7.1 EXPONENTIAL NOTATION Friday, January 31 st

Math Message In your Math notebook, write lesson 7.1 on top and include today’s date. Turn to SRB pg. 5 and 1) write down a definition for the following terms: exponential notation, standard notation 2) give an example of each 2

Standard Notation Standard notation- the way numbers are usually written in everyday situations Digits 0-9 and place value is being used Commas separate the periods and commas also make a number easier to read Examples: ,256 3

Exponential Notation Exponential notation- a shorthand way to write repeated- factor expressions It has two parts: a base and an exponent. The exponent is written just above and to the right of the base. The exponent tells how many times the base is used as a factor. Examples:4 3 is shorthand for 4 * 4 * 4 Power of a number- the product of factors that are all the same. It can be read as follows… “5 3 is read as 5 to the third power, or the third power of 5.” 4

More practice! Click on the following link about expanded notations. Look at the step-by-step and Watch This! to learn even more. ers/expanded-notation.htm 5

7.2 EXPONENTIAL NOTATION FOR POWERS OF 10 Monday, February 3rd 6

Math Message In your Math notebook, write lesson 7.2 on top and include today’s date. In your SRB, turn to pg. 6 1) Read through the entire page 2) In your notebook, number your paper #1-3 3) Complete the “Check your Understanding” questions at the bottom- you only have to complete #1, 3, and 5 7

Number-and-word notation Number-and-word notation is commonly used to express large numbers with 1 numeral and 1 word. Examples: 1 hundred, 1 million, 12 billion, 3 thousand 8

Powers of 10 Refer to SRB pg. 5 Power of 10 – a whole number that can be written using only 10s as factors. The number of zeros in a power of 10 is equal to the exponent of that number. For example: 1,000,000 has 6 zeros, so the exponent of the power 10 is 6. In other words, 1,000,000 =

Powers of 10 How many zeros are needed to write 1 trillion in standard notation? How many times will 10 appear in the repeated factor expression? How many periods are to the right of trillions? What is the relationship between the number of periods to the right of trillions and the exponent when 1 trillion is written in exponential notation? 10

Extra Enrichment Practice (optional) Read SRB pg. 7 and try the Check Your Understanding problems at the bottom of the page 11

7.3 SCIENTIFIC NOTATION Tuesday, February 4 12

Math Message In your Math notebook, write lesson 7.3 on top and include today’s date. You will need to complete your Studylink first before completing your pp notes. 1) Number your paper #1-6 2) Answer the following questions: 1) One thousand equals what power of 10? _____ 2) Which prefix means thousand? _____ 3) What is another name for 10 6 ? _____ 4) Which prefix means million? _____ 5) What does the prefix tera- mean? _____ 6) 1 trillion equals what power of 10? _____ 13

Scientific Notation Scientific notation is a useful way to write large or small numbers. When you write a number as the product of a number and the power of 10, you are using scientific notation. Example: 5 * 10 3 = 5 * (10 * 10 * 10) = 5 * 1,000 = 5,000 14

Let’s try one together… The first fish appeared about 4 * 10 8 years ago. 1) To express this number of years in standard notation, find 10 8 on the place-value chart and write 4 beneath it, followed by the appropriate number of zeros in the cells to the right. 2) From the chart, 4 * 10 8 can easily be read as four hundred million 15

7.4 PARENTHESES IN NUMBER SENTENCES Wednesday, February 5th 16

Math Message In your Math notebook, write lesson 7.4 on top and include today’s date. 1) Refer to SRB pg. 222 and read the entire page 2) Write out the following problems and insert parentheses to make the number sentence true. a) 3 * = 33 b) 27 / = 9 17

What are nested parentheses? Parentheses inside parentheses are referred to as nested parentheses Example: ( ( 6 * 4 ) ) – 2 ) / 2 = 11 **When you are not using parentheses in a number sentence, the expression is said to be ambiguous because it has more than one possible meaning 18

7.5 ORDER OF OPERATIONS Thursday, February 6 th 19

Math Message In your Math notebook, write lesson 7.5 on top and include today’s date. 1) Refer to SRB pg. 223 and read about Order of Operations 2) In your notebooks, complete the “Check your Understanding” problems at the bottom (#1-3). Be ready to share your answers. 20

How do parentheses help clarify ambiguous expressions? Answer: Operations inside parentheses are done first, the order for computation in an expression can be shown with the parentheses 21

Rules for Order of Operations 1) Parentheses 2) Exponents 3) Multiplication and Division 4) Addition and Subtraction P.E.M.D.A.S. or Please Excuse My Dear Aunt Sally 22

Let’s practice! 1) * 6 = ? 2) 3 * 10/ / 3 = ? 3) (4 + 5) * (2 + 3) – (10 * 2) = ? 23

Look at the following link to learn more about Order of Operations. Why not even try the Karaoke!!! em-solving/psorder-of-operations.htm 24

7.6 AMERICAN TOUR: LINE GRAPHS Friday, February 7 th 25

Math Message In your Math notebook, write lesson 7.6 on top and include today’s date. In your Math notebooks, answer the following question: List two methods that can be used to organize collected data. 26

What is the difference between Bar Graphs and Circle Graphs? Bar Graphs Use bars to show data Use a vertical and horizontal axis to display data Circle Graphs Use sectors to show data values 27

Line Graphs Refer to SRB pg. 124 to learn more about Line Graphs A trend is how something has changed over a period of time. 28

7.7 USING NEGATIVE NUMBERS Monday, February 10th 29

Math Message In your Math notebook, write lesson 7.7 on top and include today’s date. 1) Number your paper #1-4 2) Complete the following problems in your notebook: 1) 4 * 10 2 = 2) 5 * 10 4 = 3) 9 * 10 6 = 4) 3.2 * 10 3 = 30

The meanings of “negative” and “positive” Negative (-), positive (+), and zero (0) depend on the given situation. In some cases, the numbers describe situations, like the instant of a rocket blast-off, a temperature of zero degrees, or sea level. Positive and negative numbers can be used for the following: Measuring seconds before and after a blast-off Degrees above and below zero Elevations above or below sea level Increases and decreases Gain or loss 31

Watch the following clip to get a better sense of using positive and negative integers ers/integers.htm 32

7.8 ADDITION OF POSITIVE AND NEGATIVE NUMBERS Tuesday, February 11 th

Math Work In your math notebook, title the page 7.8, and complete the following problems. Use, and = to compare dictated number pairs. 1.) -5 and -7 2.) 3/8 and -1 3.) -8/4 and -2 34

Today’s Lesson In this lesson, we will add positive and negative numbers. We will pretend to be accountants and will keep track of an imaginary balance for today! The account balance = the current total value of an account. An account balance is said to be in the black when there is more cash in an account than there are debt. (Think of our behavior chart) 35

Continued Lesson A balance is in the red when there are more debts that there is cash in the account. For example, take $5 in the black and $3 in the red. What does this show? What is the account balance? $5 in cash and $3 in debts. It shows a balance of $2. The account balance is in the black. 36

7.9 SUBTRACTION OF POSITIVE AND NEGATIVE NUMBERS WEDNESDAY, FEBRUARY 12 TH

Math Work In your math notebook, title the page 7.9, and answer the following questions. 1) 9 + (-3) =? 2) = ? 3) (-16) = ? 38

Number-Line Walking One way to subtract and add positive and negative numbers is to imagine walking on a number line! The first number tells you where to start. The operation sign (subtraction or addition) tells you which way to face:(-) means face toward the negative end of the number line If the second number is negative (has a – sign), then you will walk backward! Otherwise, walk forward. The second number tells you how many steps to take! The number where you end up is the answer. 39

For Example -2 – (-4) = ? Start at -2 The operation sign is -, so face the negative end of the number line. The second number is negative, so walk backward 4 steps. You end up at 2 So, - 2 – (-4) = 2 40

7.10 USING A SLIDE RULE TO ADD AND SUBTRACT Thursday, February 13 th

Math Work In your math notebook, title the page 7.10, and complete the following questions. 1) 4+ (-6) = ? 2) -5 – 3 = ? 3) -6 – (-7) = ? 42

Addition with a Slide Rule We will be using the same slide rule from adding and subtracting fractions. Let’s take the problem, = ? First, line up the 0-mark on the slide with -4 on the holder. Next, imagine facing in the positive direction on the slider. After that, go forward 3 on the slider. Next, the 3 on the slider lines up with -1 on the holder. Finally, you have arrived at your answer! = -1 43

Subtraction with a Slide Rule Let’s take the problem, 2 – 3 = ? First, line up the 0-mark on the slider with 2 on the holder. Next, imagine facing in the negative direction on the slider. After that, go forward 3 on the slider. (So you are actually going in the negative direction on the slider.) Next, the 3 on the slider is lined with -1 on the holder. Finally, you have arrived at your answer! 2 – 3 = -1 44

7.11 CALCULATOR PRACTICE: WORKING WITH NEGATIVE NUMBERS Tuesday, February 18 th

Math Work In your math notebook, title the page 7.11, answer the following questions. Covert fractions to whole or mixed numbers. 1) 272/8 = ? 2) 1,234/4 = ? 3) 937/6 = ? 46

Entering Negative Numbers on a Calculator The minus key on a calculator represents subtraction and that subtraction is different from negative numbers. Negative numbers are numbers that are less than zero, to the left of zero on a horizontal number line, or below zero on a vertical number line. Another way to think of a negative number is as the opposite of a positive number! 47

Entering Negative Numbers on a Calculator The (-) or +/- key is usually called a change-sign key in calculator manuals. It can also be called the OPP key, where OPP is short for opposite! The change-sign key allows you to enter a negative number, or it converts a number to its opposite. Calculators always display a – sign in a negative number. Unless a – sign appears, the number displayed is positive. 48

7.12 REVIEW Wednesday, February 19 th

Concepts to Review Order and compare positive and negative numbers. Add and subtract positive and negative numbers. Identify number sentences and tell whether they are true or false. Understand and apply order of operations to evaluate expressions and solve number sentences. Understand and apply the use of parentheses in number sentences. 50

SRB Reference Pages

Oral Assessment Use >, <, or = to compare numbers. 1) -7 and 7 2) 0 and -¾ 3) -5/10 and -9/18 4) -4 and -10 5) -3/8 and -3/8 6) -35 and 34 Which power of 10 do these numbers express? 1 billion1 thousand10 million100 million 52

Slate Assessment Solve the following: 1) (-15) = 2) -5 + (-7) = 3) -5 – 7 = 4) = 5) -5 – (-7) = 6) 0 – (-8) = 53

Slate Assessment Write numbers given in scientific notation in number-and- word notation: 1) 5 * ) 4 * ) 1 * ) 7 * ) 6 * ) 3.2 *

Order of Operations Insert parentheses where necessary: 1) * 5 = 19 2) / 5 = 7 3) * 2 – (-6) = 16 55

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