6th grade - njctl

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6th Grade

Fraction & Decimal Computation

2015-10-20

www.njctl.org

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Fraction and Decimal Computation

· Long Division Review· Adding Decimals· Subtracting Decimals

Click on the topic to go to that section

· Multiplying Decimals· Dividing Decimals· Glossary & Standards

· Fraction Division

· Distributive Property & Product of Decimals

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http://www.njctl.org

http://www.njctl.org

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Fraction and Decimal Computation

· Long Division Review· Adding Decimals· Subtracting Decimals

Click on the topic to go to that section

· Multiplying Decimals· Dividing Decimals· Glossary & Standards

· Fraction Division

· Distributive Property & Product of Decimals

[This object is a pull tab]

Teac

her N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.

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Fraction Division

Return toTable ofContents

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Modeling DivisionRecall from 5th grade:

When we are dividing, we are breaking apart into equal groups.

The model below represents: 8 ÷ 4 = 2

2 groups of 4

Dividend ÷ Divisor = Quotient

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Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.

The same strategy can be applied when dividing with fractions.

Use the model below to demonstrate: 8 ÷ =

8

The pink rectangle represents .

See how many you can fit in the 8 squares.

12

12

12

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Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.

The same strategy can be applied when dividing with fractions.

Use the model below to demonstrate: 8 ÷ =

8

The pink rectangle represents .

See how many you can fit in the 8 squares.

12

12

12


Teac

her N

otes The "half" square is infinitely

cloned and students should "fill" the 8 squares with 16

half squares to show

8 / 0.5 = 16


ExampleUse the model below to demonstrate 2 ÷ =

2

13

13

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1 Evaluate the following problem using the model below.

3

14

3 ÷ =

14

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3

14

3 ÷ =

14


Ans

wer

12



5

12

5 ÷ =

12

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5

12

5 ÷ =

12


Ans

wer

10


A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4

Divide into 4 groups

1 2 3 4

Visual Model

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A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4

Divide into 4 groups

1 2 3 4

Visual Model


Ans

wer

3/5 ÷ 4 = 3/20


The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn?

1 2 3 4

Each friend will receive 3/20 lb. of popcorn.

Word Problem

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(Answer) / 215

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Vocabulary Review

Complex Fraction: A fraction with another fraction in the numerator, denominator or both.

Original Number 4

Reciprocal 2

Reciprocal: The inverse of a number/fraction.

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PatternsDo you notice a pattern between the division of fractions and their solution?

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PatternsDo you notice a pattern between the division of fractions and their solution?


Teac

her N

otes

Discuss Patterns either from model or number sentence.


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If you think about it, we are dividing by a fraction which creates a complex fraction.

You need to eliminate the fraction in the denominator in order to solve the problem.

To do this, multiply the numerator and denominator of the complex fraction by the reciprocal of the denominator (making the denominator = 1).

You can then simplify the fraction by rewriting it without the denominator of 1 and solve the new multiplication problem.

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source - http://www.helpwithfractions.com/dividing-fractions.html

There are rules that can be applied to fraction division problems to eliminate steps from this lengthy procedure.

1 2

x 3 2

= 1 2

2 3

=

1 2

2 3

=

1 2 2 3

x 3 2

x 3 2

=

1 2

x 3 2

1

OriginalProblem

ComplexFraction

Multiply byReciprocal

SimplifyDenominator

RewriteWithout 1

Example

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Algorithm

Step 1: Leave the first fraction the same.

Step 2: Multiply the first fraction by the reciprocal of the second fraction.

Step 3: Simplify your answer.

Dividing Fractions Algorithm

1 5

x 2 1

= 1 x 2 5 x 1

= 2 5

1 5

1 2

=

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http://www.helpwithfractions.com/dividing-fractions/

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Some people use the saying " Keep Change Flip" to help them remember the algorithm.

3 5

x 8 7

= 3 x 8 5 x 7

= 2435

3 5

7 8

=

KeptChanged

FlippedKeepChange

Flip

Dividing Fractions Algorithm

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Checking Your AnswerTo check your answer, use your knowledge of fact families.

35

78

2435

÷ =

35

= 2435

78

x

35 is 7

8of 24

35

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7 )

True

False

8 10

= 5 4

x 8 10

4 5

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7 )

True

False

8 10

= 5 4

x 8 10

4 5


Ans

wer

FALSE


8 )

True

False

2 7

= 3 4

2 7 8

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8 )

True

False

2 7

= 3 4

2 7 8


Ans

wer

FALSE


9 )

3940

8 10

= 4 5

4042

A 1

B

C

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9 )

3940

8 10

= 4 5

4042

A 1

B

C[This object is a pull tab]

Ans

wer

A


10 )

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10 )


Ans

wer


11 )

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(Answer) / 215

Sometimes you can cross simplify prior to multiplying.

without cross simplifying

with cross simplifying

3

1

2

5

Simplify

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12 Can this problem be cross simplified?

Yes

No

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Yes

No


Ans

wer

YES



Yes

No

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Yes

No


Ans

wer

NO



Yes

No

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Yes

No


Ans

wer

NO



Yes

No

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Yes

No


Ans

wer

YES


16 )

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16 )


Ans

wer


17 )

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17 )


Ans

wer


18 )

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18 )


Ans

wer


19 )

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19 )


Ans

wer


A mixed number can be divided by a mixed number using the following visual model.

First find the least common denominator (LCD) which is 6.

If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?

Visual Model

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A mixed number can be divided by a mixed number using the following visual model.

First find the least common denominator (LCD) which is 6.

If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?

Visual Model


Ans

wer

18


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Since our LCD is 6, every 6 lines is considered a whole.

1 1/2 is equivalent to 9 sections on the number line.

1 1/2

2 2/3 is equivalent to 16 sections on the number line.

So 1 1/2 ÷ 2 2/3 = 9/16

2 2/3

Visual Model

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1/2

2 2/3

1 1/2

What if the problem were written as ?

How many times does 1 1/2 divide into 2 2/3?

Visual Model

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Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / 1)

Step 2: Follow the same steps for dividing fractions

Dividing Mixed Numbers Algorithm

6 1

x 2 3

= 12 3

=6 1 2

1 6 1

3 2

= = 4

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5 3

x 2 7

= 1021

2 3

=1 1 2

3 5 3

7 2

=

Example

Evaluate:

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20 )

= 1 2

2 2 3

1

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20 )

= 1 2

2 2 3

1


Ans

wer


21 )

= 1 2

52

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21 )

= 1 2

52


Ans

wer


22 )

= 2 5

5 1 2

4

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22 )

= 2 5

5 1 2

4


Ans

wer


23 )

= 1 2

2 3 8

3

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23 )

= 1 2

2 3 8

3


Ans

wer


Winnie needs pieces of string for a craft project. How many 1/6 yd pieces of string can she cut from a piece that is 2/3 yd long?

16

23 ÷

23

x 61

123 == 4 pieces4

1

or

23

x 61 =

1

241

= 4 pieces

Application Problem

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One student brings 1/2 yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive?

12 ÷ 3

12

x 13

16

yards of ribbon=

Application Problem

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Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut?

6 ÷34

61

÷ 34

61 x 4

3 = 243

81 8 rungs= =

Application Problem

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A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb apiece. How many toy robots are in the box?

9 13

1 16÷

283

76÷

67

283

x

1

4

1

2

= 81

8 robots=

Application Problem

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24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?

A 8 pounds

B 4 1/2 pounds

C 2/5 pounds

D 1/8 pound

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24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?

A 8 pounds

B 4 1/2 pounds

C 2/5 pounds

D 1/8 pound


Ans

wer

D


25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?

A 84 miles

B 62 miles

C 42 miles

D 38 miles

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25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?

A 84 miles

B 62 miles

C 42 miles

D 38 miles


Ans

wer

D


26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?

A 48 tablespoons

B 24 tablespoons

C 12 tablespoons

D 6 tablespoons

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26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?

A 48 tablespoons

B 24 tablespoons

C 12 tablespoons

D 6 tablespoons


Ans

wer

C


27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?

A 5/12 pound

B 2 2/5 pounds

C 8 2/5 pounds

D 86 2/5 pounds

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27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?

A 5/12 pound

B 2 2/5 pounds

C 8 2/5 pounds

D 86 2/5 pounds


Ans

wer

B


28 There is gallon of distilled water in the

class science supplies. If each pair of

students doing an experiment uses

gallon of distilled water, there will be

gallon left in the supplies . How many

students are doing the experiments?

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28 There is gallon of distilled water in the

class science supplies. If each pair of

students doing an experiment uses

gallon of distilled water, there will be

gallon left in the supplies . How many

students are doing the experiments?


Ans

wer


29 Carol makes cups of snack mix. She

puts all the snack mix into plastic bags. She

puts cup of the snack mix in each bag.

How many plastic bags does Carol need?

Enter your answer in the box.

bags

From PARCC EOY sample test non-calculator #9

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29 Carol makes cups of snack mix. She

puts all the snack mix into plastic bags. She

puts cup of the snack mix in each bag.

How many plastic bags does Carol need?


bags



Ans

wer

& M

ath

Prac

tice

14 bags

MP 4

Word problems allow students to recognize math in everyday like and use the math they know to solve problems.


http://practice.parcc.testnav.com/#


30 Part AA group of hikers buy 8 bags of trail mix.

Each bag contains cups of trail mix. The

trail mix is shared evenly among 12 hikers.

How many cups of trail mix will each hiker

receive? Show your work or explain your

answer.

From PARCC PBA sample test calculator #10

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30 Part AA group of hikers buy 8 bags of trail mix.

Each bag contains cups of trail mix. The

trail mix is shared evenly among 12 hikers.

How many cups of trail mix will each hiker

receive? Show your work or explain your

answer.



Ans

wer


31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker

will hike. Show your work or explain your answer.


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31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker

will hike. Show your work or explain your answer.



Ans

wer


32 Part B (continued)· Determine the total number of gallons of

water each hiker will bring. Show your work or explain your answer.


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32 Part B (continued)· Determine the total number of gallons of

water each hiker will bring. Show your work or explain your answer.



Ans

wer





33 This diagram shows a number line.

Part A

James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.


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33 This diagram shows a number line.

Part A

James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.



Ans

wer

The number line diagram show segments marked that are spaces 1/8 unit apart. I know James' board is 3/4 foot long. I counted the number of 1/8 units until I got to 3/4 on the number line. There are 6 of these. So James can cut a total of 6 pieces from the board.


34 Part B

Write an equation using division that represents how James can find the number of pieces he can cut from the board.


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34 Part B

Write an equation using division that represents how James can find the number of pieces he can cut from the board.



Ans

wer


Long Division Review


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Some division terms to remember....· The number to be divided into is known as the dividend

· The number which divides the other number is known as the divisor

· The answer to a division problem is called the quotient

divisor 5 20 dividend

4 quotient

20 ÷ 5 = 420__5

= 4

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When we are dividing, we are breaking apart into equal groups

EXAMPLE 1

Find 132 3

Step 1: Can 3 go into 1, no so can 3 go into 13, yes

4

- 12 1

3 x 4 = 1213 - 12 = 1Compare 1 < 3

3 132

3 x 4 = 1212 - 12 = 0Compare 0 < 3

- 12 0

Step 2: Bring down the 2. Can 3 go into 12, yes

2

4

Click for step 1

Click for step 2

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Step 3: Check your answer.

44 x 3 132

click

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Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.

What place value should we round to?

Round to the largest place value.

357 rounds to ____

15 rounds to ____

Our answer should approximately be ...

20

357 ÷ 15

click

click

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EXAMPLE 2(change pages to see each step)

Step 1: Can 15 go into 3, no so can 15 go into 35, yes

2

-30 5

15 x 2 = 3035 - 30 = 5Compare 5 < 15

15 357

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2

-30 5

15 35715 x 3 = 4557 - 45 =12Compare 12 < 15

7 - 45 12

Step 2 : Bring down the 7. Can 25 go into 207, yes

3


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2

-30 5

15 357.0

7 - 45 120 - 120 0

3

Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division.

15 x 8 = 120120 - 120 = 0Compare 0 < 15

.8


Is our answer close to our estimate?

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Check your answer.

23.8 x 15

357click

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Estimate the following problems. Discuss your answers with your group.

35 300

15 20

click

clickclick

click

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Now solve the following problems. Discuss your answers with your group.

41 324

19.5 23.2

click

click click

click

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35 Estimate the quotient.

779 ÷ 19

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779 ÷ 19


Ans

wer

40


36 Compute.

779 ÷ 19 =

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36 Compute.

779 ÷ 19 =


Ans

wer

41



1,551 ÷ 55

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1,551 ÷ 55


Ans

wer

Approximately 33


38 Compute.

1,551 ÷ 55 =

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38 Compute.

1,551 ÷ 55 =


Ans

wer

28.2



1,288 ÷ 35

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1,288 ÷ 35


Ans

wer

25


40 Compute.

1,288 ÷ 35 =

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40 Compute.

1,288 ÷ 35 =


Ans

wer

36.8


41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.

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41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.


Ans

wer

30


42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?

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42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?


Ans

wer

26


43 Compute.

4706 ÷ 104 =

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43 Compute.

4706 ÷ 104 =


Ans

wer

45.25


44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?

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44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?


Ans

wer

49


45 Compute.

1032 ÷ 24 =

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45 Compute.

1032 ÷ 24 =


Ans

wer

43


46 Compute.

4922 ÷ 92 =

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46 Compute.

4922 ÷ 92 =


Ans

wer

53.5


47 Enter your answer in the box.

34,992 ÷ 81 =


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34,992 ÷ 81 =



Ans

wer

432


Adding Decimals


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page3svg

If you know how to add whole numbers then you can add decimals. Just follow these few steps.

Step 1: Put the numbers in a vertical column, aligning the decimal points.

Step 2: Add each column of digits, starting on the right and working to the left.

Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

Adding Decimals

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When adding or subtracting decimals, always remember to align the decimals vertically...

0.250.250.250.251.00+

Adding Decimals

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When adding or subtracting decimals, always remember to align the decimals vertically...

0.250.250.250.251.00+

Adding Decimals


Mat

h Pr

actic

e

MP 5

Students who struggle to line up the digits correctly for an addition of decimals problem may find it useful to line them up using graph paper. This will help them to choose to use graph paper as a tool to help them solve problems.


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Round to the nearest whole number.

5.1 rounds to ____

1.25 rounds to ____

0.04 rounds to ____

1.99 rounds to ____


8

5.1 + 1.25 + 0.04 + 1.99

click

click

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Now, try this - Don't forget - LINE THEM UP

5.1 + 1.25 + 0.04 + 1.99

5.101.250.041.99+

8.38

You can add a zero as a place holder to help line your numbers up.

Adding Decimals

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TRY THESE.Estimate the following sums in your notebook. Check with the rest of your group.

1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9

3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656

8 + 4 + 0 = 12 3 + 12 + 9 = 24

17 + 3 + 8 = 28 10 + 3 + 5 = 18

click

click

click

click

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TRY THESE.Complete in your notebook then check with the rest of your group.

1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9

8.23 3.178 4.125 12.28 + 0.1189 + 9. 12.4739 24.458

3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656

17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213

click click

click click

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1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9

8.23 3.178 4.125 12.28 + 0.1189 + 9. 12.4739 24.458

3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656

17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213

click click

click click


Mat

h Pr

actic

e MP 1

Remind students to compare their estimates to their exact answers to see if their exact answers make sense.


48 Add the following:

0.6 + 0.55 =

A 6.1

B 0.115

C 1.15

D 0.16

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48 Add the following:

0.6 + 0.55 =

A 6.1

B 0.115

C 1.15

D 0.16[This object is a pull tab]

Ans

wer

C


49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?

A JoanneB Peter

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49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?

A JoanneB Peter


Ans

wer

Joanne is correct because 0.6 rounds to 1 and 0.55 rounds to 1. So the estimation is 2. Peter only looked at the whole number and did not round the decimals.


50 Find the sum.

1.025 + 0.03 + 14.0001 =

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50 Find the sum.

1.025 + 0.03 + 14.0001 =


Ans

wer

15.0551


51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.

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51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.


Ans

wer

$66


52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?

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52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?


Ans

wer

$65.85


53 What is the sum of

12.034 and 0.0104?

A 12.1344

B 12.0444

C 12.138

D 1.20444

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53 What is the sum of

12.034 and 0.0104?

A 12.1344

B 12.0444

C 12.138

D 1.20444 [This object is a pull tab]

Ans

wer

B


54 Estimate the sum.

8.5 + 0.042 + 12.31

A 20B 21C 22D 23

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54 Estimate the sum.

8.5 + 0.042 + 12.31

A 20B 21C 22D 23


Ans

wer

B


55 Find the sum.

8.5 + 0.042 + 12.31 =

A 13.58

B 21.23

C 20.852

D 20.14

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55 Find the sum.

8.5 + 0.042 + 12.31 =

A 13.58

B 21.23

C 20.852

D 20.14


Ans

wer

C


56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?

A .561 cm.B .452 cm.

C .480 cm.

D .473 cm.

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56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?

A .561 cm.B .452 cm.

C .480 cm.

D .473 cm.


Ans

wer

D


57 Find the sum.

5 + 100.145 + 57.8962 + 2.312 =

Slide 105 / 215

57 Find the sum.

5 + 100.145 + 57.8962 + 2.312 =


Ans

wer

165.3532


58 What is the sum of 74.835 and 2.67?



Slide 106 / 215

58 What is the sum of 74.835 and 2.67?




Ans

wer

77.505




Let's go to Cool Math and practice addition.

Cool Math Link

Web Link

Slide 107 / 215

Subtracting Decimals


Slide 108 / 215

If you know how to subtract whole numbers then you can subtract decimals. Just follow these few steps.

Step 1: Put the numbers in a vertical column, aligning the decimal points.

Step 2: Subtract the numbers from right to left using the same rules as whole numbers.

Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

1.1- 0.3

1.1- 0.3

0.8

0 1


Slide 109 / 215

http://www.coolmath.com/prealgebra/02-decimals/decimals-cruncher-addition.html

page3svg


21.7 - 8.21



21.7 rounds to ____

8.21 rounds to ____


14click

click

Slide 110 / 215

What do we do if there aren't enough decimal places when we subtract?

21.7 - 8.21

Don't forget...Line Them Up!

21.7 8.21

What goes here?

21.70 8.2113.49

6111


Slide 111 / 215

TRY THESE.Estimate the following differences in your notebook. Then check with the rest of your group.

1) 8.23 - 0.1189 2) 12.283 - 9.025

3) 17.009 - 8.4 4) 9.999 - 4.5656

8 - 0 = 8 12 - 9 = 3

10 - 5 = 517 - 8 = 9

click click

click click

Slide 112 / 215


1) 8.23 - 0.1189 2) 12.283 - 9.025

8.23 12.283 - 0.1189 - 9.025 8.1111 3.258

3) 17.009 - 8.4 4) 9.999 - 4.5656

17.009 9.999 - 8.4 - 4.5656 8.609 5.4334

click

click

click

click

Slide 113 / 215


1) 8.23 - 0.1189 2) 12.283 - 9.025

8.23 12.283 - 0.1189 - 9.025 8.1111 3.258

3) 17.009 - 8.4 4) 9.999 - 4.5656

17.009 9.999 - 8.4 - 4.5656 8.609 5.4334

click

click

click

click[This object is a pull tab]

Mat

h Pr

actic

e MP 1



59 ) 5 - 0.238 =

Slide 114 / 215

59 ) 5 - 0.238 =


Ans

wer

4.762


60 ) 12.809 - 4 =

Slide 115 / 215

60 ) 12.809 - 4 =


Ans

wer

8.809


61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit?

A $20B $18C $13D $12

Slide 116 / 215

61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit?

A $20B $18C $13D $12


Ans

wer

D


62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit ?

A $37.57

B $12.43

C $13.57

D $12.00

Slide 117 / 215

page96svg

page96svg

page96svg

page96svg

62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit ?

A $37.57

B $12.43

C $13.57

D $12.00


Ans

wer

B


63 ) 1897.112 - 0.647 =

Slide 118 / 215

63 ) 1897.112 - 0.647 =


Ans

wer

1896.465


page96svg

page96svg

page96svg

page96svg

64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?

Slide 119 / 215

64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?


Ans

wer

2.65 seconds


65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo

Slide 120 / 215

65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo


Ans

wer

Timothy is correct but he still has to use decimals instead of whole numbers. He would get the same

estimate for this problem if he rounded to the nearest whole

number.


66 ) 4.1 - 0.094 =

Slide 121 / 215

66 ) 4.1 - 0.094 =


Ans

wer

4.006


67 ) 17 - 13.008 =

Slide 122 / 215

67 ) 17 - 13.008 =


Ans

wer

3.992


68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths?

A 27.85 - 12.91B 14.17 - 8.2C 7.9 - 3.88D 21.25 - 18.16

Slide 123 / 215

68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths?

A 27.85 - 12.91B 14.17 - 8.2C 7.9 - 3.88D 21.25 - 18.16


Ans

wer

D


69 If you buy two movie tickets for $8.25 each, what will your change be from $20?

Slide 124 / 215

69 If you buy two movie tickets for $8.25 each, what will your change be from $20?


Ans

wer

$3.50


Cool Math Link

Let's go to Cool Math and practice subtraction.

Web Link

Slide 125 / 215

The Distributive Property and

the Product of Decimals


Slide 126 / 215

If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps.

Step 1: Ignore the decimal points.

Step 2: Multiply the numbers using the same rules as whole numbers.

Step 3: Count the total number of digits to the right of the decimal point. Put that many digits to the right of the decimal point in your answer.

Multiplication

Slide 127 / 215

http://www.coolmath.com/prealgebra/02-decimals/decimals-cruncher-subtraction.htm

page3svg

Evaluate 200 x 41.5

8,300

We can also use the distributive property to calculate the product.

200 x 41.5

200 x (41 + 0.5)

(200 x 41) + (200 x 0.5)

8,200 + 100 = 8,300

Separate 41.5 into an addition expression with two addends

Apply the distributive property

Apply the order of operations

click

Distributive Property

Slide 128 / 215

Evaluate 200 x 41.5

8,300

We can also use the distributive property to calculate the product.

200 x 41.5

200 x (41 + 0.5)

(200 x 41) + (200 x 0.5)

8,200 + 100 = 8,300

Separate 41.5 into an addition expression with two addends

Apply the distributive property

Apply the order of operations

click



Mat

h Pr

actic

e MP 7

The use of the distributive property will help students to see the structure of the problem.


Evaluate 400 x 18.33

400 x ( ________ + ________ )

(400 x ________ ) + (400 x ________ )

________ + ________ = ________7332

This method is known as partial products.


Slide 129 / 215

page174svg

page174svg

How can we use partial products to calculate the area of the rectangle shown below?

58 ft

200 ft

0.6 ft200 x 58.6

200 x ( ________ + ________ )

(200 x ________ ) + (200 x ________ )

________ + ________ = ________11,720

Click to reveal

58.6 ft

200 ft


Slide 130 / 215

How can we use partial products to calculate the area of the rectangle shown below?

58 ft

200 ft

0.6 ft200 x 58.6

200 x ( ________ + ________ )

(200 x ________ ) + (200 x ________ )

________ + ________ = ________11,720

Click to reveal

58.6 ft

200 ft



Teac

her N

otes

Click on the yellow box to show the visual

representation of partial products.


70 ) 12(43) = 12(40) x 12(3)

TrueFalse

Slide 131 / 215

70 ) 12(43) = 12(40) x 12(3)

TrueFalse


Ans

wer

FALSE


71 Use the distributive property to rewrite the expression.

3(76.8) Students type their answers here

Slide 132 / 215

71 Use the distributive property to rewrite the expression.

3(76.8) Students type their answers here


Ans

wer

3(76 + 0.8)


72 Calculate the product using partial products.

5(48)

Slide 133 / 215


5(48)


Ans

wer

240



13(5.2)

Slide 134 / 215


13(5.2)


Ans

wer

67.6



300(7.4)

Slide 135 / 215


300(7.4)


Ans

wer

2,220



200(6.5)

Slide 136 / 215


200(6.5)


Ans

wer

1,300


76 Calculate the area of the rectangle using partial products.

300units

43.9 units

Slide 137 / 215

76 Calculate the area of the rectangle using partial products.

300units

43.9 units


Ans

wer

13,170


Multiplying Decimals


Slide 138 / 215

Convert the following decimal numbers into fractions.

0.7 x 0.09

What is the product?

631000

We multiplied seven tenths by nine hundredths.What place value will the last digit in the product be in if we convert it into a decimal number?

Thousandths

click

click

Multiplication

Slide 139 / 215

page3svg

Try These!What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first.

Fractions Product Place Value

1) 0.3 x 0.7

2) 0.2 x 0.13

3) 0.08 x 0.231

Slide 140 / 215

Do you notice a pattern for multiplying decimals?

3.5 x 1.72

3 510 1 72

100x

3510

x 172100

60201000

Where does the decimal point go? Drag the decimal point.

6 0 2 0

Multiplication

Slide 141 / 215

If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps.

Step 1: Ignore the decimal points.

Step 2: Multiply the numbers using the same rules as whole numbers.

Step 3: Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer.

Multiplication

Slide 142 / 215

3.21x .04

.1284

There are a total of four digits to the right of the decimal points.

There must be four digits to the right of the decimal point in the answer.

} 2 digits

Multiplication

} 2 digits

Slide 143 / 215

Estimate Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.

23.2 x 4.04



23.2 rounds to ____

4.04 rounds to ____


92click

click

Slide 144 / 215

23.2x 4.04

928

92800 0000

93.728

} 1 digit

There are a total of three digits to the right of the decimal points.

There must be three digits to the right of the decimal point in the answer.

Estimating helps us recognize where the decimal point belongs!

Exact Answer

} 2 digits

Slide 145 / 215

Estimate your answer for the following problem by rounding the numbers to the nearest whole number.

9.5 x 0.05

9.5 rounds to _____

0.05 rounds to _____

What is your estimate?

For problems like these, use your number sense!

You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5.

So your answer must be smaller than 9.5!click

Estimate Your Answer

Slide 146 / 215

smallerthan 3.214

TRY THESE.Estimate the following products in your notebook then check with the rest of your group.

1) 14.512 2) 8.31 x 4.21 x 1.008

3) 7.0045 4) 3.214 x 5.2 x 0.0034

15 x 4 = 60 8 x 1 = 8

7 x 5 = 35

click

clickclick

click

Slide 147 / 215


1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552

3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340

66480000

00000831000

8.37648

1285696420

0.0109276

click

click

click

click

Slide 148 / 215


1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552

3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340

66480000

00000831000

8.37648

1285696420

0.0109276

click

click

click

click


Mat

h Pr

actic

e MP 1



77 Estimate the product.

0.42 x 0.032

A The product will be less than 1B The product will be equal to 1C The product will be greater than 1

Slide 149 / 215

77 Estimate the product.

0.42 x 0.032

A The product will be less than 1B The product will be equal to 1C The product will be greater than 1


Ans

wer

A


78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.

TrueFalse

Slide 150 / 215

78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.

TrueFalse


Ans

wer

False


79 Multiply 0.42 x 0.032

Slide 151 / 215

79 Multiply 0.42 x 0.032


Ans

wer

0.1344


80 Multiply 3.452 x 2.1

Slide 152 / 215

80 Multiply 3.452 x 2.1


Ans

wer

7.2492


81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?

Estimate to determine your answer. Do not solve.

YesNo

Slide 153 / 215

81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?

Estimate to determine your answer. Do not solve.

YesNo


Ans

wer

NO


82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?

Slide 154 / 215

82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?


Ans

wer

$5.22


83 Multiply 53.24 x 0.089

Slide 155 / 215

83 Multiply 53.24 x 0.089


Ans

wer

4.73836


84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.

What would the total cost be of four pairs

of jeans on sale?

A $119.96B $90.00

C $86.00

D $52.49

Slide 156 / 215

84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.

What would the total cost be of four pairs

of jeans on sale?

A $119.96B $90.00

C $86.00

D $52.49


Ans

wer

B


85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?

A 2B 3C 4D 5

Slide 157 / 215

85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?

A 2B 3C 4D 5


Ans

wer

D


86 Multiply 4.0156 x 7.8

Slide 158 / 215

86 Multiply 4.0156 x 7.8


Ans

wer

31.32168


87 Multiply 0.012 x 0.21

Slide 159 / 215

87 Multiply 0.012 x 0.21


Ans

wer

0.00252



18.3 x 4.39 =


Slide 160 / 215



18.3 x 4.39 =



Ans

wer

80.337


89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.

How much profit, in dollars, will Thomas earn if he sells all the bottles of water?


$


Slide 161 / 215

89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.

How much profit, in dollars, will Thomas earn if he sells all the bottles of water?


$



Ans

wer

& M

ath

Prac

tice

$22.31

MP 2

Make sure to also check that the students have used good reasoning habits and can show an understandable representation of the problem solved.





Dividing Decimals


Slide 162 / 215

Divide Decimals by Whole Numbers

56.08

28 04

2

Step 1: Use long division.

Step 2: Bring the decimal point up into the quotient.

Slide 163 / 215

Try This!

12.45 ÷ 5 =

Slide 164 / 215

page3svg

Try This!

12.45 ÷ 5 =


Ans

wer

2.49


The Power of Ten10

Multiplying by a power of ten makes dividing by decimals easier!

1) 13 x 10 = _______

2) 94 x 100 = _______

3) 28 x 1000 = _______

4) 6.2 x 10 = _______

5) 4.78 x 100 = _______

6) 51.293 x 1000 = _______

Do you see a pattern for multiplying by a power of ten?

The decimal point moves to the right depending on the number of zeros in the power of ten!Click to

Reveal

Slide 165 / 215

The Power of Ten10

Multiplying by a power of ten makes dividing by decimals easier!

1) 13 x 10 = _______

2) 94 x 100 = _______

3) 28 x 1000 = _______

4) 6.2 x 10 = _______

5) 4.78 x 100 = _______

6) 51.293 x 1000 = _______

Do you see a pattern for multiplying by a power of ten?

The decimal point moves to the right depending on the number of zeros in the power of ten!Click to

Reveal


Mat

h Pr

actic

e MP 8

Noticing the pattern when multiplying by a power of ten will help students to understand the algorithm for multiplication of decimals.


Divisor Dividend

Step 1: Change the divisor to a whole number by multiplying by a power of 10.

Step 2: Multiply the dividend by the same power of 10.

Step 3: Use long division.

Step 4: Bring the decimal point up into the quotient.

Divide by Decimals

Quotient

Slide 166 / 215

15.6 6.24

Multiply by 10, so that 15.6 becomes 1566.24 must also be multiplied by 10

156 62.4

.234 23.4

Multiply by 1000, so that .234 becomes 23423.4 must also be multiplied by 1000

234 23400

Try rewriting these problems so you are ready to divide!

Power of Ten

Slide 167 / 215

6789.2109

415 25020

Rewrite each problem after multiplying by a power of 10.

1)

2)

3)

4)

250.2 ÷ 4.15

.008

0.9

68.342 ÷ 2.2

4.2

678.921

4200008

22 683.42

Power of Ten

click

click

click

click

Slide 168 / 215

page93svg


23.2 ÷ 4.04



23.2 rounds to ____

4.04 rounds to ____


5click

click

Slide 169 / 215

4.04 23.2

Try This! Be sure to round your answer to the thousandths.

5.743click

Slide 170 / 215


9.5 ÷ 0.05

9.5 rounds to _____




If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5?

Your answer must be greater than 9.5!click

Estimate

Slide 171 / 215


9.5 ÷ 0.05

9.5 rounds to _____




If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5?

Your answer must be greater than 9.5!click

Estimate


Mat

h Pr

actic

e MP 6

This standard is addressed when you ask the students if they will get a quotient smaller or greater than 9.5


90 Divide

0.78 ÷ 0.02 =

Slide 172 / 215

90 Divide

0.78 ÷ 0.02 =


Ans

wer

39


91 Use estimation to figure out if the quotient will be

A less than 4.866

B around 4.866

C greater than 4.866

4.866 ÷ 0.6

Slide 173 / 215

91 Use estimation to figure out if the quotient will be

A less than 4.866

B around 4.866

C greater than 4.866

4.866 ÷ 0.6


Ans

wer

C


92

0.6 4.866

Slide 174 / 215

92

0.6 4.866


Ans

wer

8.11


93 ) 10 divided by 0.25 =

Slide 175 / 215

93 ) 10 divided by 0.25 =


Ans

wer

40


94 ) 12.03 ÷ 0.04 =

Slide 176 / 215

94 ) 12.03 ÷ 0.04 =


Ans

wer

300.75


95

0.012 24.6

Slide 177 / 215

95

0.012 24.6


Ans

wer

2050


96 Estimate.

36 ÷ 1.2

Slide 178 / 215

96 Estimate.

36 ÷ 1.2


Ans

wer

36


97 Evaluate.

36 ÷ 1.2 =

Slide 179 / 215

97 Evaluate.

36 ÷ 1.2 =


Ans

wer

30


98 Estimate.

9.116 ÷ 2.12

Slide 180 / 215

98 Estimate.

9.116 ÷ 2.12


Ans

wer

4.5


99 Evaluate.

9.116 ÷ 2.12 =

Slide 181 / 215

99 Evaluate.

9.116 ÷ 2.12 =


Ans

wer

4.3



33.8 ÷ 32.5 =

From PARCC EOY sample test #2 non-calculator

Slide 182 / 215


33.8 ÷ 32.5 =

From PARCC EOY sample test #2 non-calculator


Ans

wer

1.04


There are two types of decimals - terminating and repeating.

A terminating decimal is a decimal that ends.All of the examples we have completed so far are terminating.

A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern.

To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded.

Terminating and Repeating

Slide 183 / 215



page94svg

page95svg

Let's consider the following...

Click to Reveal

Terminating or Repeating

Slide 184 / 215

Let's consider the following...

Click to Reveal

Terminating or Repeating


Teac

her N

otes

Explain how this is a repeating decimal and how

we put a bar over the numbers that repeat.


63 48 45 39 36 32 27 51 45 60 54 6

Click to Reveal

Repeating Example

Slide 185 / 215

6600 2342 2200 14200 13200 10000 8800 12000 11000 10000 8800 12000 11000

Click to Reveal

Repeating Example

Slide 186 / 215

101 ) 15.5 ÷ 0.3

Slide 187 / 215

101 ) 15.5 ÷ 0.3


Ans

wer


102 ) 0.8 ÷ 0.003 =

Slide 188 / 215

102 ) 0.8 ÷ 0.003 =


Ans

wer


103 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy?

Slide 189 / 215

103 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy?


Ans

wer 5.571

gallons


104 ) 25 ÷ 1.1 =

A 2.27B 22.73C 22.7D 22.72

Slide 190 / 215

104 ) 25 ÷ 1.1 =

A 2.27B 22.73C 22.7D 22.72


Ans

wer

D


105

Slide 191 / 215

105


Ans

wer


106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person.

Slide 192 / 215

page78svg

page78svg

106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person.


Ans

wer

155.26 pounds


107 ) 0.007 ÷ 0.9 =

Slide 193 / 215

107 ) 0.007 ÷ 0.9 =


Ans

wer


page78svg

page78svg

108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?

Slide 194 / 215

108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?


Ans

wer

0.647 lbs


109

Slide 195 / 215

109


Ans

wer


110 ) 91.84 ÷ 4.8 =

Slide 196 / 215

110 ) 91.84 ÷ 4.8 =


Ans

wer


111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?

Slide 197 / 215

111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?


Ans

wer

102.65o F


112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?

Slide 198 / 215

112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?


Ans

wer

$5.00


113 ) 9 ÷ 0.22

A 40.9B 40.90C 40.91D 40.9

Slide 199 / 215

113 ) 9 ÷ 0.22

A 40.9B 40.90C 40.91D 40.9


Ans

wer

B


Glossary & Standards

Return to Table of Contents

Slide 200 / 215

Glossary & Standards

Return to Table of Contents


Teac

her N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.


Algorithm

A step-by-step process to find a solution.

It's like a cooking

recipe for mathematics.

24 + 12 =Add the ones

then add the tens

How to...Step 1:Step 2:Step 3:

Back to

Instruction

Slide 201 / 215

page3svg

page3svg

page114svg

Average

3 + 4 + 2 = 9

= 9 3 = 3

The value/amount of each item when the total is distributed

across each item equally.

Back to

Instruction

Slide 202 / 215

Back to

Instruction

A fraction whose numerator or denominator or both contain fractions.

315

15

23= 3 1

5 = 15

23

15

23

Must be written as a fraction.

Complex Fraction

Slide 203 / 215

Used to make operations with fractions easier. Divide the numerator of one fraction and the denominator of another fraction by their GCF.

15

1520+

=3201+1

51520+

1

3

GCF of 5 and 15 is 5.

Back to

Instruction

Cross Simplify

Slide 204 / 215

page110svg

page75svg

page123svg

Back to

Instruction


5

(3 + 2)3

3x5=3(3+2)2(3+4)=(2x3)+(2x4)

23 4

a(b+c)=ab+ac

Multiplying a sum by a number is the same as multiplying each addend in the sum by the

same number and then adding the products.

a(b-c)=ab-ac

also applies to subtraction

Slide 205 / 215

Dividend

24 ÷ 8 = 32483

248 = 3

Dividend Dividend

Dividend

The number being divided in a division equation.

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Instruction

Slide 206 / 215

Divisor

2483 25

8 = 3R1

Divisor Divisor

The number the dividend is divided by. A number that divides

another number without a remainder.

Must divide evenly.

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Instruction

24 ÷ 8 = 3

Slide 207 / 215

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Instruction

101 10=

Power of 10

Any integer powers of the number ten. (Ten is the base, the exponent is the power.)

102 100= 103 1,000=

10x10 =10 = 10x10x10 =

Slide 208 / 215

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Instruction

ProfitThe difference between the amount

earned and the amount spent.

EarnedSpentProfit

-______$30 Washing

Cars

$12-______

$18Supplies

Profit

Slide 209 / 215

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Instruction

Quotient

The number that is the result of dividing one number by another.

12 ÷ 3 = 4Quotient 12

4 3

Quotient 12 4 3 =Quotient

Slide 210 / 215

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Reciprocal

One of two numbers whose product is one.

1 x 1 = 11 is the

reciprocal of 1.

2 x 12 = 1

Number

Reciprocal

r x r = 1

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Instruction

Slide 211 / 215

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Instruction

Repeating Decimal

A decimal with a digit or group of digits that repeats endlessly.

3 1.0.3

9-___1

30

0___9-

1

03

09___-1

...

13

= .3__ 7

33= .21

__

(.212121...)

Slide 212 / 215

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Instruction

Terminating Decimal

A decimal that ends and doesn't go on forever.

3 1.0.3

9-___1

30

0___9-

1

03

09___-1

...

1/2 = .5 3/8 = .375

Slide 213 / 215

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Instruction

Vertical

In an up-down position.ve

rtic

al

horizontaldiagonal

Slide 214 / 215

Standards for Mathematical Practice

MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.

Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.

If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

Slide 215 / 215

Standards for Mathematical Practice

MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.

Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.

If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.


Mat

h Pr

actic

e


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6th grade - njctl

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