December 10, 2015

Unit Two - Operations with decimals

December 10, 2015

Unit Two - Operations with Decimals

Place Value

Introduction (or re-introduction) to place value

Read the following numbers (properly!)

145

2.35

1 567 043.793

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ones

1

tens

10

hund

reds

100

tent

hs

0.1

hund

redt

hs

0.01

thou

sand

ths

0.001

thou

sand

s1000

ten-

thou

sand

s

10,000

ten-

thou

sand

ths

0.0001

hund

red

thou

sand

s

100,000

mill

ions

1,000,000 Place Value

December 10, 2015

Place Value

The value of a digit is based on its place in a number. This is known as its place value.

Place Value Chart

thousandths

ten thousandths

hundred thousandths

millions

decimal point

ones

tenths

hundredths

tenths

hundredths

thousandths

ten thousandths1,356,426.7142 Ex

ampl

e

The place value of the digit 6 in the number 1234.5679 is hundredths.

Teac

her's

Not

es

1. Explain the concept of place value of a digit in a number.

2. Explain the place value of each digit in the given place value chart.3. Cite some more examples for the students to practice.

December 10, 2015

3.085 →

1,085.06 →

To write a number in expanded notation, take each digit times its place-value, then add the pieces together. For zeros in the number, just skip over those place

values, you don’t need to write them.

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Write the number in expanded notation

12.25

308.4

2400.0542 x 1000 + 4 x 100 + 5 x 0.01 + 4 x 0.001

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Write the number in standard form.(3 x 1) + (2 x 0.1) + (2 x 0.01)

(4 x 100) + (1 x 1) + (6 x 0.001) + (3 x 0.0001)

(6 x 10) + (7 x 1) + (3 x 0.1) + (9 x 0.001)

December 10, 2015

Standard Form ↔ WordsTo write a number in words:• say the whole number part• say AND in place of the decimal• say the decimal part, finishing with the place value where the number ends.

13.28 ⇒

0.405 ⇒

3.007 ⇒

Click to hear number said in words.

9.075 ⇒

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Going from words to standard (number) form:

Ex: Three hundred sixteen and fifteen thousandths

316.015

Tells you where the decimal part ends

thirty-four and sixteen hundredths

one hundred twenty-two thousandths

eleven and three hundredths

34.160.122

11.03

December 10, 2015

Match the number in standard form and in words.

1

6

5

4

3

2

Click on a number to hear it said in words.

31850.45

0.318

0.9099.09

5.045

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Drag the numbers to the right to reveal the number in words.

44.04 forty-four and four hundredths

4.404 four and four hundred four thousandths

440.4 four hundred forty and four tenths

0.46 forty-six hundredths

0.046 forty-six thousandths

4.6 four and six tenths

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December 10, 2015

December 10, 2015

Round off to Number of Digits

Round off the number 56.782398 to three decimal places.

5 6 . 7 8 2 3 9 8

Teac

her's

Not

es

1. Explain the reasons to round off decimal numbers. We round off decimal numbers to: Avoid repetitive decimals. Make it easy to calculate. Delete the irrelevant number of digits (For example, third decimal digit has little value in amounts expressed in dollars).

2. Explain how to round off values to a specified number of places.3. Ask a student to count three decimal digits and circle the fourth digit.4. Call another student to check if the circled digit is more than or equal to 5. If so, tell him or her to add one to the third decimal digit to get the correct answer as 56.7825. Cite more examples for the students to practice.

December 10, 2015

Activity

Write the correct round off values of pi (3.1415927) to the specified number of digits.

0 decimal digits

1 decimal digit2 decimal digits

3 decimal digits

4 decimal digits5 decimal digits

6 decimal digits

Cor

rect

Ans

wer

Teac

her's

Not

es

1. Call six students one-by-one to write the value of pi to the number of decimal digits in each column.2. Congratulate the students who write the correct answers.3. Pull the Correct Answer box, if required.4. You may try the same activity with other decimal numbers too.

December 10, 2015

Select the correct answer.

Check Your Understanding

1 Round off the number 384.225 to two decimal points.

A 384.20

B 384.22

C 384.23

D 384.25

December 10, 2015

Round off to Place Values

In the year 2009, the population of the state of New York stood at 19,541,453.Round off the population to its nearest thousands.

1 9 , 5 4 1 , 4 5 3Teac

her's

Not

es

1. Explain how to round off values to the nearest place value.2. Ask a student to circle the digit in the hundreds place.3. Call another student to check if the circled number is more than or equal to 5. 4. If so, tell him or her to add one to the digit in the thousands place and rewrite the other digits on the right side as zeroes to get the correct answer as 19,541,000.5. Cite more examples for the students to practice.

December 10, 2015

Activity

Round off the number 78956.34854 to:

Thousands

HundredsTens

Ones

TenthsHundredths

Thousandths

Cor

rect

Ans

wer

Teac

her's

Not

es

1. Call seven students one-by-one to write the round off value nearest to the given place value.2. Congratulate the students who write the correct answers.3. You may try the same activity with other decimal numbers too.

December 10, 2015

Estimating with Decimals

Why would we need to estimate?

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0.0167 0.015 0.0105 0.018 0.013

Place the decimals on the number line

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Which of the decimals round to 0.02?

0.01670.0105

0.0180.013 0.015

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0.009

0.009 0.010 0.011

Place the decimals on the number line

0.00950.009450.0104 0.0107

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0.009

0.009 0.010 0.011

Which of the decimals round to 0.01?

0.0095

0.00945

0.0104

0.0107

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20

100

50

0.9

0.003

101.34

53.973

0.9234

0.0027

17.6

Round to the highest place value

?

?

?

?

?highest place value

December 10, 2015

25.89 + 12.27 + 9.704

0.043 + 0.057 + 0.099

0.00095 + 0.578 + 0.063

+ + =

+ + =

+ + =

Use rounding to estimate these sums

30 + 10 + 10 = 50

0.04 + 0.06 + 0.1 = 0.2

0.001 + 0.6 + 0.06 = 0.661

December 10, 2015

86.89 - 9.532

0.894 - 0.25

0.078 - 0.021 - 0.0099

- =

- - =

- =

Use rounding to estimate differences

90 - 10 = 80

0.9 - 0.3 = 0.6

0.08 - 0.02 - 0.01 = 0.05

December 10, 2015

Homework

Complete the Estimating side of the worksheet

December 10, 2015

Adding and Subtracting Decimals

December 10, 2015

How to Add and Subtract Decimals:

Adding Decimals

The key is to line up all the decimal points in a vertical line.

Subtracting Decimals

45.123.71_____+

48.83

48.183.01

45.17

December 10, 2015

Adding Decimals

10.3427.5645.33+

10 + 27 + 45 = 70 + 12 = 820.34 + 0.56 + 0.33 = 1.1 + 0.13 = 1.23 82 + 1.23 = 83.23

9.0816.99+

9 + 16 = 250.99 + 0.08 = 1.0725 + 1.07 = 26.07

December 10, 2015

9.09

8.32

8.7

9.53

What was Courtney's total score?

How much more did she score on the beam than the floor?

December 10, 2015

December 10, 2015

Homework

p 48-51Complete any 10 questions (1 a.b.c counts as one question)

Worksheet - adding and subtracting decimals

December 10, 2015

Working with powers of tenMultiplying Decimals

1 000 000100 00010 0001 0001001010.10.010.0010.00010.0001

December 10, 2015

Review: Multiplying Whole Numbers by 1, 10, 100, and 1,000.

36 x 1 =

36 x 10 =

36 x 100 =

36 x 1,000 =

36

360

3,600

36,000

2 x 1 = 2

2 x 10 = 20

2 x 100 = 200

2 x 1,000 = 2,000

Click on each black dot to reveal answers to the problems in the second column.

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

0.0007 x 1 =

0.0007 x 1,000 =

0.0007 x 10 =

0.0007 x 100 =

0.007

0.07

0.7 The decimal point moves 3 places to the right.0.71 2 3

The decimal point moves 2 places to the right.0.071 2

The decimal point moves 1 place to the right.0.0071

0.00070.0007 The decimal point stays in the same place.

Click on each problem's answer to see the pattern.

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

0.521 x 1 =

Click on each black dot to reveal the answer for the problems.

0.521 x 1,000 =

0.521 x 100 =

0.521 x 10 =

0.521

5.21

52.1

521

The decimal point stays in the same place.

The decimal point moves right 1 place.

The decimal point moves right 2 places.

The decimal point moves right 3 places.

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

0 0 0 0 2 x 10Help Deci the Frog jump the correct number of lily pads and reveal the answer!

0.002Answer

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

0 3 2 x 100Help Deci the Frog jump the correct number of lily pads and reveal the answer!

32Answer

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

3 0 1 6 8 x 1000Help Deci the Frog jump the correct number of lily pads and reveal the answer!

3,016.8Answer

December 10, 2015

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

3.5 x 1 =

3.5 x 1,000 =

3.5 x 100 =

3.5 x 10 =

3.5

35

350

3,500

The decimal point stays in the same place.

The decimal point moves right 1 place.

1 zero must be added as a place holder.

2 zeroes must be added as place holders.

Sometimes you must add zeroes to the end as place holders!

00

0

Click on each black dot to reveal the answer for the problems.

December 10, 2015

Answer

70,160

0 7 0 1 6 x 1000Draw Deci's path and then move Deci to the lily pad to check your answer.

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

December 10, 2015

Answer

0

40

0 4 x 100Draw Deci's path and then move Deci to the lily pad to check your answer.

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

December 10, 2015

Move the decimal point to the correct postion and then click on Deci to check your answer!

Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000.

0.542 X 10 = 0 5 4 2

$6.75 x 100 = $6 7 5

You may need to add zeroes as placeholders.

1000 x 0.5 = 0 5

5.42

$675

500

December 10, 2015

Decimals

Continue the pattern with decimal powers of ten.

December 10, 2015

Multiplying Decimals

Use estimation to help determine if your answers are correct.

December 10, 2015

0.8

x

X 0.2

=

= n

Modeling Decimal Multiplicationexample

What decimal represents the part of the whole that is orange?

0.16Click herefor theanswer

Click herefor theanswer

December 10, 2015

0.28

22 0.6 x 0.5 =

33 0.1 x 0.9 =

44 0.8 x 0.3 =

11 0.4 x 0.7 =

Modeling Decimal Multiplication

0.30

0.09

0.24

pull for problem

December 10, 2015

Guided Practice

4 x 0.5 = _____

9 x 0.2 = _____

6 x 0.23 = _____

1.8

2.0

1.38

SolutionSolution

SolutionSolution

SolutionSolution

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=

= n3 x 0.4

n = 1.20SolutionSolution

Multiply Decimals by Whole Numbersexample

December 10, 2015

6.4x 5

6x 5 30

PullPull

0.989x 27

1x 27 27

PullPull

Estimate Decimal Products

To estimate decimal products, round each factor to the first

significant (non-zero) digit or nearest whole number.

(Pull for examples)

Estimating the product can help you correctly

position the decimal point in the product.

PullPull

Position the decimal point show a reasonable the product.

.

December 10, 2015

The number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

3.

Hit th

e bull

's ey

eMultiplying when one or more of the

factors is a decimal number is like

multiplying with whole numbers.

Multiply Decimals

9.01x 6.8 72085406061 268

Remember!You can use your estimate to check your decimal placement in the product.

December 10, 2015

Using Decimal Multiplication

The average lab rat weighs 0.425 kilogram. If there are 15 rats in the lab, how much do they weigh altogether?

The Boston Marathon is about 26 miles. A mile is equal to 1.609 kilometers. How many kilometers does a runner who completes the race run?

work space

work space

6.375

41.834

SolutionSolution

SolutionSolution

December 10, 2015

How to Multiply Decimals:

Multiply decimals just as if they were whole numbers.

3.772.8

3016754

10.556

x _____

_____+

Click beside 3.77 to place the decimal point.

(2 decimal places)

(1 decimal place)

(3 decimal places)10 556

Click me to check the product.

December 10, 2015

x =

x x =

0.073 x 0.375

x =

9.56 x 0.345

0.019 x 0.67 x 0.97

Use rounding to estimate products

10 x 0.3 = 3

0.07 x 0.4 = 0.028

0.02 x 0.7 x 1 = 0.014

December 10, 2015

0.013 x 0.232

97.04 x 27.25

0.352 x 27.1

Use rounding to choose the most reasonable answer

9.5392 95.3920.95392

2,644.34 26,443.4264.434 264,434

953.92

0.3 x 30

100 x 30

0.0003016 0.03016 0.30160.003016

0.01 x 0.2 = 0.0020.003016

2,644.34

9.5392

December 10, 2015

Practice Multiplying

.076x___

.056

.0076x___

.6x 7___

.9

.06x___.8.07x___

December 10, 2015

Content/writing space

December 10, 2015

Content/writing space

December 10, 2015

Content/writing space

December 10, 2015

Content/writing space

December 10, 2015

Homework

p 58 # 9 - 12, 17, - 20

December 10, 2015

Dividing Decimals

December 10, 2015

Dividing with powers of ten

December 10, 2015

December 10, 2015

1. Dividing a Decimal Number by a Whole Number

To divide a decimal number by a whole number:

• Use Long Division (ignoring the decimal point)

• Then put the decimal point in the same spot as the dividend (the number being divided)

December 10, 2015

Example: Divide 9.1 by 7

Ignore the decimal point and use Long Division:

137 )91 9 7 21 21 0

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Practice

December 10, 2015

Put the decimal point in the answer directly

above the decimal point in the dividend:

1.37 )9.1The answer is 1.3

December 10, 2015

2. Dividing by a Decimal NumberBut what if you want to divide by a Decimal Number?The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:

Now you are dividing by a whole number, and can continue as normal.It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.

December 10, 2015

Example 2: Divide 5.39 by 1.1You are not dividing by a whole number, so you need to move the decimal point so that you are dividing by a whole number:

move 1 1.1115.39

53.9move 1

December 10, 2015

Since you have to move the decimal 1 time to the right so that 1.1 no longer has a decimal, you must also move the decimal in 5.39 once to the right. You are now dividing by a whole number, so you can proceed:Ignore the decimal point and use Long Division: 04911 )539 5 0 53 44 99 99 0

December 10, 2015

Put the decimal point in the answer directly above the decimal point in the dividend:

04.911 )53.9The answer is 4.9

December 10, 2015

How to Divide Decimals:

16.9 6.5 6.5 16.9

Study this example:

Move the decimal in the divisor to the right to make a whole number. Move the decimal the same number of places in thedividend. Then divide as usual.

PullPull

December 10, 2015

Practice Dividing

5.7 0.3 19

3.2 0.2 16

9.6 0.4 24

1.86 0.03 62

1.74 0.03 58

December 10, 2015

÷ =

0.874 ÷ 0.295

÷ =

÷ =x

0.442 ÷ 1.87

0.095 x 3.21 ÷ 9.56

Use rounding to estimate quotients

0.9 ÷ 0.3 = 3

0.4 ÷ 2 = 0.2

0.1 x 3 ÷ 10 = 0.03

December 10, 2015

December 10, 2015

Answer the following2

6 - 1 × 0 + 2 ÷ 2

December 10, 2015

Now try this one3

6 ÷ 2(1 + 2)

December 10, 2015

Order of Operations

B - bracketsE- exponentsD - divideM - multiplyA - additionS - subtraction

December 10, 2015

4 + 5 x 6 = 34

(5 + 5)2 = 100

102 + (3 x 8) - 14 x 2 = 96

December 10, 2015

3 x (4 + 7) = 33

6 + 9 x 5 = 51

115 - 102 + 3 x 5 = 30

(8 + 42) ÷ 5 = 10

1 + 2 x 32 = 19

MAGIC TUNNEL

Solve the equations.Drag through the tunnelto reveal the solution.

December 10, 2015

14 - 7 + 5 + 1 = 13

15 + 10 x 4 = 55

10 - 4 ÷ 2 x 3 = 4

9.5 x 2 ÷ 0.5 + 45 ÷ 5 = 47

(18 - 11) x 3 + 7 = 28

Solve the equations.Drag through the tunnelto reveal the solution.

MAGIC TUNNEL

December 10, 2015