
Lesson 3 2
163
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP7, SMP8
Content Standards
Getting Started
4.OA.1, 4.OA.4, 4.OA.5
Mental Math and Reflexes
Math Message
In preparation for discussing multiples, pose calculator
skip-counting problems, starting with 0. Suggestions:
Cut apart the Multiplication/Division Fact Triangles
on Activity Sheets 1–4 at the back of your journal.
Write your initials on the back of each one.
20s 0, 20, 40, 60, 80, 100, ...
50s 0, 50, 100, 150, 200, 250, ...
6s 0, 6, 12, 18, 24, 30, ...
8s 0, 8, 16, 24, 32, 40, ...
Back by 4s 0, -4, -8, -12, -16, -20, ...
Back by 7s 0, -7, -14, -21, -28, -35, ...
Put the Fact Triangles and two paper clips into a plastic bag or
envelope.
Study Link 3 1 Follow-Up
Have partners discuss the pattern in Problem 1 and
explain why the numbers will always change from
odd to even or even to odd when moving from the in
column to the out column.
1 Teaching the Lesson
NOTE For Multiplication/
Division Fact Triangles and
a Facts Table with facts
through 12 º 12, see
www.everydaymathonline.com.
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Tell the class they will use Fact Triangles to practice
multiplication facts and another tool, the Multiplication/Division
Facts Table, to discuss the terms factor, product, and multiple.
Reviewing the Multiplication/
Division Facts Table
WHOLE-CLASS
DISCUSSION
ELL
(Math Journal 1, inside front cover; Math Masters, p. 408)
square
numbers
∗,/
1
1
2
3
4
5
6
7
8
4
20
9
4
30
16
5
product
24
60
36
7
70
49
8
64
9
10
20
30
40
50
40
50
25
6
10
10
10
3
multiples
of 10
9
1
2
factor
multiples
of 10
factor
60
70
80
80
81
90
90
100
Multiplication/Division Facts Table from the inside front
cover of Math Journal 1 and Math Masters, page 408
164
Introducing the Symbols º and /
Ask students to look at the inside front cover of Math Journal 1.
Display an overhead transparency of Math Masters, page 408.
Remind students of the following:
The table shows the multiplication facts.
The 0s facts have been omitted to avoid confusion about
division by 0 (which is not possible).
The 10s facts are included.
Point out the ∗ and / symbols in the upper left-hand corner
of the table. Explain that in Grades 4, 5, and 6 of Everyday
Mathematics, an asterisk (∗) is usually used to indicate
multiplication. A slash
_ (/) is often used to indicate division,
but the ÷ and the RR symbols are also used.
NOTE The symbols ∗ and / are used for multiplication and division on computer
keyboards. The asterisk helps avoid confusion between the × symbol and the
variable x in algebra. Using the _
slash for division clearly relates division to
1
fractions. 1 / 2, _2 , 1 ÷ 2, and 2 12 all represent the same number.
Unit 3 Multiplication and Division; Number Sentences and Algebra
Reviewing the Meaning of Factors, Products,
and Multiples
Remind students that the numbers in the shaded row and
shaded column in the table are called factors, and the rest of the
numbers are called products. For example, in 4 ∗ 6 = 24, 4 and 6
are factors of 24, and 24 is the product of 4 and 6. 4 and 6 are a
factor pair of 24. A number may have more than one factor pair.
For example, the factor pairs for 24 are 1 and 24, 2 and 12, 3 and
8, and 4 and 6. To support English language learners, label and
identify the factors and products on the transparency of Math
Masters, page 408 as students do so on the inside front cover of
Math Journal 1.
Adjusting
the Activity
Have students find common multiples of 2
and 3 or common multiples of 2, 3, and 5 and
organize them in Venn diagrams. For example:
2
4
6
3
8
10
12
15
14 16
18
Direct students to look across a row or down a column to find
the multiples of a number. The multiples of 10, for example,
are 10, 20, 30, 40, and so on. Point out that a whole number is a
multiple of each of its factors.
Multiples
of 2
9
Multiples
of 3
Multiples
of 2
Reviewing Square Numbers
Next point out the shaded products on the diagonal. Remind
students that these products are called square numbers. Each
square number is the product of a counting number multiplied by
itself. For example, 9 is a square number, because 3 ∗ 3 = 9.
Reviewing Turn-Around Facts
Point out that the products above the diagonal of square
numbers are “mirror images” of the products below the diagonal.
For example, 6 ∗ 3 and 3 ∗ 6 both equal 18. These are called
turn-around facts. If you know a fact, you also know its
turn-around fact. To support English language learners, ask:
Why do you think these facts are called turn-around facts?
ELL
2
4 8
14 16 22
26 28
10
6 12
20
18 24
30
5
3
25
21 27
15
Multiples
of 5
AUDITORY
9
Multiples
of 3
KINESTHETIC
TACTILE
VISUAL
Reviewing Other Multiplication Shortcuts
Ask students if they know any other multiplication shortcuts.
For example:
0 times any number equals 0.
1 times any number equals the number.
To find 2 times a number, double the number.
To find 10 times a number, write 0 after the number.
Factor Pairs of Prime
WHOLE-CLASS
ACTIVITY
Numbers
(Student Reference Book, p. 8; Math Journal 1, p. 56;
Math Masters, p. 409)
On the board, draw the Fact Triangle in the margin, or fill in the
numbers on a transparency of Math Masters, page 409.
Have students identify the product and the factors. Product: 2.
Factors: 1, 2. Point out that every Fact Triangle illustrates a factor
pair of the product. For example, the Fact Triangle in the margin
shows that 1 and 2 make up a factor pair of the product, 2.
•
2
∗, /
1
2
Lesson 3 2
165
Student Page
Date
Factor Pairs of Prime Numbers
32
1.
Factor Pairs
2
1 and 2
3
1 and 3
1 and 4; 2 and 2
1 and 5
4
5
6
7
8
9
10
11
12
3.
8
In the table below, list all the factor pairs of each number.
Number
2.
Then have students complete Problem 1 on journal page 56. They
may use their Fact Triangles or a Multiplication/Division Facts
Table. Ask students to name the numbers in the table that have
only one factor pair. 2, 3, 5, 7, and 11 Explain that there is a name
for numbers that have only one factor pair. Ask: Does anyone know
what these numbers are called? Prime numbers List the prime
numbers on the board along with their factor pairs:
Time
LESSON
1 and 6
2 and 3
Prime Number
1 and 7
1 and 8; 2 and 4
1 and 9; 3 and 3
1 and 10; 2 and 5
1 and 11
1 and 12; 2 and 6; 3 and 4
2
1 and 2
3
1 and 3
5
1 and 5
7
1 and 7
11
1 and 11
Name a number in the table above that is not a prime number. Explain how you
know it is not prime.
Sample answer: 12; it has three factor pairs: 1 and
12, 2 and 6, and 3 and 4. A prime number has only
one
factor pair.
Name at least three prime numbers that are not in the table above.
Factor Pair
Sample answers: 13, 17, 19
4.
Choose one of your answers from Problem 3. Explain how you know it is a
prime number.
Sample answer: 13 is a prime number because its
only factor pair is 1 and 13.
Math Journal 1, p. 56
EM3MJ1_G4_U03_53-77.indd 56
1/6/11 10:43 AM
Ask students if they notice anything about the factor pairs of
the prime numbers. If no one suggests it, point out that each
factor pair consists of 1 and the original number. Explain that a
counting number is a prime number if it has exactly two factors:
1 and itself.
Next, ask students to name the numbers that are not prime.
4, 6, 8, 9, 10, and 12 Tell students that these are called composite
numbers. A composite number is a counting number with
more than two factors. Composite numbers have at least two
factor pairs.
For more information about prime and composite numbers,
students can refer to Student Reference Book, page 8. Ask students
to complete journal page 56.
Reviewing the Models
WHOLE-CLASS
ACTIVITY
of Multiplication
(Student Reference Book, pp. 178A and 178B)
Tell students that thinking about what a multiplication fact
means can help them figure out facts they can’t remember. For
example, a student who could not remember the answer to 7 ∗ 6
could think about this fact in several ways:
Equal groups: How many objects are in 7 groups of 6?
Arrays or area: How many objects are in an array with 7 rows
and 6 objects in each row?
Multiplicative comparison: What number is 7 times as many as 6?
These interpretations are described on Student Reference Book,
pages 178A and 178B.
Suggest additional facts and have students record the
corresponding questions on their slates. For example:
●
166
8∗7
Unit 3 Multiplication and Division; Number Sentences and Algebra
●
9∗4
●
6∗9
Sorting Fact Triangles
PARTNER
ACTIVITY
(Math Journal 1, inside front cover; Math Masters, p. 409)
Ask students to count the Fact Triangles they stored—there
should be 36.
6
Draw a large Multiplication/Division Fact Triangle on the board,
or display a transparency of Math Masters, page 409, with
numbers inserted. Remind students that the numbers in the
bottom corners of the triangle are factors and that the number
under the dot is the product of the two factors. Demonstrate how
to use the Fact Triangle by covering the product.
7
“6 times 7 equals what number?” or
“What number is 6 times as many as 7?”
Divide the class into partnerships. As students practice their facts,
remind them to sort the Fact Triangles into two piles —“OK” and
“Try Again”—as they did with the +, - Fact Triangles in Unit 1.
Use this Fact Triangle session to screen the class to determine
which students are proficient with the basic multiplication facts.
Students with triangles in the “Try Again” pile will need
additional support. Games and Fact Triangles are available to
provide opportunities for students to practice these facts. See
the Teacher’s Reference Manual for ideas on establishing a game
routine in your classroom. Students identified in this initial
screening as needing additional support should participate in the
50-Facts Test routine throughout the year. See Lesson 3-3 for more
information.
ⴱ, Ⲑ
Adjusting
the Activity
ELL
Encourage the use of tools and strategies,
such as:
counters or pictures to illustrate facts,
calculators for skip counting to find
products, and
the Multiplication/Division Facts Table to
find products.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
2 Ongoing Learning & Practice
Playing Name That Number
PARTNER
ACTIVITY
(Student Reference Book, p. 254; Math Masters, p. 489)
Student Page
Date
Time
LESSON
Math Boxes
3 2
䉬
Students play Name That Number to practice representing
numbers in different ways. See Lesson 2-2 for additional
information.
1.
The numbers 28, 35, and 42 are all
multiples of __. Circle the best answer.
2.
Complete the “What’s My Rule?” table
and state the rule.
in
out
Rule:
⫹95
A
7
B
4
682
777
6
391
486
C
D
2
236
938
Ongoing Assessment:
Recognizing Student Achievement
Math Masters
Page 489
Use Math Masters, page 489 to assess students’ ability to use
numerical expressions involving one or more of the basic four arithmetic
operations to give equivalent names for whole numbers. Students are making
adequate progress if they are able to create numerical expressions to name the
target number for two rounds of play. Some students may write numerical
expressions that include parentheses or exponents.
[Number and Numeration Goal 4]
647
9
3.
Elements Found in Earth’s Crust
(percent by weight)
Is there more aluminum or silicon in Earth’s crust?
silicon
b.
What percentage of Earth’s crust is aluminum?
8%
c.
1,033
742
162–166
Earth is covered by a rocky outer layer called the
crust, which is made up of many elements.
a.
331
Iron, Calcium,
Sodium,
Potassium,
Others
17%
Aluminum
8%
Oxygen
47%
Silicon
28%
Which element makes up most of Earth’s crust?
oxygen
4.
Name as many line segments as you can
in the figure below.
A
B
C
5.
Put these numbers in order from smallest
to largest.
0.6 0.06 0.43 0.9
D
AB
៮៮៮, AC
៮៮៮, AD
៮៮៮, BC
៮៮៮, BD
៮៮៮, CD
៮៮៮
90
0.06
0.43
0.6
0.9
32 33
Math Journal 1, p. 57
Lesson 3 2
167
Study Link Master
Name
Date
32
䉬
1.
Math Boxes 3 2
Time
Multiplication Facts
STUDY LINK
16 20
Complete the Multiplication/Division Facts Table below.
º, /
1
2
3
4
5
6
(Math Journal 1, p. 57)
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
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 3-4. The skill in Problem 5
previews Unit 4 content.
Study Link 3 2
List all the factors of 36.
3.
List the factor pairs of 16.
1
Practice
53
6.
⫽ 91 ⫺ 38
388
7.
⫽ 630 ⫺ 242
8.
1,462 ⫺ 697 ⫽
INDEPENDENT
ACTIVITY
(Math Masters, p. 75)
1, 2, 3, 4, 6, 9, 12, 18, 36
and 16 , 2 and 8 , 4 and 4
4. Name the product of 8 and 7. 56
Sample answers:
8 , 16 , 20 , 24
5. Name four multiples of 4.
2.
INDEPENDENT
ACTIVITY
765
Home Connection Students complete a Multiplication/
Division Facts Table and name factors, products, and
multiples of numbers.
3 Differentiation Options
Math Masters, p. 75
READINESS
Making Rectangular Arrays
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 76)
NOTE For practice with
facts through 12 º 12, have
students use the Online Master at
www.everydaymathonline.com
in place of Study Link 32.
To provide experience with multiplication facts using a concrete
model, have students make rectangular arrays with centimeter
cubes and record a number model for each array.
EXTRA PRACTICE
Playing Buzz and Bizz-Buzz
Teaching Master
Name
Date
32
䉬
(Student Reference Book, p. 234)
Rectangular arrays can be used to model multiplication facts.
Follow these steps to build arrays with centimeter cubes.
2.
◆
Use one card for the number of rows in the array.
◆
Use the other card for the number of cubes in each row.
4
To practice naming multiples, have students play Buzz and
Bizz-Buzz. Before playing the game, remind students that a whole
number is a multiple of each of its factors.
ELL SUPPORT
Use centimeter cubes to build the array.
Example:
2
4
If
and
are turned
over, you can make either array:
3.
7
Place a deck of number cards (1⫺10) facedown on the table.
Turn over 2 cards.
2
1.
2 rows,
4 cubes per row
4 rows,
2 cubes per row
Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 140)
Record some of the arrays you made in the table below.
How many
rows?
4
How many cubes
in each row?
2
How many
cubes in all?
Number
model
8
4 º 2⫽8
To provide language support for multiplication, have students
use the Word Bank Template found on Differentiation Handbook,
page 140. Ask students to write the term square numbers, draw
pictures relating to the term, and write other related words. See
the Differentiation Handbook for more information.
Math Masters, p. 76
168
5–15 Min
Time
Rectangular Arrays
LESSON
SMALL-GROUP
ACTIVITY
Unit 3 Multiplication and Division; Number Sentences and Algebra