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Multiplication and Division

- Everyday Mathematics
- Unit 7
- Mr. Brumfield

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

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?

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

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

Math Message

- Turn to page 161 in your new math journal and

find the products in exercises 1-10.

What are products?

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

Square Numbers

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

Link to Smart notebook Square Number Matching

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.

Remember the Multiplication Fact Chart?

How does this work?

Independent Practice

- Complete the Product Patterns on math journal

page 161. - When you have finished, complete the math boxes

on page 162.

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?

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?

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?

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.

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.

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

Independent Practice

- When you have finished, complete the math boxes

on page 164.

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?

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

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?

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!!!

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.

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?

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 _______________

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?

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.

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?

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.

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.

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.

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.

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?

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?

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.

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?

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

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.

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?

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?

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?

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.

Lets Practice!

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

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?

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?

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?

Independent Practice

- Complete the Extension facts on math journal

page 173. - When you have finished, complete the math boxes

on page 174.

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?

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

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

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.

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?

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?

Practice Estimating Costs

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

Use math journal page 175 to solve this problem.

Practice Estimating Costs

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

Use math journal page 175 to solve this problem.

Practice Estimating Costs

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

Use math journal page 175 to solve this problem.

Practice Estimating Costs

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

Use math journal page 175 to solve this problem.

Practice Estimating Costs

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

Use math journal page 175 to solve this problem.

Independent Practice

- Complete the Extension facts on math journal

page 176. - When you have finished, complete the math boxes

on page 177.

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?

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

Math Message

- Do problems 1-6 on journal page 178.

How were you able to complete these

problems? Is there a shortcut?

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.

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?

Practice with Multiples of 10

- 10 students each have 50 cents. How many cents

would there be altogether?

How did you solve this problem?

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?

More Multiples of 10

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

Independent Practice

- Complete the remaining problems on math journal

page 178. - Complete the math boxes on math journal page

179.

Enrichment (time permitting)

- Baseball Multiplication

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?

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.

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?

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

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?

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.

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?

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?

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?

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

Test Review Prep

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