2012-2013

1. April 16, 2013Please Get a RED Workbook, then get out a pencil, your homework packets and your notes journal.Please be ready as soon as the bell rings!

2. STAAR Review 2012-2013

3. Order of Operations • Evaluate expressions by using the order of operations… • Parenthesis- from left to right • Exponents-(you won’t see these in 6th grade order of operations) • Multiplication and Division- From left to right • Addition and Subtraction-From left to right

4. Order of Operations Continued • 14 + (10 − 7 ) ∙ 3 = First work parenthesis. • 14 + 3 ∙ 3 = Next work multiplication (the dot represents multiplication. • 14 + 9 = Last addition. • 23

5. Exponents • Exponent- tells you how many times a number is multiplied by itself. • Base- the number that you are multiplying by itself. • 3² The 3 is the Base and the 2 is the exponent. • Means: 3 x 3 = 9

6. Exponents Continued • 4³ = 4 x 4 x 4 = 16 x 4 = 64 • Remember that you have to multiply the base (the big number) by itself the number of the exponent. • So if you have 6 to the power of 5 it means to multiply 6 x 6 x 6 x 6 x 6… It does not equal 30!!!!!!!!!!!!!!!!!!!!

7. Patterns and Sequences • Sequence-a set of numbers in a specific order. • Term-Each number in a sequence. • Arithmetic Sequence- When the terms in a sequence change by the same amount each time. • Example: 3, 6, 9, 12, ?, ?,…(+3 each time)

8. Helpful Hint Look for a relationship between the 1st term and the 2nd term. Check if this relationship works between the 2nd term and the 3rd term, and so on.

9. + 3 • + 3 • + 3 Each month, Eva chooses 3 new DVDs from her DVD club. Position Value 6 9 12 The number of DVDs Eva has after each month shows a pattern: Add 3. This pattern can be written as a sequence. 3, 6, 9, 12, 15, 18, …

10. Variables and Expressions • Variable- a letter that represents a number. The number represented by a letter is not always the same value. It is the missing number. • Algebraic Expression- Contains one or more variables and can contain math operations. Ex: 7 + p =13 3∙c = 18

11. In word problems, you may need to translate words to math. Put together or combine Add Find how much more or less Subtract Put together groups of equal parts Multiply Separate into equal groups Divide

12. Comparing and Ordering Decimals • To compare decimals you look at the biggest(furthest left) place value and compare digits going from left to right, just like you read a book. • Fastest to slowest means to go from least to greatest. Don’t you want to have the smallest time to win a race???? • Slowest to fastest means to go from greatest to least. You don’t want to have the slowest time in a race, do you?

13. Adding/Subtracting Decimals • To add/subtract decimals you have to line up your decimal point. • Ex: 1.2 + 12.3= 3.4 - 2.35= 1.2 3.40 +12.3 - 2.35 13.5 1.05 • You add zero’s to the end of your decimal to make it easier to add or subtract, when needed.

14. Integers • Integers are the counting numbers, their opposites and zero. • Ex: 1, 2, 6, -1, -2, -6, 0 Positive Integers are integers above zero. Negative Integers are integers below zero.

15. Coordinate Graphing • Coordinate graphing is done when there are two number lines that intersect(Crosses) with one another, this is called the Coordinate Plane. These are called the X-Axis and Y-Axis. The points are named by the part of the x-axis and y-axis that it intersects. • These are called ordered pairs. The x comes first then the y. It is written with ( , ). • (3,4) means to go right 3, then up 4.

16. Prime Factorization • Prime factorization- Is a number written as the product (multiplication) of only its prime factors. • 18 (2 ∙ 3 ∙ 3) or 2 ∙ 3² • 100 (2 ∙ 2 ∙ 5 ∙ 5) or 2² ∙ 5²

17. Factors and Multiples • A factor is a number that you multiply together to get another number. • The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 • The greatest common factor (GCF)is the biggest factor at least two numbers have in common or the same. • A multiple is when you count by a certain number. • The multiples of 4 are: 4, 8, 12, 16, 24, … • The Least Common Multiple is the smallest multiple that at least two numbers have in common (the same)

18. Changing between fractions and decimals • To change between a fraction and a decimal, you divide the numerator by the denominator…Remember: the cowboy rides the horse. • To change from a decimal to a fraction you read the decimal, then write the fraction, finally reduce/simplify the fraction to lowest terms.

19. Equivalent Fractions • An equivalent fractions are fractions that represent the same value. • You can find equivalent fractions by multiplying or dividing the numerator and the denominator by the same number.

20. Comparing and Ordering fractions • To compare and order fractions you need to find a common denominator. You find a common denominator by finding the LCM of the denominators you have and finding equivalent fractions with those denominators. • You then compare the numerators. • If you only have two or three fractions you can compare and order them by cross multiplication.

21. Adding or Subtracting Fractions with Like Denominators. • To add/subtract fractions with like denominators you add the numerator and keep the denominator the same. • You simplify(reduce) the fraction if you can by dividing the numerator and the denominator by the same factor (number).

22. Adding/subtracting Fractions with UNLIKE denominators • To add/subtract fractions with different denominators you have to find a common denominator by finding the LCM of the denominators. Then you find equivalent fractions using the new denominator. • You then add/subtract the numerators and keep the denominator the same. • You simplify(reduce) the fraction if needed.

23. Adding and subtracting Mixed Numbers • To add mixed numbers you add the fractions just like you add normal fractions. Then add the whole numbers. You may have to convert the fraction into a mixed number and combine(add) it to the whole number. • To subtract mixed numbers it is a lot like subtracting numbers, but you might have to regroup(borrow) from the whole number. If you regroup remember you are borrowing a WHOLE (2/2, 4/4, 8/8, 16/16).

24. Mean, Median, Mode, Range • Mean is the average. You have to add up all the numbers and then divide by the number of numbers in the set. • Median is the middle number in a set of data. You have to put them in order from smallest to biggest. You cross out the smallest then the biggest until there is a middle number. • The mode is the number or numbers that occur the most. • Range is the difference between the biggest number and the smallest number. You have to subtract.

25. Graphs • Line Plot- Is a graph on a number line that shows each item of information. (It has the shape of a bar graph) • Circle Graph- Is a graph in the shape of a circle or pie. It shows how the total amount has been divided.

26. Graphs • Bar Graph-Is a kind of graph that we use to compare categories or groups of information. Can be horizontal or vertical. • Line Graph-Is a graph using line segments to connect points. They show changes over time.

27. Graphs • Stem and Leaf Plot- is a graph that organizes data so that frequencies can be compared. Scores for a football team 1 1 2 5, 2, 7 3 1 LEAF STEM