1.01 NEGATIVE NUMBERS09-02-08 ____________________________________________________

1.01 NEGATIVE NUMBERS 09-02-08

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Understanding Integers

1. What is a positive number?

1. It’s a number greater than zero. *

* Represented with a + or no sign

2. What is a negative number?

2. It’s a number less than zero.

* Always written with a - sign

3. What are opposites?

3. The same number with a different sign

* They are the same distance from 0 but are on different sides of 0

4. Show opposites on a number line:

Understanding Integers

5. What are integers?

5. Integers are the set of all whole numbers and their opposite

6. What is absolute value?

6. An integer’s distance from 0 * Represented by I n I

* Never negative * Always positive

Negatives are always less than positives Opposites are the same #

but one is + and one is --

Absolute values are never negative

Is it positive or negative? Write the integer: A. I owe my friend $10.00

Graphing Opposites. Graph the integer and it’s opposite:

.

B. I live 100 feet above sea level

C. It’s 20 degrees below zero outside

D. I gained 15 yards in my football game

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4

Write the absolute value of:

1. I-2I =

2. I0I =

3. I5I =

4. I-4I =

5. I-1I =

1.03 Ordering integers 09-03-08

Comparing and Ordering Integers

1. How do I compare integers?

1. Use a number line.

* Numbers to the left are less than number to the right

-4 2

Order: 2, -4, -1, 5, 0

-4 -3 -2 -1 0 1 2 3 4

6 -4-14 -20-9 8

-4 -3 -2 -1 0 1 2 3 4 5

3 4 12 14

2. Compare the following integers:

3. How do I order integers?

3. GRAPH them on a number line, then order them.

Comparing and Ordering IntegersComparing and Ordering Integers

4. Graph then order the following integers greatest to least:

-5 -4 -3 -2 -1 0 1 2 3 4 5

5. Graph and order the same integers least to greatest.

4. 5, -2, 1, -4, -1, 3

5. 5, -2, 1, -4, -1, 3

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L.L. = LEFT IS LESS

* Use a # line to compare or order integers

ALL objectives 09-04-08

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Solving Word Problems

1. How do I solve word problems?

1. 1. Read the problem until you understand what the question is.

2. List the important information

3. Make a plan: how are you going to solve the problem? Draw pictures, diagrams, etc. if necessary

4. Solve the problem

5. Check your answer and look back at the problem. Does your answer make sense?

1.03 Compare & order decimals 09-04-08

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Ordering and Comparing Decimals:

1. What are the place values for decimals?

1. 204.986732 = hundreds place0 = tens place4 = ones place9 = tenths place8 = hundredths place

6 = thousandths place7 = ten-thousandths place3 = hundred-thousandths place

Ordering and Comparing Decimals:

2. How do I say a decimal number?

2. Always say the decimal as “and”

Say the number the same way you would if it wasn’t a decimal, then say the place value of the last digit

Example: 82.34 =

Eight two and thirty four hundredths

3. How do I compare decimals?

3. Line up all the decimals then compare each column left to right

Example: 2.014 2.03

3 is greater than 1 so

2.014 < 2.03

Ordering and Comparing Decimals:

4. How do I order decimals?

4. Line up all the decimals then compare each column left to right

Example: 2.4, 1.9, 2.19 (L --> G)

5. Compare these decimals:

5. 1.1 1.01

2.354 2.6

5.5 5.98

6. Order these decimals L -> G:

5. 1.1, 1.001, 1.01

2.354, 2.55, 2.6

5.5, 5.05, 5.98

Always line up decimals when comparing or ordering

Compare columns left to right

1.03 Compare & order fractions 09-04-08

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1. What are the parts of a fraction?

1. Whole number 2 ¾ 2. How do I

compare two fractions?

2. Cross multiply bottom to top and compare the quotients

Example: ⅔ ⅝

⅝ ¾

Numerator

Denominator

* If the denominators are the same, you can compare the numerators

Example: ⅜ ⅞

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3. How do I order fractions?

4. How do I change fractions to decimals?

4. Divide the numerator by the denominator

3. Change the fractions into decimals then compare the decimals

1. The nice numerator goes in the house

2. The dorky denominator stays outside the house 3. Add a decimal and two zeros to the nice numerator4. Divide as usual

5. Bring the decimal straight up into your answer

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5. Change these fractions to decimals:

5. ⅞

⅝

⅜

⅛

⅔

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6. Order these fractions least to greatest:

6.

⅞, ⅔, ½, ⅝

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7. How else can I order fractions?

7. Find a common denominator (a number all of the denominators can go into evenly) then order the numerators.

1. Find a common denominator

2. Set up each fraction equal to that denominator

3. Whatever # you x the denominator by, you MUST x the numerator by4. Order fractions based on their numerators

8.

8. Order L using a common denominator:

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9. 9. Order GL using a common denominator:

The nice numerator goes in the house, the dorky denominator stays outside the house

Denominator Down

Cross multiply to compare TWO fractions

Change fractions to decimals or find a common denominator to order fractions or compare more than 2 fractions

1. The run got pushed backwards 12 yards.

2. Andi jumped 12 feet high.

3. Clinton owes $48.00.

4. The city is 1,895 feet below sea level.

5. The diver dove 60 feet under the surface.

6. The temperature was 5 degrees F but then it dropped 7 degrees. What’s the temperature now?

7. In the game of golf, the lowest score wins. Who won the game?

Amy = -7

Clinton = -4

Kira = 2

Andi = -9

1. -12 -14

2. -2 2

3. -43 -31

Clinton dove 45 feet under water. Amy dove 60 feet under water. Kira dove 12 feet under water. Who dove the deepest?

1. What is the opposite of -12?

2. Graph 4 and its opposite:

3. Graph -3 and its opposite:

1. Clinton has 2.3 gallons of gas. He needs 2.76 gallons. Does he have enough?

2. Write in words: 2.16

3. Clinton dove 23.89 feet. Amy dove 23.66 feet. Andi dove 23.9 feet. Kira dove 23 feet. Put their names in order from the deepest to shallowest dives.

4. What place is the 6 in?

45.688

5. Andre has three sticks. Their lengths are 2.21 inches, 2.20 inches and 2.222 inches. What is the length of the shortest stick?

1. Our gas tank has 4/9 of a gallon in it. We need 7/13 of a gallon for the lawn mower. Do we have enough?

2. Order least to greatest:

3/6, 2/7, 4/5

3. The store has 3 nails left. One is 3/5 inches, one is 8/11 inches, and one is 6/9 inches. Which one is shortest?

4. Turn this fraction into a decimal:

5/9

5. The recipe calls for 1/3 cups of sugar. I have 3/9 cups of sugar. Is that enough?

1. Put all cards face down on your desk2. Mix them all up (please)! be gentle so the cards don’t

bend or rip3. Distribute them evenly between you and your partner4. Flip them over one at a time5. The LOWEST number wins6. The first player with all of the cards wins

1.03 Fractions 09-13-09

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1. What are like fractions?

1. They’re fractions with the same denominator (de nomber on de bottom)

2. What are unlike fractions?

2. They’re fractions with different denominators

3. What are proper fractions?

3. Fractions in which the numerator is less than the denominator

4. What are improper fractions?

4. Fractions in which the numerator is greater than the denominator

EX: ⅝ ⅞ ⅛

EX: ⅛, , ½

EX: ½ ⅞ ⅛

EX: , ,

5. What are equivalent fractions?

5. Fractions that have the same value

6. How do I make an equivalent fraction?

6. * Multiply the numerator and denominator by the same number

OR

EX:

EX: x = x =

= = = =

* Divide by a number that goes into the numerator AND denominator evenly

EX: ÷ = ÷ =

7. What does simplest form mean?

7. The fraction cannot be reduced

* No numbers other than 1 can go into the numerator and denominator evenly

8. How do I change a whole number into fraction?

EX: ⅝ , ⅔ , ⅞

8. Put the whole number over 1

EX: = 1 = 1 = 1

EX: 7=   10= 5=

9. How do I make a fraction equal to 1?

9. The numerator must be the same as the denominator

10. What is a mixed number?

10. A whole number with a fraction

11. How do I change a mixed number into an improper fraction?

EX: 4⅝ , 7⅔ , 3⅞

11. 1. Multiply the whole number and denominator 2. Add the numerator to your answer 3. The sum becomes the numerator 4. The denominator stays the same

EX: 4⅝ 7⅔ 3⅞

Multiply.

233

Then add.

11. How do I change an improper fraction into a mixed number?

1

4__ 1. Divide the numerator by

the denominator.

2. The remainder becomes the numerator, the denominator stays the same.

4 9- 8

2

1

11.

=

12. Change the improper fractions to mixed numbers:

12.1.

2.

3.

1.03 Multiply fractions

2. How do I multiply a fraction by a whole number?

2. A. Change the whole number into a fraction

** put it over 1

B. Multiply the numerators

C. Multiply the denominators

D. Write your answer in simplest form

Example: 4 * 7/8

1. How do I multiply fractions?

1. A. Multiply the numerators

B. Multiply the denominators

C. Write the answer in simplest form

Example: 1/3 * 3/5

1.03 Multiply fractions

3. How do I multiply mixed numbers?

3. A. Change the mixed numbers to improper fractions

B. Multiply the numerators

C. Multiply the denominators

D. Write the answer in simplest form or as a mixed number

Example 1: 1/3 * 1 1/2

Example 2: 2 1/2 * 1 1/3

4. How do I evaluate fraction expressions?

4. A. Replace x with the given number

B. Multiply

C. Write your answer in simplest form

Example: x = 5/8

1/3 * x

1.03 Multiply fractions

6. How do I multiply a whole number by a mixed number?

6.

A. Write both numbers as improper fractions

B. Multiply the numerators and denominators

C. Change your answer to a mixed number

1.03 Divide fractions

1. What is a reciprocal?

1. It’s when you flip a fraction upside down

* Two fractions are reciprocals if their product is 1

2. How do I find the reciprocal of a fraction?

2. Switch the numerator and denominator

Example: 2/5 =

8/9 =

1.03 Divide fractions

3. How do I divide fractions?

3. 1. Copy the first fraction

2. Change the division sign to multiplication

3. Flop (flip) the second fraction

4. Multiply

5. Write your answer in simplest form

Example: 4/5 - 5

Example 2: 1/2 - 1/4

1. How do I add like fractions?

1. A. Add the numeratorsB. Keep the same denominatorC. Write your answer in simplest form

Example: 2/7 + 3/7

2.How do I subtract like fractions?

2. A. Subtract the numerators B. Keep the same denominator C. Write your answer in simplest form

Example 1: 4/5 - 1/5 =Example 2: 1- 4/5=

3. How do I subtract like mixed numbers?

3. A. Subtract the fractions B. Subtract the whole numbers C. Write your answer in simplest form

Example: 2 3/4 - 1 1/4 =

1.03 Add & subtract fractions

1.03 Add & subtract fractions

4. How do I evaluate expressions with fractions?

4. A. Write the expressionB. Replace x with the given numberC. Subtract/Add the numeratorsD. Keep the same denominatorE. Write your answer in simplest form

Example 1 : x = 5/8 x - 2/8

Example 2: x = 3/8 x + 1 1/8