Download Division Facts and Extensions

Division Facts and
Extensions
Objectives To review multiplication and division facts and
apply
basic facts to division with 1-digit divisors.
a
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ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Generate equivalent names for
whole numbers. [Number and Numeration Goal 4]
• Apply multiplication facts, related division
facts, or extended facts to identify
friendly numbers. [Operations and Computation Goal 2]
• Use friendly numbers to divide 2-digit by
1-digit numbers. [Operations and Computation Goal 3]
Key Activities
Students practice division facts and
extended facts. They use multiples of a
given number to rename numbers. They use
friendly numbers to solve problems with
1-digit divisors.
Ongoing Assessment:
Informing Instruction See page 233.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 99. [Operations and Computation Goal 3]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Student Reference Book, p. 325
per partnership: 1 complete deck
of number cards (from the Everything
Math Deck, if available)
Students apply number properties,
equivalent names, arithmetic
operations, and basic facts.
Quadrangle Relationships
Math Masters, p. 440A
Students practice classifying and
comparing relationships among
quadrangles.
Math Boxes 4 1
Curriculum
Focal Points
Differentiation Options
READINESS
Using Equivalent Names for Numbers
Math Masters, p. 421
per partnership: 4 each of number cards 1–9
(from the Everything Math Deck, if available)
Students complete name-collection boxes
focusing on number properties to make
equivalent names for numbers.
ENRICHMENT
Exploring More Divisibility Rules
Math Masters, p. 103
Students apply divisibility rules to 5-, 6-, and
7-digit numbers.
Math Journal 1, p. 100
Geometry Template
Students practice and maintain skills
through Math Box problems.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 25, 28, and 183
Students solve division problems.
Study Link 4 1
Math Masters, p. 102
Students practice and maintain skills
through Study Link activities.
Key Vocabulary
dividend divisor quotient multiples
Materials
Math Journal 1, p. 99
slates per partnership: 4 each of number
cards 1–9 (from the Everything Math Deck,
if available)
Advance Preparation
For Part 1, make classroom posters showing the names of multiplication and division problem parts and
relating those names to the three numbers of a fact family.
Teacher’s Reference Manual, Grades 4–6 pp. 16, 269–271
230
Unit 4
Division
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP5, SMP6, SMP7, SMP8
Getting Started
Content Standards
5.OA.1, 5.OA.2, 5.NBT.2, 5.NBT.6, 5.NF.5a, 5.G.3, 5.G.4
Mental Math and Reflexes
Math Message
Use your slate procedures. Remind students to think of missing factors.
Example: How many 9s are in 72? Think: 9 times what number equals 72?
How many 3s are in 21? 7 How many 30s are in 210? 7 How many 3s are in 210? 70
How many 7s are in 49? 7 How many 70s are in 490? 7 How many 7s are in 490? 70
Estimate: About how many 4s are in 21? About 5 About how many 40s are in 210?
About 5 About how many 4s are in 210? About 50
1 Teaching the Lesson
▶ Math Message Follow-Up
For each problem below,
write two related division facts.
6 ∗ 7 = 42
9∗6=x
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
DISCUSSION
Algebraic Thinking Ask volunteers which 3 numbers are in the
fact family for 6 ∗ 7 = 42. 6, 7, and 42 Ask: Is this an addition/
subtraction or multiplication/division fact family? Multiplication/
division How do you know? Sample answers: The numbers come
from a multiplication fact; it can’t be addition/subtraction because
6 + 7 is not equal to 42. Fact families have opposite operations;
division is the opposite of multiplication. Pose questions such as
the following:
●
Use the related multiplication and division facts for 6, 7, and 42
to write a statement similar to the following: 42 is 7 times as
great as 6. Sample answer: 42 is 6 times as great as 7.
●
In a related division fact, which number is the dividend? 42
Ask volunteers to state the related division facts, naming the
divisor and the quotient. In 42 / 7 = 6, 7 is the divisor and
6 is the quotient. In 42 / 6 = 7, 6 is the divisor and 7 is the
quotient.
●
Which 3 numbers are in the fact family for 9 ∗ 6 = x?
9, 6, and x Expect that some students might respond 9, 6, and
54. In this case, ask students whether they think x can be used
as a member of the fact family. Yes, because x is a variable and
represents a number. Ask volunteers to give the related
division facts. x / 6 = 9; x / 9 = 6
●
Use the related multiplication and division facts for 6, 9, and
x to write a statement similar to the following: x is 9 times as
great as 6. Sample answer: x is 6 times as great as 9.
●
What number is in the multiplication/division fact family with
20 and 5? 4 How do you know? 5 ∗ 4 = 20; 20 / 5 = 4;
there are 4 [5s] in 20.
Conclude the discussion by summarizing that knowing one
multiplication fact leads to knowing 2 division facts. Ask students
to compare the size of a product to one of its factors, based on the
other factor. Tell them, for example: Using the numbers 4, 5, and 20,
NOTE Everyday Mathematics reinforces
students’ understanding of the link between
multiplication and division. It is expected that
students who have automatic recall of the
multiplication facts will be able to state related
division facts.
Lesson 4 1
231
you could say that 20 (the product) is 4 (one of the factors) times as
great as 5 (the other factor). Ask: What other comparisons can you
make using the product and the factors? Sample answers: 20 is
5 times as great as 4. Using 5: 4 times is 20. Using 4: 5 times is 20.
Pose questions to have students compare the size of a product to
one of its factors:
●
20 is how many times as great as one of its factors, 4? 5 times as
great
●
x / 9 = 6 means that x is how many times as great as its
quotient, 6? 9 times as great
●
2 ∗ (4 + 5) is how many times as great as one of its factors,
(4 + 5)? 2 times as great
▶ Practicing Division Facts
WHOLE-CLASS
ACTIVITY
and Extended Division Facts
Use your slate procedures to practice division facts and their
extensions. Dictate problems like the following, varying your
language. For example, ask: What is 63 divided by 7? How many
7s are in 63? If necessary, give a clue, such as, Think: 7 times what
number equals 63?
63 / 7 9
64 / 8 8
240 / 30 8
630 / 7 90
1,000 / 10 100
2,000 / 50 40
27 / 3 9
200 / 20 10
360 / 9 40
270 / 30 9
120 / 10 12
4,900 / 70 70
What number is 7 times as great as 6? 42
What number is 90 times as great as 7? 630
What number is one-fourth the size of 48? 12
What number is 1,000 times as great as 5? 5,000
▶ Renaming Numbers
PARTNER
ACTIVITY
PROBLEM
PRO
PR
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
E
M
SO
S
SOLVING
OL
O
LV
VING
VIN
IIN
NG
N
G
Use the following activity to prepare students for the mental
division strategy on journal page 99. On a transparency, or the
board, draw a name-collection box.
Shuffle the cards (4 each of number cards 1 through 9).
Turn over 2 cards and make a 2-digit number.
8
6
68
63 + 5
7º9+5
7
35 + 21 + 7 + 5
21 + 21+ 21+ 5
232
Unit 4
Division
Write the number in the collection box tag. Ask volunteers
what they think you should do next. Most students will
recognize the name-collection box format and will respond that
you should write equivalent names for the number in the box.
Explain that for this activity, students will look for equivalent
names that contain multiples of another number.
Turn over a third card. Survey the class for equivalent names
that contain multiples of the number from the third card.
Student Page
Use follow-up questions to guide students to see that the largest
multiple can be broken into smaller parts to make other
equivalent names. Allow partners time to try at least three
different name-collection boxes, drawing them on scrap paper or
using slates. Circulate and assist.
Date
Time
LESSON
Mental Division Strategy
4 1
Fact knowledge can help you find how many times a 1-digit number will divide any
large number.
Example: Divide 56 by 7 mentally.
Think: How many 7s in 56?
Or think: 7 times what number equals 56?
Continue: Since 7 8 56, there must also be 8 [7s] in 56. So 56 divided by 7 equals 8.
Knowing basic facts helps you break the larger number into two or more friendly
numbers—numbers that are easy to divide by the 1-digit number.
Example: Divide 96 by 3 mentally.
Break 96 into friendly numbers. Here are two ways.
▶ Using a Mental Division
WHOLE-CLASS
ACTIVITY
Strategy
90 and 6. Ask yourself: How many 3s
60 and 36. Ask yourself: How many 3s
in 90? (30) How many 3s in 6? (2)
in 60? (20) How many 3s in 36? (12)
Total: 30 2 32
Total: 20 12 32
So 96 divided by 3 equals 32. Check the result: 3 32 96.
Complete the following statements. List the friendly parts that you used.
(Math Journal 1, p. 99)
1.
Explain that using equivalent names for numbers, knowing
multiplication and division facts, and recognizing fact extensions
in order to break numbers into friendly parts will simplify
calculations.
14 .
30 and 12; 36 and 6
42 divided by 3 equals
(friendly parts for 42)
13 R5 .
60 and 23; 72 and 11
3.
83 divided by 6 equals
5.
Fifteen-year-old oak trees are often
about 25 feet tall. Rose, a 15-year-old
girl, is about 5 feet tall. How many times
taller are the trees than Rose?
(friendly parts for 83)
17
.
40 and 28; 20 and 48
2.
68 divided by 4 equals
4.
99 divided by 7 equals
6.
The job of interviewing 500 students
in a school is to be divided equally among
10 interviewers. How many students
should each interviewer talk to?
(friendly parts for 68)
14 R1 .
77 and 22; 70 and 29
(friendly parts for 99)
50 students
About 5 times taller
Refer students to journal page 99. As a class, discuss the
presented division strategy.
Have students complete Problems 1–6. Remind them to use
multiplication to check their results. Circulate and assist.
Math Journal 1, p. 99
Ongoing Assessment: Informing Instruction
Watch for students who use paper-and-pencil exclusively, rather than mental
arithmetic. Encourage these students to try to visualize what they might write
before they actually write anything.
Survey the class for methods of breaking numbers into friendly
parts. Use follow-up questions to help students recognize how to
use a multiple of the divisor.
Adjusting the Activity
Student Page
Have students break the dividend into two friendly numbers so that
one number is the divisor times 10 and the other is the remaining part. For
42 divided by 3, use 3 ∗ 10, or 30, as the first friendly number, and 12 as the
second. For larger dividends, it might be necessary to use the divisor times a
multiple of 10. For 132 divided by 3, use 3 ∗ 40, or 120, as the first friendly
number and 12 as the second.
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
Date
Time
LESSON
Math Boxes
41
1.
V I S U A L
Write the value of each of the following
digits in the numeral 34,089,750.
a.
4
b.
8
c.
5
d.
9
e.
3
2.
millions
ten-thousands
tens
thousands
ten-millions
Write the following numbers in standard
notation.
a.
62 =
b.
105 =
c.
142 =
d.
83 =
e.
34 =
36
100,000
196
512
81
34–36
243
4
3.
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 99
Problems 1–4
Use journal page 99, Problems 1–4 to assess students’ facility using
multiplication and division facts for division with 1-digit divisors. Students are
making adequate progress if they successfully identify friendly numbers and use
these to solve the problems.
Roger had saved $10.05 from his
allowance. Then he bought a paint-bynumbers kit for $7.39. How much money
does he have left?
4.
$2.66
Javier has $5.00 to buy school supplies.
He wants one pack of pencils for $1.38, a
notebook for $2.74, and some writing
paper for $1.29. If he has enough money,
how much change will he get back?
Not enough money
If not, how much more money does he need?
$0.41
243
5–7
5.
Use your full-circle protractor to measure
angle CAT.
6.
T
Complete the table.
Fraction
Decimal
1
_
0.3
33.3% or 33 13 %
0.65
65%
3
65
13
_
_
100 or 20
_
_
4 _
, 4 or 2
[Operations and Computation Goal 3]
C
A
100 10
1
_
Circle the best answer.
A.
about 318°
B.
about 50°
C.
about 42°
D.
about 140°
20
5
Percent
0.4
40%
0.05
5%
_
89 90
204 205
Math Journal 1, p. 100
EM3cuG5MJ1_U04_099-120.indd 100
1/18/11 6:55 PM
Lesson 4 1
233
Teaching Aid Master
Name
Date
Time
2 Ongoing Learning & Practice
á sides of
equal length
next to
each other
▶ Playing Name That Number
Properties of Parallelograms
PARTNER
ACTIVITY
(Student Reference Book, p. 325)
Students practice applying number properties, equivalent names,
arithmetic operations, and basic facts by playing Name That Number.
á exactly 2 pairs
of parallel
á 2 pairs of
sides
sides are the
same length
á sides of
equal length á quadrangle
opposite
each other
Properties of Kites
á no pairs of
parallel sides
Venn Diagram
▶ Quadrangle (Quadrilateral)
PARTNER
ACTIVITY
Relationships
(Math Masters, p. 440A)
Students practice and extend their thinking about classifying and
comparing relationships among quadrangles. Draw a Venn diagram
on the board with the headings Properties of Parallelograms and
Properties of Kites. (See margin.)
Math Masters, p. 440A
EM3MM_G5_U11_323-347_501.indd 440A
1/19/11 1:38 PM
Briefly review how to use a Venn diagram. The properties
unique to parallelograms are listed below the label Properties of
Parallelograms, and properties unique to kites are listed below
Properties of Kites. The properties the two shapes have in common
are listed in the intersection of the two ovals. Students complete
Math Masters, page 440A with a partner. Assign additional
pairings for additional practice.
Possible pairings include square and rectangle, trapezoid and
parallelogram, kite and rhombus, square and rhombus, and
parallelogram and rhombus.
▶ Math Boxes 4 1
Study Link Master
Name
Date
STUDY LINK
41
(Math Journal 1, p. 100)
Time
Uses of Division
Use multiplication and division facts to solve the following problems mentally.
Remember: Break the number into two or more friendly parts.
INDEPENDENT
ACTIVITY
11 21
Example: How many 4s in 71?
Mixed Review Math Boxes in this lesson are paired with
Math Boxes in Lesson 4-3. The skill in Problem 6
previews Unit 5 content.
Break 71 into smaller, friendly numbers. Here are two ways.
◆ 40 and 31. Ask yourself: How many 4s in 40? (10) How many 4s in 31? (7 and 3 left
over) Think: What multiplication fact for 4 has a product near 31? (4 7 28)
Total 17 and 3 left over.
◆ 20, 20, 20, and 11. Ask yourself: How many 4s in 20? (5) How many 4s in three 20s?
(15) How many 4s in 11? (2 and 3 left over) Total 17 and 3 left over.
So 71 divided by 4 equals 17 with 3 left over.
1.
19
.
Sample answer: 30 and 27
57 divided by 3 equals
12
.
Sample answer: 80 and 16
2.
96 divided by 8 equals
4.
The weight of an object on Earth is
6 times heavier than its weight on the
moon. An object that weighs 30 lb
on Earth weighs how many pounds
on the moon?
(friendly parts for 57)
3.
(friendly parts for 96)
The diameter of Earth, about 8,000 miles,
is about 4 times the diameter of the
moon. What is the approximate
diameter of the moon?
8,000 mi
Writing/Reasoning Have students write a response to the
following: Explain your answer to Problem 4. Sample
answer: I added to find the total cost for the supplies
Javier wanted. It was more than $5.00, so I subtracted $5.00 from
the total cost to see how much more money he needed.
▶ Study Link 4 1
INDEPENDENT
ACTIVITY
(Math Masters, p. 102)
About 2,000 mi
5 lb
unit
unit
Practice
Solve. Then write the other problems in the fact families.
5.
878
1,803 878 925
925 878 1,803
878 925 1,803
1,803 925 Math Masters, p. 102
234
Unit 4
Division
6.
875
377 498 875
875 377 498
875 498 377
498 377 Home Connection Students use friendly numbers,
division facts, and related multiplication facts to solve
division problems and number stories.
Teaching Aid Master
Name
3 Differentiation Options
READINESS
▶ Using Equivalent Names
Date
Time
Equivalent Names for Numbers
PARTNER
ACTIVITY
5–15 Min
for Numbers
(Math Masters, p. 421)
To provide experience with finding equivalent names for numbers,
have students use name-collection boxes, focusing on number
properties and relationships. For example, they might use
multiples of ten, add 0, or multiply by 1 to make equivalent
names.
Partners take turns dealing two cards from a deck comprised of
4 each of the numbers 1–9. Each partner uses the numbers on
the cards to form a 2-digit number. Their numbers can be the
same or different. Partners write their numbers in one of the
name-collection box tags on Math Masters, page 421 and find
as many different equivalent names for the number as they can.
Math Masters, p. 421
NOTE In Part 1, students rename numbers using multiples of given numbers.
However, do not restrict the forms of the equivalent names students collect for
this activity.
ENRICHMENT
▶ Exploring More Divisibility
PARTNER
ACTIVITY
15–30 Min
Rules
(Math Masters, p. 103)
To apply students’ understanding of divisibility, have
them solve problems using divisibility rules for prime
numbers. Partners complete Math Masters, page 103.
Teaching Master
Name
LESSON
41
After partners finish, have them create and exchange 6-digit
numbers to test for divisibility by 7, 11, or 13. They might also
find numbers that are divisible by more than one of these primes.
Products of multiples of primes are easy to find.
Example: (65 ∗ 7) (89 ∗ 13) = 526,435
EXTRA PRACTICE
▶ 5-Minute Math
SMALL-GROUP
ACTIVITY
Time
Testing for Divisibility by 7, 11, and 13
Use these divisibility rules to test large numbers.
To test if a number is divisible by 7:
◆ Take the rightmost digit.
25,809
◆ Double it.
9 2 18
◆ Subtract the result from the
remaining digits.
2,580 18 2,562
◆ Repeat, each time doubling the
rightmost digit and subtracting,
until the result is small enough
to know that it is, or is not,
divisible by 7.
1.
Is 33,992 divisible by 7?
2,562
224
256 4 252
252
224
25 4 21
21 is divisible by 7, so 25,809 is
divisible by 7.
Yes, because 14 is divisible by 7
To test if a number is divisible by 11:
5–15 Min
To offer students more experience with whole-number division, see
5-Minute Math, pages 25, 28, and 183.
Date
2.
◆ Find the sum of every other digit.
10,648
◆ Find the sum of the digits that are left.
044
◆ Subtract.
15 4 11
11 is divisible by 11, so 10,648 is
divisible by 11.
Is 9,723 divisible by 11?
1 6 8 15
No, because 1 is not divisible by 11
To test if a number is divisible by 13:
3.
◆ Multiply the rightmost digit by 4.
1,166,932
◆ Add the result to the remaining
digits.
116,693 8 116,701
◆ Repeat, each time multiplying
the rightmost digit and adding,
until the result is small enough to
know that it is, or is not, divisible
by 13.
116,701
11,670 4 11,674
1,167 16 1,183
118 12 130
130 13 10, so 1,166,923
Is 89,362 divisible by 13?
248
144
4 4 16
3 4 12
is divisible by 13.
Yes, because 91 is divisible by 13
Math Masters, p. 103
Lesson 4 1
235
Copyright © Wright Group/McGraw-Hill
Name
Date
Time
Venn Diagram
440A