Transcript Chapter 4 Multiplication Concepts and Facts

Chapter 4
Multiplication Concepts and Facts
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4
Multiplication Concepts and Facts
Lesson 4-1
Multiplication as Repeated Addition
Lesson 4-2
Arrays and Multiplication
Lesson 4-3
Multiply by 2
Lesson 4-4
Multiply by 4
Lesson 4-5
Problem-Solving Skill: Extra or
Missing Information
Lesson 4-6
Multiply by 5
Lesson 4-7
Multiply by 10
Lesson 4-8
Problem-Solving Investigation:
Choose a Strategy
Lesson 4-9
Multiply by 0 and 1
4-1
Multiplication as Repeated Addition
Five-Minute Check (over Chapter 3)
Main Idea and Vocabulary
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
4-1
Multiplication as Repeated Addition
(over Chapter 3)
Use + or – to make the number sentence true.
75 = 250 – 50
125
A.
+
B.
–
4-1
Multiplication as Repeated Addition
(over Chapter 3)
Use + or – to make the number sentence true.
300 – 10 = 250
A.
+
B.
–
40
4-1
Multiplication as Repeated Addition
(over Chapter 3)
Use + or – to make the number sentence true.
562 – 42 > 512
A.
–
B.
+
30
4-1
Multiplication as Repeated Addition
(over Chapter 3)
Use + or – to make the number sentence true.
600
50 < 400 + 240
A.
+
B.
–
4-1
Multiplication as Repeated Addition
• I will relate multiplication and addition.
• multiply
• factor
• product
4-1
Multiplication as Repeated Addition
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
Standard 3MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to
explain mathematical reasoning.
4-1
Multiplication as Repeated Addition
For Alejo’s party, his mother made 7 cupcakes.
There were 3 walnuts on top of each cupcake. How
many walnuts were there in all?
Find how many are in 7 equal groups of 3.
4-1
Multiplication as Repeated Addition
One Way: Counters
There are 7 groups. There are 3 counters in
each group. This is a total of 21 counters.
4-1
Multiplication as Repeated Addition
Another Way: Repeated Addition
Write an addition sentence to show equal
groups.
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
Answer: So, 7 equal groups of 3 are 21. There were
21 walnuts in all.
4-1
Multiplication as Repeated Addition
Jamie made ants on a log for a snack. She had 6
pieces of celery and put 4 raisins on each piece.
How many raisins in all?
A. 24
B. 18
C. 10
D. 16
4-1
Multiplication as Repeated Addition
Mongo drew 6 pentagons. A pentagon has 5 sides.
How many sides did he draw?
Find how many are in 6 equal groups of 5.
4-1
Multiplication as Repeated Addition
One Way: Repeated Addition
5 + 5 + 5 + 5 + 5 + 5 = 30
4-1
Multiplication as Repeated Addition
Another Way: Multiplication Sentence
number of
of sides
number of
pentagons (groups)
6
factor
×
5
factor
Answer: So, there is a total of 30 sides.
total
=
30
product
4-1
Multiplication as Repeated Addition
Pam drew 5 octagons. An octagon has 8 sides.
How many sides did she draw?
A. 35 sides
B. 45 sides
C. 40 sides
D. 13 sides
4-2
Arrays and Multiplication
Five-Minute Check (over Lesson 4-1)
Main Idea and Vocabulary
California Standards
Key Concept: Commutative Property
Example 1: Use an Array
Example 2: Use an Array
Example 3: Real-World Example
4-2
Arrays and Multiplication
(over Lesson 4-1)
Multiply. Use repeated addition.
5×3
A. 10
B. 25
C. 20
D. 15
4-2
Arrays and Multiplication
(over Lesson 4-1)
Multiply. Use repeated addition.
3×5
A. 15
B. 10
C. 25
D. 30
4-2
Arrays and Multiplication
(over Lesson 4-1)
Multiply. Use repeated addition.
4×6
A. 16
B. 24
C. 10
D. 12
4-2
Arrays and Multiplication
(over Lesson 4-1)
Multiply. Use repeated addition.
6×4
A. 24
B. 10
C. 12
D. 26
4-2
Arrays and Multiplication
(over Lesson 4-1)
Multiply. Use repeated addition.
4×4
A. 8
B. 12
C. 16
D. 1
4-2
Arrays and Multiplication
• I will use arrays to multiply.
• array
• Commutative Property of Multiplication
4-2
Arrays and Multiplication
Standard 3AF1.5 Recognize and use the
Commutative and Associative Properties of
Multiplication (e.g., if 5 × 7 = 35, then what
is 7 × 5? and if 5 × 7 × 3 = 105, then what is
7 × 3 × 5?).
4-2
Arrays and Multiplication
4-2
Arrays and Multiplication
Sue’s mom made cereal bars for her class. She
arranged them in 3 rows of 7. How many cereal
bars did she make?
To find the total number of cereal bars, you can use
addition or multiplication.
One Way: Add
Another Way: Multiply
7 + 7 + 7 = 21
3 × 7 = 21
Answer: So, 3 equal groups of 7 cereal bars is 21 in all.
4-2
Arrays and Multiplication
Jenny’s sister made brownies for her scout troop.
She arranged them in 4 rows of 8. How many
brownies did she make?
A. 12
B. 24
C. 36
D. 32
4-2
Arrays and Multiplication
Donato bought a carton of eggs that had 3 rows of
6 eggs. How many eggs were in the carton?
To find the total number in the array of eggs, you can
write a multiplication sentence.
3 × 6 = 18
Answer: So, 3 rows of 6 eggs is 18 eggs.
4-2
Arrays and Multiplication
Anne Marie bought a box of chocolates.
They were in 3 rows of 4. How many pieces
of chocolate were in the box?
A. 7 pieces
B. 12 pieces
C. 14 pieces
D. 15 pieces
4-2
Arrays and Multiplication
In The Jam Shop, Mrs. Hessle arranged jars of
jam in 8 rows with 4 jars in each row. She then
decided she could display more jars of jam if
she arranged 4 rows with 8 in each row. Was
Mrs. Hessle correct? Explain.
4-2
Arrays and Multiplication
number in
each row
rows
8
×
4
total
=
32
4-2
Arrays and Multiplication
number in
each row
rows
4
×
8
total
=
32
Answer: Both arrangements show 32 jars of jam.
Mrs. Hessle was not correct.
4-2
Arrays and Multiplication
In the candle shop, Mr. Montoya arranged the
candles in 7 rows with 3 jars in each row.
Choose another way he could display them to
show the same amount of candles.
A.
2 rows of 12 jars
B.
4 rows of 5 jars
C.
3 rows of 7 jars
D.
5 rows of 5 jars
4-3
Multiply by 2
Five-Minute Check (over Lesson 4-2)
Main Idea
California Standards
Example 1: Multiply by 2
Example 2: Use Skip Counting
4-3
Multiply by 2
(over Lesson 4-2)
ALGEBRA Use the Commutative Property of
Multiplication to find the missing number.
6 × 2 = 12
2 × = 12
A. 6
B. 4
C. 12
D. 2
4-3
Multiply by 2
(over Lesson 4-2)
ALGEBRA Use the Commutative Property of
Multiplication to find the missing number.
3 × 7 = 21
× 3 = 21
A. 3
B. 4
C. 21
D. 7
4-3
Multiply by 2
(over Lesson 4-2)
ALGEBRA Use the Commutative Property of
Multiplication to find the missing number.
4 × 5 = 20
5×4=
A. 4
B. 5
C. 20
D. 9
4-3
Multiply by 2
• I will multiply by 2.
4-3
Multiply by 2
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-3
Multiply by 2
The students in Ms. Dennis’s class work in 2
groups of 6. How many students are there in all?
You need to find 2 groups of 6 or 2 × 6.
4-3
Multiply by 2
One Way: Draw a Picture
Draw 2 groups of 6.
6 + 6 or 12
4-3
Multiply by 2
Another Way: Use an Array
Show an array with 2 rows and 6 columns.
2 rows of 6 = 6 + 6 or 12
Answer: So there are 2 × 6 or 12 students in all.
4-3
Multiply by 2
There were 2 teams of 10 players in the soccer
finals. How many players were there in all?
A. 20 players
B. 22 players
C. 24 players
D. 30 players
4-3
Multiply by 2
Mr. Murphy drove 2 miles round trip to work every
day. How many miles did he drive in a five-day
work week?
There are 5 days. Each day he drives 2 miles. To find
how many miles he drives altogether, find 2 × 5.
4-3
Multiply by 2
Count 2 jumps of 5.
Answer: So, Mr. Murphy drives 2 × 5, or 10 miles in
a work week.
4-3
Multiply by 2
Mrs. Ankrum drove 2 miles round trip to work
every day. How many miles did she drive in a 3day work week?
A.
2 miles
B.
3 miles
C.
4 miles
D.
6 miles
4-4
Multiply by 4
Five-Minute Check (over Lesson 4-3)
Main Idea
California Standards
Example 1: Multiply by 4
Example 2: Use a Number Sentence
Example 3: Double a Known Fact
4-4
Multiply by 4
(over Lesson 4-3)
Multiply 2 × 5.
A. 10
B. 20
C. 7
D. 12
4-4
Multiply by 4
(over Lesson 4-3)
Multiply 8 × 2.
A. 16
B. 10
C. 18
D. 6
4-4
Multiply by 4
(over Lesson 4-3)
Multiply 2 × 7.
A. 16
B. 5
C. 14
D. 12
4-4
Multiply by 4
(over Lesson 4-3)
Multiply 9 × 2.
A. 11
B. 13
C. 18
D. 20
4-4
Multiply by 4
• I will multiply by 4.
4-4
Multiply by 4
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-4
Multiply by 4
There were 6 cars in the parking lot. How many
tires were on the 6 cars?
You need to find 6 groups of 4 or 6 × 4.
4-4
Multiply by 4
One Way: Repeated Addition
Use repeated addition to find 6 × 4.
4 + 4 + 4 + 4 + 4 + 4 = 24
4-4
Multiply by 4
Another Way: Skip Count
Count 6 jumps of 4.
6 jumps of 4 is 24.
Answer: So, there are 6 × 4 or 24 wheels in all.
4-4
Multiply by 4
There were 7 minivans in the school parking lot.
How many tires were on the 7 minivans?
A.
49 tires
B.
28 tires
C.
30 tires
D.
35 tires
4-4
Multiply by 4
There are 4 tomatoes on each tomato plant in
Chee’s garden. There are 7 plants. How many
tomatoes are there in all?
number of
groups
7
number in
each group
×
4
total
=
Answer: So, there are 28 tomatoes.
28
4-4
Multiply by 4
There are 5 cows in each field on Mario’s farm.
There are 4 fields. How many cows in all?
A.
15 cows
B.
16 cows
C.
20 cows
D.
25 cows
4-4
Multiply by 4
Apples are packed in a box in 4 rows. Each row
has 8 apples. How many apples are in the box?
You need to find 4 × 8.
4 is double of 2. So, 4 × 8 is double 2 × 8.
4-4
Multiply by 4
4×8
=
2×8
+
2×8
16
+
16
= 32
Answer: So, 4 × 8 = 32. There are 32 apples in
the box.
4-4
Multiply by 4
Pineapples are packed in a carton in 4 rows. Each
row has 6 pineapples. How many pineapples are in
the carton?
A.
10 pineapples
B.
28 pineapples
C.
24 pineapples
D.
40 pineapples
4-5
Problem-Solving Skill: Extra or Missing Information
Five-Minute Check (over Lesson 4-4)
Main Idea
California Standards
Example 1: Problem-Solving Skill
4-5
Problem-Solving Skill: Extra or Missing Information
(over Lesson 4-4)
Multiply 4 × 5.
A. 9
B. 1
C. 19
D. 20
4-5
Problem-Solving Skill: Extra or Missing Information
(over Lesson 4-4)
Multiply 8 × 4.
A. 32
B. 12
C. 24
D. 42
4-5
Problem-Solving Skill: Extra or Missing Information
(over Lesson 4-4)
Multiply 7 × 4.
A. 24
B. 11
C. 21
D. 28
4-5
Problem-Solving Skill: Extra or Missing Information
(over Lesson 4-4)
Multiply 4 × 6.
A. 10
B. 24
C. 12
D. 28
4-5
Problem-Solving Skill: Extra or Missing Information
• I will decide if there is extra or missing
information.
4-5
Problem-Solving Skill: Extra or Missing Information
Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
4-5
Problem-Solving Skill: Extra or Missing Information
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-5
Problem-Solving Skill: Extra or Missing Information
My school’s hayride will start at 6:00 P.M. There are
4 wagons that hold 9 children each. Half of the
children going are girls. What is the total number
of children that can ride on the 4 wagons?
4-5
Problem-Solving Skill: Extra or Missing Information
Understand
What facts do you know?
• The hayride starts at 6:00 P.M.
• There are 4 wagons that hold 9 children.
• Half of the children are girls.
What do you need to find?
• Find the number of children that can ride on the
4 wagons.
4-5
Problem-Solving Skill: Extra or Missing Information
Plan
Decide what facts are important
to solve the question.
• the number of wagons
• the number of children each
wagon holds
4-5
Problem-Solving Skill: Extra or Missing Information
Solve
To find the total number, multiply the number of
wagons by the number of children each wagon
holds.
4×9=
4 × 9 = 36
Answer: So, 36 children can ride on the hay
wagons.
4-5
Problem-Solving Skill: Extra or Missing Information
Check
Look back at the problem. Since 9 + 9 + 9 + 9 = 36,
you know the answer is correct.
4-6
Multiply by 5
Five-Minute Check (over Lesson 4-5)
Main Idea
California Standards
Example 1: Multiply by 5
Example 2: Skip Count
Example 3: Use a Number Sentence
4-6
Multiply by 5
(over Lesson 4-5)
Solve. If there is missing information, tell what
facts you need to solve the problem. Kari is 12
years old. Her brother is 3 years older and is 52
inches tall. How old is Kari’s brother?
A. 15
B. 9
C. You need to know how tall Kari is.
D. 32
4-6
Multiply by 5
(over Lesson 4-5)
Solve. If there is missing information, tell what
facts you need to solve the problem. Filipe spent
$23 at the store. How much change did he receive?
A.
$21
B.
None
C.
$3
D.
You need to know how much money
he gave to the clerk.
4-6
Multiply by 5
• I will multiply by 5.
4-6
Multiply by 5
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-6
Multiply by 5
A farmer has a pumpkin patch with 8 rows. Each
row has 5 pumpkins. How many pumpkins does the
farmer have?
You need to find 8 × 5.
4-6
Multiply by 5
One Way: Draw a Picture
Use repeated addition.
5 + 5 + 5 + 5 + 5 +
5 + 5 + 5 = 40
4-6
Multiply by 5
Another Way: Use an Array
8 rows of 5 =
8 × 5 or 40
Answer: So, 8 × 5 = 40
pumpkins.
4-6
Multiply by 5
Laurie has a set of curlers that has 5 rows. Each
row has 7 curlers. How many curlers does Laurie
have?
A.
28 curlers
B.
35 curlers
C.
40 curlers
D.
42 curlers
4-6
Multiply by 5
There are 4 bracelets with 5 beads on each
bracelet. How many beads in all?
You need to find 4 groups of 5 or 4 × 5.
Answer: So, 4 × 5 = 20 beads.
4-6
Multiply by 5
There are 3 necklaces with 8 charms on each
necklace. How many charms in all?
A.
25 charms
B.
16 charms
C.
24 charms
D.
11 charms
4-6
Multiply by 5
Lila has 9 nickels. How much money does she have?
You know that a nickel is 5¢. Use a multiplication
sentence to find 9 × 5¢.
number of
groups
number in
each group
9
×
5¢
=
9
×
5¢
=
Answer: So, Lila has 45¢.
45¢
4-6
Multiply by 5
Joy has 8 nickels. How much money does she
have?
A.
45 cents
B.
40 cents
C.
38 cents
D.
58 cents
4-7
Multiply by 10
Five-Minute Check (over Lesson 4-6)
Main Idea
California Standards
Example 1: Skip Count
Example 2: Double a Known Fact
Example 3: Use a Number Sentence
4-7
Multiply by 10
(over Lesson 4-6)
Multiply 5 × 9.
A. 14
B. 24
C. 45
D. 4
4-7
Multiply by 10
(over Lesson 4-6)
Multiply 3 × 5.
A. 2
B. 13
C. 15
D. 8
4-7
Multiply by 10
(over Lesson 4-6)
Multiply 6 × 5.
A. 30
B. 11
C. 13
D. 9
4-7
Multiply by 10
(over Lesson 4-6)
Multiply 5 × 8.
A. 40
B. 13
C. 44
D. 38
4-7
Multiply by 10
• I will multiply by 10.
4-7
Multiply by 10
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-7
Multiply by 10
Yago and his two sisters made their hand prints on
a poster. How many fingers were on the poster?
Find 3 × 10.
Count 3 jumps of 10.
Answer: So, 3 × 10 = 30 fingers.
4-7
Multiply by 10
Joe and his friend made their footprints on the
sidewalk. How many toes were on the sidewalk?
A.
20 toes
B.
30 toes
C.
10 toes
D.
15 toes
4-7
Multiply by 10
Roberto found 7 dimes in his pocket. How much
money did he find?
You need to find 7 × 10¢.
10 is the double of 5. So,
7 × 10¢ is double 7 × 5¢.
4-7
Multiply by 10
7 × 10¢ = 7 × 5¢ + 7 × 5¢
= 35¢ + 35¢
= 70¢
Answer: So, 7 × 10¢ = 70¢.
4-7
Multiply by 10
Gus found a bag with 8 dimes in it. How much
money did he find?
A.
8 cents
B.
80 cents
C.
800 cents
D.
18 cents
4-7
Multiply by 10
Pam sold 5 tickets for the school play. Each ticket
cost $10. How much money did Pam receive for the
tickets?
To solve the problem, you need to multiply 5 by $10.
5 × $10 =
5 × $10 = $50
Answer: So, Pam received $50 for the tickets.
4-7
Multiply by 10
Check
The model shows that 5 × 10 = 50.
4-7
Multiply by 10
Conchita bought 6 boxes of clay from the art
supply store for $10 each. How much money did
she spend?
A.
$16
B.
$50
C.
$60
D.
$40
4-8
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 4-7)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
4-8
Problem-Solving Investigation: Choose a Strategy
(over Lesson 4-7)
Multiply 3 × 10.
A. 13
B. 30
C. 7
D. 300
4-8
Problem-Solving Investigation: Choose a Strategy
(over Lesson 4-7)
Multiply 8 × 10.
A. 18
B. 80
C. 2
D. 88
4-8
Problem-Solving Investigation: Choose a Strategy
(over Lesson 4-7)
Multiply 10 × 0.
A. 0
B. 10
C. 100
D. 1
4-8
Problem-Solving Investigation: Choose a Strategy
(over Lesson 4-7)
Multiply 10 × 2.
A. 20
B. 12
C. 10
D. 200
4-8
Problem-Solving Investigation: Choose a Strategy
(over Lesson 4-7)
Multiply 9 × 10.
A. 9
B. 19
C. 0
D. 90
4-8
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
4-8
Problem-Solving Investigation: Choose a Strategy
Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information,
and observing patterns.
4-8
Problem-Solving Investigation: Choose a Strategy
Standard 3NS2.2 Memorize to
automaticity the multiplication table for
numbers between 1 and 10.
4-8
Problem-Solving Investigation: Choose a Strategy
DENZELL: Our third grade class
will make 6 holiday baskets to
give away. We will fill each
basket with 7 food items.
YOUR MISSION: Find out how many
items are needed to fill the food
baskets.
4-8
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• You know the class will make 6 baskets.
• You also know they will fill each one with
7 items.
What do you need to find?
• You need to find out the total number
of food items needed.
4-8
Problem-Solving Investigation: Choose a Strategy
Plan
You can use the draw a picture strategy to solve
this math problem.
4-8
Problem-Solving Investigation: Choose a Strategy
Solve
Draw a picture to
represent the situation.
The picture shows that
6 × 7 = 42.
Answer: So, the third grade class needs
42 food items to fill the baskets.
4-8
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Check by using
repeated addition. 7 + 7 + 7 + 7 + 7 + 7 = 42.
So you know the answer is correct and
reasonable.
4-9
Multiplying by 0 and 1
Five-Minute Check (over Lesson 4-8)
Main Idea and Vocabulary
California Standards
Key Concept: Multiplication Properties
Example 1: Use Properties to Multiply
4-9
Multiplying by 0 and 1
(over Lesson 4-8)
Use any strategy to solve. Marion bought 4 lbs of
apples at $2 a pound, 2 lbs of tomatoes at $3 a
pound, and lettuce at $1.50. How much change did
she receive from a $20 bill?
A.
$0.50
B.
$1.00
C.
$4.00
D.
$4.50
4-9
Multiplying by 0 and 1
• I will multiply by 0 and 1.
• Zero Property of Multiplication
• Identity Property of Multiplication
4-9
Multiplying by 0 and 1
Standard 3NS2.6 Understand the special
properties of 0 and 1 in multiplication and
division.
4-9
Multiplying by 0 and 1
4-9
Multiplying by 0 and 1
Find 8 × 1. Tell what property you used.
8×1=8
Answer: The product is 8. Identity Property of
Multiplication.
4-9
Multiplying by 0 and 1
Find 9 × 1. Which property did you use?
A.
9; Identity Property of Multiplication
B.
10; Associative Property
C.
10; Identity Property of Multiplication
D.
9; Associative Property