Multiplication and Division

1
Multiplication and Division

• Everyday Mathematics
• Unit 7
• Mr. Brumfield

2
Unit Table of Contents

• Patterns in Products
• Multiplication Facts Survey
• Fact Power
• Number Models with Parentheses
• Scoring in Basketball (application)
• Extended Facts
• Estimating Costs
• Extended Facts, Products of 10s
• Exploring Ratios and Geometry
• Unit 7 Review and Assessment

3
Patterns in Products
Lesson 7.1

• Our objectives are to extend our square
  number facts and to review multiplication and
  division patterns.

What are square numbers?
4
Vocabulary Review

• Factors
• Product
• Square Number
• Square Product

The numbers being multiplied
The answer in a multiplication problem
Multiplying a number times itself
The product of a square number
5
Mental Math
Write the numerals for the number Seven million
four hundred one thousand eight hundred
eighty-nine. Circle millions Put an X on top of
the thousands Underline the ten-thousands
Write the numerals for the number Five million
thirty-three thousand one hundred
twenty-nine. Circle the ones Put an X on top of
the ten-thousands Underline the hundreds

• Write the numerals for the number
• three million four hundred twenty-seven thousand
  two.
• Circle the thousands
• Put an X on top of the hundred-thousands
• Underline the tens

6
Math Message

• Turn to page 161 in your new math journal and
  find the products in exercises 1-10.

What are products?
7
Math Message Follow Up

• What do you notice about all of the products
  that you found?
• What is it called when you multiply a number
  times itself?

Square Number
8
Square Numbers

• 1x1
• 2x2
• 3x3
• 4x4
• 5x5
• 6x6
• 7x7
• 8x8
• 9x9
• 10x10

Link to Smart notebook Square Number Matching
9
Looking for a Pattern

• 1 4 9 16 25 36 49 64 81 100

What is the pattern of difference?
Using the pattern, find the next two square
numbers in the series.
10
Remember the Multiplication Fact Chart?
How does this work?
11
Independent Practice

• Complete the Product Patterns on math journal
  page 161.
• When you have finished, complete the math boxes
  on page 162.

12
Multiplication Facts Survey
Lesson 7.2

• Our objectives is to find out which
  multiplication facts you still need to learn.

Which times tables do you know?
13
Mental Math

• 1. A spider has 8 legs. If there are 4 spiders,
  how many legs are there in all?
• Answer __________________________
• 2. There are 6 eggs in each nest. If there are 4
  nests, how many eggs are there altogether?
• Answer________________________
• 3. Mom brought 7 plates with 3 donuts on each
  plate. How many donuts were there altogether?
• Answer ___________________________
• 4. David has 5 boxes with 8 baseball cards in
  each. How many baseball cards does he have
  altogether?
• Answer __________________________
• 5. There are 4 plates with 2 cupcakes and 3
  scoops of ice cream on each plate. a. How
  many cupcakes are there in all? b. How many
  scoops of ice cream are there in all?

14
Math Message

• Each of the following products is a square
  product. Fill in the missing factors
• __ x __ 9 __ x __ 25
• __ x __ 49 __ x __ 81

If both factors and odd numbers is the product
odd or even? What if both factors are even
numbers? What if one factor is even and the other
odd?
15
Show me what you know!

• We are going to highlight the multiplication
  facts you know by heart.
• Be honest, because you need to know the facts
  that you still have to learn.

16
Facts Test

• We are going to take a timed test to see how
  well you know your multiplication facts.
• You will have 90 seconds to complete the test.

17
Multiplication Practice

• We are going to cut out the remaining fact
  triangles, activity sheet five, to practice.
• Below are some fun websites to build your
  schools.

http//www.mathmastery.com/cyberchallenge/index.cf
m http//www.aaastudy.com/g3-mulbuttond.htm http/
/www.multiplication.com/interactive/quickflash/fla
sh/index.html http//www.aplusmath.com/Games/games
.html
18
Independent Practice

• When you have finished, complete the math boxes
  on page 164.

19
Fact Power
Lesson 7.3

• Our objectives is to practice multiplication
  and division facts. Practice can be fun!

How do we improve our knowledge of multiplication
facts?
20
Which Decimal Value is Greater?

• .25 or .67
• 1.54 or 1.5
• 7.0 or 70
• .03 or .3
• .78 or .9

Show the greater value on your slate
21
Math Message

• Fill in the missing tables. Find the missing rule
  for the second table.

Rule x 5
Rule __
In 30 ___ 21 ___ 15
Out 10 6 7 10 ___
In 3 ___ 7 ___ 9
Out ___ 20 ___ 10 ___
What do you need to do when you are not given the
"in" box?
22
Multiplication Bingo
Who wants to play a game?

• The directions can be found in the SRB, pages
  218 219.
• Turn to page 165 of your math journal so that
  we can play!!!

23
Independent Practice

• Complete the multiplication and division
  practice on page 166 of your math journal.
• When you finish, complete the math boxes on page
  167.

24
Number Models with Parentheses
Lesson 7.4

• Our goal is to introduce parentheses in
  numbers models and to write number models for
  number stories.

How do you use parentheses in a math problem?
25
Mental Math

• Lila has 7 bags of apples. Each bag has eight
  apples. How many apples does Lila have in all?
• Number Model _________________
• Answer _______________
• Philip collected 25 cents from six of his
  friends. How much money did Philip collect?
• Number Model _________________
• Answer _______________

26
Math Message?

• Can you find more than one meaning from each of
  these sentences?
• Nancy fed Tom the big cat.
• My sister Tess and Jimmy are going.

What do you need to add to these sentences to
make the meaning more clear?
27
How Does This Relate to Math?

• Just like commas can be necessary to show the
  correct meaning of a sentence, parentheses can
  change the order of a number model.
• Parentheses show you what part of a number model
  should be completed first.

28
Parentheses Practice

• Complete the following number models, which
  have the exact same numbers.
• Remember to complete parentheses first.

(25-8) 7 25- (87)
What do you notice about your answers?
29
More Parentheses Practice

• 53 (17 23)
• (17 8 ) X 3
• 68 (4 X 5 )
• (12 38) 15

Please write your first answer below the
parentheses, so I can check your math.
30
More Parentheses Practice

• 32 5 7 20
• 38 14 9 15
• 40 5 X 2 20
• 32 5 7 34
• 38 14 9 33
• 40 5 X 2 70

Put the parentheses around the correct numbers to
make the answer match.
31
Exit Slip

• Before you begin to work independently, you need
  to complete an exit slip.
• Your exit slip will explain what you just
  learned.
• I will use the information you provide on your
  exit slip to check your understanding.

32
Independent Practice

• Complete the number models and parentheses
  practice on page 168 of your math journal.
• When you finish, complete the math boxes on page
  169.

33
Scoring in Basketball An Application
Lesson 7.5

• Our goal is to add the products of
  multiplication problems, using number models
  containing parentheses.

How well can you solve number model problems?
34
Mental Math

• Six children share 49 pennies equally. How many
  does each child get? How many extra pennies are
  there.?
• Answer __________________________
• 2. Martin bought a package of stickers of his
  favorite cartoon dog. The package contained 25
  stickers. There were five stickers on each sheet.
  How many sheets were in the package?
• Answer________________________
• 3. Yolanda brought jelly beans for her birthday
  treat. She gave each table a cup of jelly beans
  to share. There are 4 children at each table.
  There are 35 jelly beans in the cup at Marthas
  table. How many jelly beans did each child at
  Marthas table receive?
• Answer ___________________________
• 4. Ms. Grant replaced her desks with tables. She
  has 31 students and six tables. Can she seat the
  same number at each table?
• Why or why not?
• What are 3 different ways she could arrange her
  class?

35
Math Message

• Sheila made two 3-point baskets in a basketball
  game. How many points did she score in all?
• Write the number model using parentheses.

36
Scoring in Basketball

• How many points do you make for a free throw?
• How many points for a regular shot?
• How many points for a far-away shot?

37
How Can Someone Score 10 Points?
Example 1

• Today you are going to be working with a partner
  to find several ways to score ten points. You
  will be using wonderful parentheses!
• I need you to give me three examples before we
  break into groups.

Example 2
Example 3
38
Partner Practice

• Complete the fact triangles on page 171.
• With your partner, find as many possible number
  models for scoring 10-points in basketball on 170.

Independently complete the math boxes on page
172.
39
Extended Facts Multiplication Division
Lesson 7.6

• Our goal is to multiply by 10, 100, and
  1,000 and to divide such multiples by 1-digit
  numbers.

How can you simplify large number operations?
40
Mental Math

• One side of a square is 10 centimeters long.
• What is the perimeter?
• What is the area?
• 2. The sides of an equilateral triangle are 5
  centimeters long.
• What is the perimeter of the triangle?
• 3. The longer side of a rectangle measures 8
  inches. The shorter side measures 4 inches.
• What is the perimeter of the rectangle?What is
  the area?

41
Math Message

• The distance around a racing track is 500
  meters. How far does a racer travel in 8 laps?

How can you simplify this problem?
42
Simplifying Big Numbers

• If you know your basic facts, extending your
  products to 10s, 100s, and 1,000s is easy!
• Multiply the basic facts, then add the number of
  zeroes in the factors.

43
Lets Practice!

• 6 (80s)
• 9 (500s)
• 3 (8,000s)
• 50 (5-dollar bills)

44
Dividing Multiples of 10, 100, 1000 by 1-digit
Numbers

• How many 3s in 21?
• How many 3s in 210?
• How many 3s in 2,100?
• How many 30s in 2,100?

45
Dividing Multiples of 10, 100, 1000 by 1-digit
Numbers

• How many 5s in 50?
• How many 5s in 500?
• How many 5s in 5,000?
• How many 50s in 5,000?
• How many 500s in 5,000?

46
Dividing Multiples of 10, 100, 1000 by 1-digit
Numbers

• How many 7s in 63?
• How many 7s in 630?
• How many 7s in 6300?
• How many 70s in 6300?
• How many 700s in 6300?

47
Independent Practice

• Complete the Extension facts on math journal
  page 173.
• When you have finished, complete the math boxes
  on page 174.

48
Estimating Costs
Lesson 7.7

• Our goal is to determine when an estimate is
  appropriate and to practice making estimates.

How do you estimate costs?
49
Multiplication Mental Math

• 4 x 10
• 4 x 100
• 4 x 100
• 4 x 1,000
• 4 x 10,000
• 4 x 100,000
• 4 x 1,000,000

• 7x 3
• 7x 30
• 7 x 300
• 7 x 3,000
• 7 x 30,000
• 7 x 300,000
• 7 x 3,000,000

• 6 x 5
• 6 x 50
• 6 x 500
• 6 x 5,000
• 6 x 50,000
• 6 x 500,000
• 6 x 5,000,000

50
Division Mental Math

• 15 divided by 3
• 150 divided by 3
• 1,500 divided by 3
• 1,500 divided by 30
• 15,000 divided by 3
• 15,000 divided by 30
• 1,500,000 divided by 3

• 20 divided by 4
• 200 divided by 4
• 2,000 divided by 4
• 2,000 divided by 40
• 20,000 divided by 4
• 20,000 divided by 40
• 2,000,000 divided by 4

51
Math Message

• Pretend you have 6.
• Do you have enough money to buy 4 bags of party
  balloons that cost 1.28 per bag?
• Do you have enough for 5 bags?
• Estimate the answers.
• Check by finding the exact costs.

52
Math Message Follow-Up

• Pretend you have 6.
• Do you have enough money to buy 4 bags of party
  balloons that cost 1.28 per bag?
• Do you have enough for 5 bags?

What cost can you estimate the bags of balloons?
What number model will you use for 4 bags?
What number model will you use for 5 bags?
How close are your estimates to the exact costs?
53
Estimating Costs

• Turn in your student reference book to the
  Stock-Up Sale posters on pages 240 and 241.
• Why are there two prices listed for each item?
• Why do stores lower the price of an item if you
  buy a certain amount?

54
Practice Estimating Costs

• You want to buy 4 cans of tennis balls.
• Estimate their cost.

Use math journal page 175 to solve this problem.
55
Practice Estimating Costs

• You want to buy 3 boxes of tissues.
• Estimate their cost.

Use math journal page 175 to solve this problem.
56
Practice Estimating Costs

• You want to buy 3 packages of batteries.
• Estimate their cost.

Use math journal page 175 to solve this problem.
57
Practice Estimating Costs

• You want to buy 8 ballpoint pens.
• Estimate their cost.

Use math journal page 175 to solve this problem.
58
Practice Estimating Costs

• You want to buy 6 paperback books.
• Estimate their cost.

Use math journal page 175 to solve this problem.
59
Independent Practice

• Complete the Extension facts on math journal
  page 176.
• When you have finished, complete the math boxes
  on page 177.

60
Extended Facts Products of Ten
Lesson 7.8

• Our goal is to multiply multiples of 10 by
  multiples of 10.
• Example 20 x 30

How can you simplify two-digit multiplication?
61
Multiplication Mental Math

• 6 x 10
• 6 x 100
• 6 x 100
• 60 x 1,000
• 6 x 10,000
• 6 x 100,000

• 9x 7
• 9 x 70
• 9 x 700
• 9 x 7,000
• 90 x 7,000
• 9 x 700,000

• 4 x 8
• 4 x 80
• 4 x 800
• 4 x 8,000
• 4 x 80,000
• 4 x 800,000

62
Math Message

• Do problems 1-6 on journal page 178.

How were you able to complete these
problems? Is there a shortcut?
63
Multiples of Ten

• When you know your basic facts you can easily
  multiply by multiples of ten.
• The shortcut is to count the number of zeroes in
  the factors and carry those zeroes over to the
  product.

64
Practice with Multiples of 10

• The Evergreen Landscape Company bought 40
  rosebushes for 30 each. How much did it pay in
  all?

How did you solve this problem?
65
Practice with Multiples of 10

• 10 students each have 50 cents. How many cents
  would there be altogether?

How did you solve this problem?
66
Practice with Multiples of 10

• There are 70 eight-year olds in third-grade. How
  many years old would the group be if you put
  their ages together?

How did you solve this problem?
67
More Multiples of 10

• 40 (20s)
• 30 (70s)
• 20 (100s)
• 60 (20s)
• 40 (80s)

68
Independent Practice

• Complete the remaining problems on math journal
  page 178.
• Complete the math boxes on math journal page
  179.

69
Enrichment (time permitting)

• Baseball Multiplication

70
Exploring Rations and Geometric Figures
Lesson 7.9

• Our goal is to explore similar polygons,
  solving ratio problems, and exploring geometric
  configurations.

What polygons are shown?
71
Mental Math Parentheses Practice

• 103 (67 23)
• (27 8 ) X 2
• 168 (40 X 3 )
• (152 38) 150

Please write your first answer below the
parentheses, so I can check your math.
72
Math Message

• Martha and George were making designs. Marthas
  designs used 9 three-leaf clovers. How many leafs
  did her design have?
• George had 17 leaves. What is the least number
  of three-leaf clovers he needed?

How did you solve this problem?
73
Small Group Polygons

• Working with your group, you need to construct a
  large square using 4 triangles.
• Use 4 large rhombuses to make the same shape.
• Use 4 small rhombuses
• Use 4 trapezoids

74
Practice with Ratios
A ratio is a comparison, where one object equals
a certain amount of another object. What
operation will we be using with ratio problems?

• A farmer is switching from raising cows to
  raising sheep. She estimates that 7 sheep eat as
  much as 1 cow.
• How many cows could she hold if she had 63 sheep?

How did you solve this problem?
75
Independent Ratio Practice

• Complete math masters page 125.
• You will be comparing sheep to cows using the
  same method we just practiced.
• When you are finished, complete the math boxes
  on page 180.

76
Unit 7 Review and Assessment
Lesson 7.10

• Our goal is to review and assess your
  progress on the material covered in Unit 7.

How can you simplify two-digit multiplication?
77
Math Message

• Angela multiplied 60 x 50 and got an answer of
  3,000. Explain how Angela solved the problem.

How did you solve this problem?
78
Slate Assessments

• 5 boxes of crayons. 8 crayons in a box. How many
  crayons in all?
• 4 puppies. 4 legs on each puppy. How many legs in
  all?
• 8 bags of marbles. 9 marbles in each bag. How
  many marbles in all?
• 5 sets of books. 8 books in each set. How many
  books in all?
• 28 jelly beans for 7 children. How many jelly
  beans per child?
• 32 children in the class. 8 tables. How many
  children will sit at each table?
• 85 pennies. 9 children to share them. How many
  pennies per child?

79
Multiplication Mental Math

• 8 x8
• 2 x 9
• 3 x 8
• 8 x 5
• 6 x 6
• 9 x 2

• 4 x 5
• 8 x 5
• 7 x 7
• 7 x 6
• 3 x 7
• 4 x 4

• 5 x 7
• 3 x 3
• 5 x 5
• 4 x 9
• 9 x 7
• 9 x 9

80
Test Review Prep