Chapter 1Whole Numbers and Decimals

Whole Numbers and DecimalsIWBAT use place value to understand whole numbers to the billions and decimals to the hundred-thousandths

Place Value Chart

Number Forms Standard Form

6,035,479,51836.00025

Short Word Form6 billion, 35 million, 479 thousand, 518

36 and 25 hundred-thousandths

Expanded Form

6,000,000,000+30,000,000+5,000,000+400,000+70,000+9,000+500+10+8

30+6+0.0002+0.00005

Example1. Write in 370,069,029 short word form and

expanded form.370 million, 69 thousand, 29

300,000,000+70,000,000+60,000+9,000+20+9

2. Write 41 hundredths standard form and expanded form.

0.41

0.4+0.01

Find the Value of the Underlined Digit in Short Word Form

1) Look at place value section

2) Read the number and add section name

341,984,654

4 ten millions

Ten Millions section

Examples

1) 12,144,754,984 2 billion

2) 144.0086 6 ten-thousandths

3) 23.00103 3 hundred-thousandths

Practice Write the value of the underlined digit in short word form.1) 5,040,123 2) 91,014,477

3) 0.062 4) 2.0002

Write each number in standard form.1) 7 ten-thousandths

2) 9 billion, 9 million, 9 thousand, 9

Write in expanded form.1) 20,065,289 2) 0.025

Comparing and Ordering DecimalsIWBAT compare and order decimals

Comparing Decimals8.499 ____ 8.5

2) Compare whole numbers

3) Compare tenths place, then the hundredths, etc.

4) Use <, >, or = to compare

8 is the same on both sides

4 is less than 5

8.499 < 8.500

1) Write vertically (Line up the decimal points). Add zeros if needed.

8.4998.500

Examples

1) 9.760 ____ 9.76

9.7609.760

9.760 = 9.76

2) 6.35 ____ 6.357

6.3506.357

6.35 < 6.357

Ordering DecimalsFollow the same steps as when comparing decimals

Order 0.04, 0.93, 0.99, and 0.75 from least to greatest

1) Write vertically (Line up decimal points). Add zeros if needed

2) Compare place values

0.040.930.990.75

3) Write in order from least to greatest using original numbers

0.04, 0.75, 0.93, 0.99

ExamplesWrite in order from least to greatest.

1) 0.56; 0.021; 0.003; 0.9 0.560

0.0210.0030.900

0.003; 0.021; 0.56; 0.9

2) 2; 0.15; 1.5; 2.7; 0.05; 17

2.00 0.15 1.50 2.70 0.0517.00

0.05; 0.15; 1.5; 2; 2.7; 17

PracticeCompare. Use <, >, or =.1) 0.34____3.4 2) 1.5674____1.59

3) 0.7____0.71 4) 1____0.99

Write the numbers from least to greatest.1) 2.05; 2.106; 4.5; 2.999

2) 57; 56.098; 50.897; 50.9; 57.47

Problem Solving Skill: Exact or Estimated DataIWBAT determine whether data in a problem is exact or estimated

Exact or Estimation

Estimation “about” “near” “close to” “between” “a little less/more

than” “around”

Exact Uses very specific

numbers

ExamplesStudents at Holy Angels took part in a project that reduced home energy usage. About half of the 305 students reported they had some success. Of these successful students, 95 use oil to heat their homes and the rest use electricity, gas or solar energy.

學生在聖潔的天使在一個項目，減少家庭能源的使用參加。大約有一半的305學生報告說，他們取得了一些成功。這些成功的學生中，有95利用石油來取暖，其餘用電，天然氣或太陽能。

How many students were involved in the project?參與該項目的有多少學生？

305 students (exact) 305名學生（具體）

2) How many homes that reduced energy used oil? 有多少家庭在減少能源使用的油？

95 homes (exact) 95家（具體）

3) About what fraction of the students reported success? 什麼分數的學生報成功？

About half of the students (estimation) 大約有一半的學生（估計）

PracticeRichard’s family bought a new car for $17,659.99. The old car got less than 20 miles per gallon. They drove the old car more than 14,000 miles each year. They will drive the new car more than 15,000 miles each year. The new car gets over 30 miles per gallon.理查德的家人買了一輛新車為$ 17,659.99 。老車之後不到20英里每加侖。他們開著一輛舊車，每年超過14000英里。他們將駕駛新車，每年超過15000英里。新車獲得超過30英里每加侖。

1) Which number is the exact number? 這數字是確切的數字？

2) About how many gallons did they buy for the old car each year? 有多少加侖，每年他們是否買了一輛舊車？

Addition PropertiesIWBAT use addition properties and mental math strategies.

Addition PropertiesIdentity Property

+ 0=

Commutative Property

+ + = + +

Associative Property

( + )+ =

+ ( + )

Distributive Property

( + ) =

( )+ ( )

Computing MentallyChoose a strategy and compute mentally

1) 28+74+32

Associative28+32 + 7460+74134

2) 325+225

Break-Apart Strategy (Distributive)

300+25+200+25(300+200)+ (25+25) Associative and Commutative500+50

550

Examples1) 88+64

80+8+60+4

Break-Apart

(80+60) +(8+4)140+12

152

2) 27+81+13

27+13+81 Commutative

40+81

121

Rounding Whole Numbers and DecimalsIWBAT estimate and round whole numbers and decimals

The Rounding Hill

4 or less, let it rest!(Stays the same)

5 or more, raise the score!

(Round up)

ExamplesRound 1,639 to the nearest hundred

1) Underline the # in the hundreds place

1,639

2) Highlight the # to the right 1,639

3) Round 1,600

More ExamplesRound each number to the place underlined

1) 65.45

65.45

60

2) 14.77

14.77

14.8

3) 123.06

123.06

120

4) 32.79

32.79

33

Round 2,593.6781 to the place named

1) Nearest hundred2,593.6781

2,600

2) Nearest thousandth

2,593.6781

2,593.678

PracticeRound each number to the place underlined.

1) 499.95 2) 17.3 3) 0.09

4) 123.106 5) 27.003 6) 1.146

Round 8,930.4692 to the place named.

1) Nearest one 2) Nearest hundredth

Adding and Subtracting Whole Numbers and DecimalsIWBAT add and subtract whole numbers and decimals

AddingAlways, ALWAYS, ALWAYS line up the

decimals!Find 1.8+250.03+16.196

1) Line up decimals 1.8250.03 16.196+ ________

2) Place zeros in as placeholders 1.800250.030 16.196+ ________

3) Add 268.026

SubtractingLine up the decimals and write in zeros as placeholders, if

needed.Find 9.38 – 8.795

1. Line up decimals

9.38

8.795- _____

2. Write in zeros 9.380

8.795- _____

3. Subtract, regroup if needed

0.585 *Write in the leading zero

Examples

1) 12 + 6.345

12.000

6.345+ ______

18.345

2) 78,839 – 51,860

78,839

51,860- ______26,979

3) 7.84 – 6.56

7.84

6.56- _____1.28

EstimatingWhen estimating whole numbers, round to the nearest place

next to a comma.When estimating decimals, round to the nearest tenth or

whole number.

1) 12,600 + 2,835

13,000 + 3,000

16,000

2) 9.38 – 8.795

9.4 – 8.8

≈0 .6

PracticeEstimate first. Then find the exact answer.1) 12,375 + 450 + 1,0552) 158,200 – 119,6783) 15.70 + 186.59 + 3.004) $55.99 – $9.455) $9,576.00 + $3.89 + $339.506) 100,000 – 49,6967) 129 – 5.063

Find a PatternIWBAT solve a problem by looking for a pattern.

Guiding Principal #1All mathematics are based on patterns.

Greeting cards are arranged with 1 card in the first row, 3 in the second row, 6 in the third row, and 10 in the fourth row. If the pattern continues, how many cards are in the fifth row?

1) Write out important information or draw a picture

13610

2) Use operations to find a pattern +2, +3, +4

3) Use the pattern to solve the problem +5; 15 cards

Using the same information from the previous problem, find out how many cards are in the sixth and tenth row.

Sixth Row +2, +3, +4, +5, +6

15 + 6

21 cards

Tenth Row +2, +3, +4, +5, +6, +7, +8, +9, +10

21 + 7 + 8 + 9 + 10

55 cards

ExamplesClare designed a card with the following pattern below. Which letter will be in the 54th place?

GOODLUCKGOODLUCKGOODLUCKGOODLUCK

1) Find the pattern 8 letters in each phrase

2) Use the information given and the pattern to solve

54 is not divisible by 8 but 48 is

Count the remainder: 7

Answer: the letter U

Practice1) Sales at Jessica’s Gift Shop were about

$10,000 in 1997, $11,000 in 1998, $13,000 in 1999, and $16,000 in 2000. If this pattern continues, approximately what will sales be in 2005?

2) Find the pattern and solve for the next number in the pattern:

1,1, 2, 3, 5, 8, 13, 21, 34, 55, _____

Order of OperationsIWBAT solve problems using operations in the correct order.

Order of Operations*Multiplication/Division andAddition/Subtraction solved from LEFT to RIGHT

Examples1) 3 + 4 Parentheses?

NoExponents? No or ? Yes3 + 20

+ or - ? Yes23

2) 17 – (3 +1) 2 Parentheses? Yes

17 – 4 2 Exponents? No or ? Yes17 - 2

+ or - ? Yes15

More Examples3) 8 – 5 + 9 Parentheses? No

Exponents? No or ? No+ or - ? Yes*Remember to work from left to right

3 + 9

12

4) 14 – 3 2 + 7Parentheses? NoExponents? No or ? Yes14 – 6 + 7

+ or - ? Yes*Remember to work from left to right

8 + 7

15

Practice1. 7 + 3 62. (2 + 3) 93. 15 – 96 124. 12 2 – 125. 16 (4 2)6. 6 – 3 2 + 47. 3 + (4 6) - 7

Variables and ExpressionsIWBAT evaluate expressions with as many as three variables

Vocabulary Variable – a symbol that represents a

number1) Variables can represent ANY #2) Variables are LOWERCASE letters

Expression – A number sentence WITHOUT an equal sign

Evaluating Variable Expressions

Evaluate for and

1) When there is a number in front of a variable, that means multiplication

means 3 times

2) Substitute the given numbers for the specific variable (Always rewrite the problem!)

3 𝑥+𝑦3 (5 )+6

3) Use order of operations to solve

15 + 6

21

Examples1) for and

2𝑎+(5𝑏−4 𝑐)

2(15) + (5 16 – 4 0)

30 + (80 – 0)

30 + 80

110

Examples2) for and

2 𝑥+3 𝑦2(10) + 3(7)

20 + 21

41

3) When Lisa is years old, her sister is years old. If Lisa is 11, how old is her sister?

𝑥+411 + 4

15 years old*Always label answers of word problems

PracticeEvaluate each expression for and

1. )

Writing ExpressionsIWBAT write algebraic expressions from word phrases

ExamplesWrite “the sum of a number and 3” as a variable expression

1) Start with the first phrase: the sum

addition

2) Second phrase: a number Use any variable ( or )

𝑥+¿

3) Last phrase: and 3 𝑥+3

ExamplesWrite “2 less than a number” as a variable expression

1) First phrase: 2 less than Subtraction

*the word “than” means you switch order

2) Last phrase: a number Use any variable

2−𝑥𝑥−2

PracticeWrite each phrase as a variable expression1. 6 less than k-62. divided by 8 t 83. and 3 more m+34. less than11 11-y5. 6 times 6t6. divided by 87. Adam raked bags of leaves. Alex raked 5

bags. How many bags were raked together?r + 5

Solving Addition and Subtraction EquationsIWBAT solve one-step equations that have only one variable.

Vocabulary Equation - a statement that two

expressions are equal (must have an equal sign)

Inverse Operation – the opposite operation

1) Addition Subtraction2) Multiplication Division

Solving EquationsBasically working backwards or undoing the operation

𝑥−26=85

2) Use inverse operation Balance the equation

𝑥−26=85 +26 +26____________

3) Solve 𝑥=111

4) Check your work! 111 – 26 = 85

1) Rewrite the problem

Examples1)

- 41.8 -41.8

______________𝑤=14.1

2)

- 17 - 17_____________

𝑎=2614.1 + 41.8 = 55.9

26 + 17 = 43

3)

+ 22 + 22

__________

𝑥=88

88 – 22 = 66

4)

- 138 -138

*Associative property_______________

𝑔=12138 + 12 = 150

Practice

Using Data from GraphsIWBAT analyze and interpret data in bar graphs

Analyzing Bar Graphs

1) How many people voted for rock?

7 people

2) Which type of music is least popular?

Rock

3) How many fewer people voted for classical than for jazz?

14 – 8 = 6 fewer people

Examples1) How many more people signed up for the most popular class than the least popular class?

24 – 9 = 15

2) How many sign ups were NOT for astronomy or archery class?

17 + 24 + 23 + 21 = 83

Practice

1) Which sports did more girls play than boys?

2) What is the total number of students that play Tennis?

3) How many more boys play basketball than girls?

4) How many students were surveyed?