1-1 Adding and Subtracting Whole Numbers Place Values of Whole Numbers.

1-1 Adding and Subtracting Whole Numbers

Place Values of Whole NumbersPlace Values of Whole Numbers

Adding Whole NumbersAdding Whole Numbers

1. Set up the problem by writing units under units, tens under tens, and so on.

2. Add each column separately, beginning at the top of the units column.

3. If the sum of any column is two or more digits, write the units digit in your answer and carry the remaining digit(s) to the top of the next column to the left.

4. Add any carried digit(s) above the column with that column.

1. Set up the problem by writing units under units, tens under tens, and so on.

2. Add each column separately, beginning at the top of the units column.

3. If the sum of any column is two or more digits, write the units digit in your answer and carry the remaining digit(s) to the top of the next column to the left.

4. Add any carried digit(s) above the column with that column.

Examples:

#1) 342+19 #2) 1678+2594

#3) 9545+8982 #4) 156+287+956

#5) 4674+8422+5533+3840

1. Set up the problem by writing units under units, tens under tens, and so on.

2. Subtract each column separately, beginning at the bottom of the units column.

3. If a digit in the number being subtracted is larger than the digit above it, “borrow” 1 from the top digit in the next column to the left, decreasing that digit by one and increasing the digit being subtracted by ten.

1. Set up the problem by writing units under units, tens under tens, and so on.

2. Subtract each column separately, beginning at the bottom of the units column.

3. If a digit in the number being subtracted is larger than the digit above it, “borrow” 1 from the top digit in the next column to the left, decreasing that digit by one and increasing the digit being subtracted by ten.

Subtracting Whole NumbersSubtracting Whole Numbers

5. Check your subtraction by adding your answer to the subtracted number.

5. Check your subtraction by adding your answer to the subtracted number.

4. If there is nothing to borrow in the next left column (column contains a zero), first borrow for that column from its next left column.

4. If there is nothing to borrow in the next left column (column contains a zero), first borrow for that column from its next left column.

Examples:

#1) 85-8 #2) 5424-756

#3) 850-172 #4) 9400-1027

Do Now: 9/15/11

1) Take out HW – Adding and Subtracting Whole Numbers WS

2) Hand in Class Expectations Form3) Hand in Summer Packet4) Problem of the Day: (Remember to include the date)

a) 1097+1876 b) 80017-2098

Homework Answers: Adding and Subtracting Whole Numbers CW WS

1. Set up the problem by writing the larger number (original number) above the smaller number (multiplier), writing units under units, tens under tens, and so on.

2. If the multiplier contains only one digit, multiply each digit in the original number by it, working from right to left.

3. If the multiplier contains more than one digit find partial products.

4. Add the partial products.

1. Set up the problem by writing the larger number (original number) above the smaller number (multiplier), writing units under units, tens under tens, and so on.

2. If the multiplier contains only one digit, multiply each digit in the original number by it, working from right to left.

3. If the multiplier contains more than one digit find partial products.

4. Add the partial products.

Multiplying Whole NumbersMultiplying Whole Numbers

Examples:

#1) 129 (3) #2) 34 (16)

#3) 46 (37) #4) 175(89)

#5) 987 (105)

1. Set up the problem by writing the original number (number to be divided) inside a division frame, and by writing the divisor (number you are dividing by) outside the frame.

2. Determine how many times the divisor will go into the first digit of the original number. If it will not, write a zero in the answer space directly above the first digit, and then determine how many times the divisor will go into the first two numbers of the original number.

1. Set up the problem by writing the original number (number to be divided) inside a division frame, and by writing the divisor (number you are dividing by) outside the frame.

2. Determine how many times the divisor will go into the first digit of the original number. If it will not, write a zero in the answer space directly above the first digit, and then determine how many times the divisor will go into the first two numbers of the original number.

Dividing Whole NumbersDividing Whole Numbers

4. Bring down the next unused digit from the original number and place it to the right of the subtracted difference (remainder) – even if the remainder is zero.

5. Determine how many times the divisor will go into this new number; write your answer in the answer space above the digit that was brought down.

4. Bring down the next unused digit from the original number and place it to the right of the subtracted difference (remainder) – even if the remainder is zero.

5. Determine how many times the divisor will go into this new number; write your answer in the answer space above the digit that was brought down.

3. Multiply the divisor by the answer (digit above frame); write this answer under the digit(s) that divisor went into, and subtract.

3. Multiply the divisor by the answer (digit above frame); write this answer under the digit(s) that divisor went into, and subtract.

7. Continue this process until all numbers in the original number have been used.

8. Write any remaining subtracted differences as a remainder.

9. Check the answer by multiplying your answer times the divisor and adding the remainder to this number.

7. Continue this process until all numbers in the original number have been used.

8. Write any remaining subtracted differences as a remainder.

9. Check the answer by multiplying your answer times the divisor and adding the remainder to this number.

6. Multiply the divisor by the last digit you wrote in the answer; write this product under the digits that divisor went into and subtract.

6. Multiply the divisor by the last digit you wrote in the answer; write this product under the digits that divisor went into and subtract.

Examples:

#1) #2) 4800 / 80

#3) #4)

Word Problems:

#1) A farm produces 864 bushels of corn per square kilometer. The farmer plants 127 km2 of corn. How many bushels of corn will the farm produce?

#2) Joan has 688 bananas stored in boxes. If the are 86 boxes, how many bananas must go in each box?

#3) A bee travels 147 m one way from its hive to the garden. If the bee makes 93 round trips between the hive and the garden, how far will it have traveled? Be careful!

Today’s Agenda:

1) CW: Basic Operation Review CW WS2) Addition, Subtraction, Multiplication, and

Division BINGO3) HW: Whole Numbers Operations Quiz Review

Do Now: 9/19/11

1) Take out HW: Whole Numbers Operations Quiz Review2) Problem of the Day: (Remember to include the date)a) 897+527 b) 506-127 c) 15 (27) d) 216÷

18

Homework Answers: Whole Numbers Operations Quiz Review

#1) 6,126 #2) 1,967 #3) 64,701 #4) 86

#5) 415,741

Comparing and Ordering Decimals

When Will I Ever Do That???!!!

Why do I have to understand decimals?

This is a good question. We need to understand what the value of each number means in order to understand what we are talking about. Here is an example:

A shirt costs $12.05, but when I wrote the number down I wrote $12.5. What is wrong with this?

Why is $12.5 wrong?

$12.5 really is saying $12.50, because when we read how much something costs it always has two places after the decimal point. If we don’t have a number after the first number we must assume it is a zero. However, when we read $12.05, the zero is the place holder so we know it is 5¢ and not 50¢. That is a 45¢ difference. I can get a piece of gum for that amount!

McDonald’s Menu….I’m Lovin It!!

• Double Cheeseburger: $ .99• Big Mac Value Meal: $ 4.79• Chicken McNuggetts Meal: $ 3.80• Small Drink: $ .99• McFlurry: $ 1.97• Salad: $ 4.80• 2 Cheeseburger Meal: $ 3.70• Ice Cream Cone: $ .87

Order Up!Least Expensive to Most Expensive

• Ice Cream Cone .87• Double Cheeseburger: .99• Small Soft Drink: .99• McFlurry: 1.97• 2 Cheeseburger Meal: 3.70• Chicken McNuggetts Meal: 3.80• Big Mac Value Meal: 4.79• Chicken Salad: 4.80

What Do I Mean Compare Decimals?

• When we compare we use terms such as:– Less than <– Greater than >– Equal to =

• Comparing decimals is similar to comparing whole numbers.– 45<47– 150>105

• When we compare decimals we use place value or a number line.

Place Value

Identify the place value of the number

#1) 1234.5678 #2) 4578643.15

#3) 4561.232843 #4) 851.4537

Activity Time!!

• Identify the place value that the indicated student represents.

Activity Time!!

Active Votes – Place Values1) Log onto your computer.2) Choose the answer that corresponds to the

question on the board.

• Compare Sara’s score with Danny’s score.

1. Line Up Decimal Points– Sara: 42.1– Danny: 42.5

2. Start at the left and find the first place where the digits differ. Compare the digits– 1<5 – 42.1<42.5– This means Sara’s score was lower

than Danny’s score.

Sara 42.1

Danny 42.5

Ross 42.0

Bethany

40.7

Jacob 46.1

Half pipe Results

Let’s Try Using A Number Line

Sara 42.1Danny 42.5Ross 42.0Bethany 40.7Jacob 46.1

42.0 42.1 42.5

Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have:

42.5>42.1

Equivalent Decimals

• Decimals that name the same number are called equivalent decimals.

• 0.60 and 0.6

• Are these the same???

0.60 0.6=

Annexing Zeros

• This means placing a zero to the right of the last digit in a decimal.

• 0.6 0.60• Although we added a zero, the value of the

decimal did not change!!• Annexing or adding zeros is useful when

ordering a group of decimals.

Ordering Decimals

• We can order decimals from least to greatest or we can order from greatest to least.

• Let’s try an example:

• Order 15, 14.95, 15.8, and 15.01 from least to greatest

One More Example

• Order these numbers from greatest to least• 35.06, 35.7, 35.5, 35.849

Adding and Subtracting Decimals

Lesson 1-5

The Basic Steps:

• Line up the numbers by the decimal point.• Fill in missing places with zeroes.• Add or subtract.

Addition Properties

Commutative Property of Addition: Numbers can be added in any order.

Example: 5+3=3+5

Associative Property of Addition: Numbers can be grouped in any way.

Example: (7+3) + 5 = 7 + (3+5)

Identity Property of Addition: The sum of any number and zero is that number.

Example: 18 + 0 = 18

Mental Math• Addition properties can be used to quickly find

sums.• Example: What is 52 + 12.4 + 48?• We can use an addition property to quickly add

this. • First, change the order: 52 + 48 + 12.4

________________ property.• Then, group the first two addends together:

(52 + 48) + 12.4________________ property

• 100 + 12.4 = 112.4

commutative

associative

Why Estimate?

• Before adding your numbers, use one of the estimating strategies you learned to see what the answer should be close to.

• When you add, you can see if your answer is reasonable.

Examples: 28.9 + 13.31

#1) 28.9+13.31 #2) 15.57+16.1

#3) 20.06+21.5789

Subtracting

• The addition properties do not work for subtraction.

• Estimate and subtract to find what the answer is close to.

• Subtract to find the real answer.

Subtracting Across Zeroes

• If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow.

• All middle zeroes become 9’s.• The final zero becomes 10.

Examples: 15 – 9.372

#1) 15-9.372 #2) 4-0.1

#3) 4.8-3.846 #4) 1.6-0.7826.5

Today’s Agenda:

1) Practice 10 WS (Google Document) **Note – Anything you don’t get done is HW***

Do Now: Problem of the Day:

1)

2)

1-4 Multiplying and Dividing Decimals

To Multiply Decimals:• You do not line up the factors by the decimal.• Instead, place the number with more digits on

top.• Line up the other number underneath, at the

right.• Multiply• Count the number of decimal places (from the

right) in each factor.• Use the total number of decimal places in your

two factors to place the decimal in your product.

Example 1: 5.63 x 3.71

Example 2: 0.53 x 2.618

Practice: 6.5 x 15.3

Multiplying and Dividing Decimals by 10, 100, and 1,000

Lesson 1-8

The Basics:• When you multiply by 10, 100, or 1,000, you can

move the decimal point to the right.• The number of decimal places you move is the

same as the number of zeroes you are multiplying by.

• When you divide by 10, 100, or 1,000, you can move the decimal point to the left. Move the decimal point once for each zero you are dividing by.

Examples:#1) 1.492 x 100 #2) 2,124.94 ÷

1,000

#3) 4.2 ÷ 100 #4) 15.36 x 1,000

Dividing Decimals

Lesson 1-9

Terminating and Repeating Decimals

• A terminating decimal is a decimal that stops, or terminates.

• Examples: 1.25 or 0.892• A repeating decimal is a decimal that has a

repeating digit or a repeating group of digits.• Examples: 1.3333… or .121212121…• Repeating decimals usually have a bar across

the repeating portion.

2.3

Remember the parts of a division problem:

Dividing a Decimal by a Whole Number

• Place the decimal point in the quotient directly above the decimal point in the dividend.

• Divide as you normally would

Examples:

#1) 26.4÷4 #2) 85.6 ÷2

#3) 13.05 ÷ 5

1. If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

2. Put decimal point directly above decimal point in the dividend.

• Divide as usual. Keep dividing until the answer terminates or repeats.

• Check your answer. Multiply quotient by divisor. Does it equal the dividend?

Examples:

#1) #2)

#3) 16.9÷6.5 #4) 55.318÷3.4

Today’s Agenda:

Online Practice: 1) http://www.math.com/school/subject1/practice/S1U1L6/S1U1L6Pract.html (Practice Questions) - Once you get a score of at least 8, make sure to show your teacher to get credit and then you make play the games below for extra practice.2) http://www.math-play.com/decimal-math-games.html (football, basketball, soccer)3) http://classroom.jc-schools.net/basic/math-decim.html (Decimal division football) 4) End of class quiz

Today’s Agenda:

1) WS: Algebra A – GCF/LCD Classwork WS2) HW: GCF/LCD Homework3) LCM and GCF Application Problems:

http://www.funtrivia.com/playquiz/quiz2715661f17598.html

Order of Operations

A standard way to simplify mathematical expressions and

equations.

Purpose

• Avoids Confusion• Gives Consistency

For example:

8 + 3 * 4 = 11 * 4 = 44

Or does it equal

8 + 3 * 4 = 8 + 12 = 20

Order of operations are a set of rules that mathematicians have agreed to follow to avoid mass CONFUSION when simplifying mathematical expressions or equations. Without these simple, but important rules, learning mathematics would be maddening.

The Rules

1. Simplify within Grouping Symbols( ), { }, [ ], | |

2. Simplify Exponents Raise to Powers

3. Complete Multiplication and Division from Left to Right

4. Complete Addition and Subtraction from Left to Right

Shortcut for Remembering:

Back to Our Example

For example:

8 + 3 * 4 = 11 * 4 = 44

Or does it equal

8 + 3 * 4 = 8 + 12 = 20

Using order of operations, we do the multiplication first. So what’s ouranswer?

20

Examples:

1) 5 + (12 – 3)

2) 8 – 3 • 2 + 7

3) 39 ÷ (9 + 4)

4) 10 + 8 ÷ 2 – 6

5) 15 • 103

6) 36 ÷ (1 + 2)2 7) 3 • 104

8) (5 – 1)3 ÷ 4

9) 14 + 3(7 -2) – 2 • 5

Order of Operations Practice:

#1) 9 - (4)(2)+5 #2) (-3)(6)+(4)(-5)

#3) 9÷(3)(5)+1 #4) –(5–9)(2) + (5)(3)

Evaluating Expressions

1. Substitute the values for the variables2. Use the order of operations to simplify.

Evaluating Expressions Let:

#1) #2)

#3) #4)

3

2

5

x

y

z

3 2x 5 2y

x y 5 3z x

Evaluating Expressions Let:

#5) #6) 4x ÷ y(z)

#7) #8)

7 2x y z

5 x

y

23 3z x y

3

2

5

x

y

z

Today’s Agenda:

1) Online Practice: http://amby.com/educate/ord-op/pretest.html

2) HW: Order of Operations (a) Homework WS (odds)

3) Order of Operations Game

Order of Operations Game

• Objective: Use the order of operations to create the numbers 1-10.

• Rules:– Each of the six numbers that you are given must

be used exactly once.– Only one person per team may be at the board

at a time.– Once a number has been correctly generated it

is no longer available to the other teams.

Goal: Create the numbers 1-10 using six random numbers and the order of operations. You must use all six numbers each time.

Example:Random numbers: 1, 3, 4, 2, 1, 2

Order of Operations Game

Do Now:

Activity Time:

1) Divide everybody into groups of 3-42) Divide a piece of paper into 4 parts (addition,

subtraction, multiplication, and division)3) Take the set of cards that you receive and

determine which operation the word on the card implies.

4) Record the word on your paper (Everybody must have their own copy)

Activity Summary

Addition: Subtraction:

Multiplication: Division:

Problem Solving

• Translate the verbal phrase into an algebraic expression:#1) Nine more than a number

#2) Five less than twice a number

#3) Difference of a number and ten

Problem Solving

#4) The product of a number and six squared

#5) The quotient of one half and a number

Problem Solving

• Write an expression/equation and then find the value of the number:#6) A number is equal to the product of six and negative five.

#7) Twice a number is equal to twelve.

#8) Nine less than the product of ten and a number is eleven.

Problem Solving

#9) Eighteen decreased by nine is three times a number.

#10) Three less than twice a number equals half of ten.

Today’s Agenda:

1) Partner Worksheetsa) Backwards Riddleb) Verbal Expressions – How does bob marley like his donutsc) Verbal Expressions – Crossword Puzzle

2) Activity3) Journal: Make up an algebraic expression that

has at least two different operations and then write a sentence describing the expression.

Directions for Activity:

• Write the equation or inequality on your paper and hold it up before the computer advances to the next slide.

• Use n for the variable

The difference of eleven and a number is five

11 - n = 5

The difference of eleven and a number is five

Twenty less than a number is three

n - 20 = 3

Twenty less than a number is three

Twelve more than a number is sixteen

12 + n = 16

Twelve more than a number is sixteen

The product of four and a number, minus three is seventeen

4n - 3 = 17

The product of four and a number, minus three is seventeen

The quotient of a number and five is greater than two

> 2

n5

The quotient of a number and five is greater than two

Six divided by a number is less than or equal to five

< 56n

Six divided by a number is less than or equal to five

The sum of six and number is at least two

6 + n > 2

The sum of six and number is at least two

Six multiplied by a number, take away five is less than seven

6n - 5 < 7

Six multiplied by a number, take away five is less than seven

The sum of six and number all divided by three is two

= 2

6 + n3

The sum of six and number all divided by three is two

Five less than twice a number is seven

2n - 5 = 7

Five less than twice a number is seven