POSITIVE & NEGATIVE #’S, Write the following on the 4th page in your strand 1 notebook. It should be written at the very top of the page. Look at the example we made Friday. ____________________________________________________ 1.01 NEGATIVE NUMBERS 09-10-08 POSITIVE & NEGATIVE #’S, OPPOSITES & ABSOLUTE VALUES ____________________________________________________

Understanding Integers 1. What is a positive number? 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. The same number with a different sign * They are the same distance from 0 but are on different sides of 0 3. What are opposites? 4. Show opposites on a number line:

Tips: 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 Tips: Absolute values are never negative Negatives are always less than positives Opposites are the same # but one is + and one is --

4 -3 -1 Graphing Opposites. Graph the integer and it’s opposite: Is it positive or negative? Write the integer: A. I owe my friend $10.00 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 Graphing Opposites. Graph the integer and it’s opposite: 4 -3 -1 . -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 =

Comparing & Ordering Integers 09-03-08 Comparing & Ordering Integers

L.L. Left is less Comparing and Ordering Integers 1. How do I compare integers? Use a number line. * Numbers to the left are less than number to the right -4 -3 -2 -1 0 1 2 3 4 2. Compare the following integers: -4 2 -14 -20 6 -4 -9 8 12 14 3 4 3. How do I order integers? 3. GRAPH them on a number line, then order them. -4 -3 -2 -1 0 1 2 3 4 5 Order: 2, -4, -1, 5, 0

TIPS: Comparing and Ordering Integers 4. Graph then order the following integers greatest to least: 4. 5, -2, 1, -4, -1, 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 5. Graph and order the same integers least to greatest. 5. 5, -2, 1, -4, -1, 3 _____________________________________________ TIPS: * Use a # line to compare or order integers L.L. = LEFT IS LESS

Solving Word Problems ALL objectives 09-04-08 _________________________________________________

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?

COMPARING & ORDERING DECIMALS 1.03 Compare & order decimals 09-10-08 COMPARING & ORDERING DECIMALS ____________________________________________________

Ordering and Comparing Decimals: 1. What are the place values for decimals? 1. 204.986 2 = hundreds place 0 = tens place 4 = ones place 9 = tenths place 8 = hundredths place 6 = 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 = Eighty two and thirty four hundredths 3. Line up all the decimals then compare each column left to right Example: 2.014 2.03 3. How do I compare decimals? 3 is greater than 1 so 2.014 < 2.03

Ordering and Comparing Decimals: 4. How do I order decimals? 3. Line up all the decimals then compare each column left to right Example: 2.4, 1.9, 2.19 (L --> G)

COMPARING & ORDERING FRACTIONS 1.03 Compare & order fractions 09-04-08 COMPARING & ORDERING FRACTIONS ____________________________________________________

COMPARING & ORDERING FRACTIONS ____________________________________________________ 1. What are the parts of a fraction? 1. Whole number 2 ¾ Numerator Denominator 2. How do I compare two fractions? 2. Cross multiply bottom to top and compare Example: ⅔ ⅝ ⅝ ¾ * If the denominators are the same, you can compare the numerators Example: ⅜ ⅞

COMPARING & ORDERING FRACTIONS ____________________________________________________ 3. How do I order fractions? 3. Change the fractions into decimals then compare the decimals 4. How do I change fractions to decimals? 4. Divide the numerator by the denominator 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 numerator 4. Divide as usual 5. Bring the decimal straight up into your answer

COMPARING & ORDERING FRACTIONS ____________________________________________________ 5. Change these fractions to decimals: 5. ⅞ ⅝ ⅜ ⅛ ⅔

COMPARING & ORDERING FRACTIONS ____________________________________________________ 6. Order these fractions least to greatest: 5. ⅞, ⅔, ½, ⅝,

INTRODUCTION TO FRACTIONS 09-13-09 INTRODUCTION TO FRACTIONS ____________________________________________________

FRACTIONS EX: ⅝ ⅞ ⅛ EX: ⅛, , ½ EX: ½ ⅞ ⅛ EX: , , 1. What are like fractions? 1. They’re fractions with the same denominator (de nomber on de bottom) EX: ⅝ ⅞ ⅛ 2. What are unlike fractions? 2. They’re fractions with different denominators EX: ⅛, , ½ 3. What are proper fractions? 3. Fractions in which the numerator is less than the denominator EX: ½ ⅞ ⅛ 4. Fractions in which the numerator is greater than the denominator 4. What are improper fractions? EX: , ,

FRACTIONS OR = = = = EX: EX: x = x = EX: ÷ = ÷ = 5. What are equivalent fractions? 5. Fractions that have the same value = = = = EX: 6. How do I make an equivalent fraction? 6. * Multiply the numerator and denominator by the same number EX: x = x = OR * Divide by a number that goes into the numerator AND denominator evenly EX: ÷ = ÷ =

FRACTIONS EX: ⅝ , ⅔ , ⅞ EX: 7= 10= 5= EX: = 1 = 1 = 1 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 EX: ⅝ , ⅔ , ⅞ 8. Put the whole number over 1 8. How do I change an whole number into fraction? EX: 7=   10= 5= 9. The numerator must be the same as the denominator 9. How do I make a fraction equal to 1? EX: = 1 = 1 = 1

FRACTIONS 2 3 EX: 4⅝ , 7⅔ , 3⅞ EX: 4⅝ 7⅔ 3⅞ 10. What is a mixed number? 10. A whole number with a 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 11. How do I change a mixed number into an improper fraction? Then add. 2 3 EX: 4⅝ 7⅔ 3⅞ Multiply.

FRACTIONS 11. How do I change an improper fraction into a mixed number? 11. 1 4 __ 1. Divide the numerator by the denominator. 2 = 4 9 - 8 1 2. The remainder becomes the numerator, the denominator stays the same. 12. Change the improper fractions to mixed numbers: 1. 2. 3.