6LEARNING GOALS By the end of this lesson, you will be able to: understand words related to exponents (power, base);understand what an exponent represents;read an exponent;Display an exponent in standard form;Transfer standard form into exponent form;
7baseXnexponentpowerBonjour my friends!! This expression is called a
8exponents powers base VOCABULARY Tells the number of times the base iss used as a factorNumbers expressed using exponentspowersNumbers expressed using exponentsbase
9Location of ExponentAn exponent is a little number high and to the right of a regular or base number.310ExponentBase
10Definition of Exponent An exponent tells how many times a number is multiplied by itself.34ExponentBase
11What an Exponent Represents An exponent tells how many times a number is multiplied by itself.4= 3 x 3 x 3 x 33
123 4 This exponent is read three to the fourth power. Base How to read an ExponentThis exponent is read three to the fourth power.34ExponentBase
133 2 This exponent is read three to the 2nd power or three squared. How to read an ExponentThis exponent is read three to the 2nd power or three squared.32ExponentBase
143 3 This exponent is read three to the 3rd power or three cubed. How to read an ExponentThis exponent is read three to the 3rd power or three cubed.33ExponentBase
22How to Multiply Out an Exponent to Find the Standard Form 43= 3 x 3 x 3 x 392781
23What is the Base and Exponent in Standard Form? 328=
24What is the Base and Exponent in Standard Form? 239=
25What is the Base and Exponent in Standard Form? 35125=
26Exponents Are Often Used in Area Problems to Show the Feet Are Squared Length x width = areaA pool is a rectangleLength = 30 ft.Width = 15 ft.Area = 30 x 15 = 450 ft.15ft.30ft2
2710 10 10 3 Length x width x height = volume A box is a rectangle Exponents Are Often Used in Volume Problems to Show the Centimeters Are CubedLength x width x height = volumeA box is a rectangleLength = 10 cm.Width = 10 cm.Height = 20 cm.Volume =20 x 10 x 10 = 2,000 cm.1010103
28Here Are Some Areas Change Them to Exponents 240 feet squared = 40 ft.56 sq. inches = 56 in.38 m. squared = 38 m.56 sq. cm. = 56 cm.222
29Here Are Some Volumes Change Them to Exponents 330 feet cubed = 30 ft.26 cu. inches = 26 in.44 m. cubed = 44 m.56 cu. cm. = 56 cm.333
30SUCCESS CRITERIA By the end of this lesson, you will be able to: I understand the meaning of power, exponent and base.I am able to read an exponent in the following ways:To the power ofTo the ____ powerSquared, cubedI am able to display an exponent in standard form;I am able to transfer an expression from standard form into exponent form;
32By the end of this lesson, you will be able to: LEARNING GOALSBy the end of this lesson, you will be able to:Recall the meaning of factors;Explain the meaning of and identify perfect squares up to 15Estimate the square root of a numberUse a calculator to find the square root of a number.
33Before we begin, you must know: Factors are numbers you can multiply together to get another number (e.g. 2 x 3 = 6)so, 2 and 3 are factors of 6A number can have MANY factors!Example: What are the factors of 12?3 and 4 are factors of 12, because 3 × 4 = 12.Also 2 × 6 = 12 so 2 and 6 are also factors of 12.And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.So 1, 2, 3, 4, 6 and 12 are all factors of 12And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives (hate and hate or bad and bad) makes a positive.
34SQUARE ROOTWhen a number is a product of 2 identical factors, then either factor is called a square root. A root is the opposite of the exponent.
35Square RootA number which, when multiplied by itself, results in another number.2 = 45 = 2510 =13 =These are all called perfect squares because the square root is a whole number.
36PERFECT SQUARE Also called a “perfect square” These are all called perfect squares because the square root is a whole number..
38What about non-perfect squares? When a number will not result in a perfect square, it can be estimated or a calculator with the (square root) function can be used.
39ESTIMATIONAs you walk around and live your life wouldn't it be good if you could easily estimate:how much a bill would be,which product was the best value for moneyand make other estimates such as lengths and angles?Also, wouldn't it be good if you could quickly guess how many people were in a room, how many cars in the street, how many boxes on the shelf, or even how many seagulls on the beach?We are not talking exact answers here, but answers that are good enough for your life.
40Equals = SymbolIn mathematics we often stress getting an exact answer.But in everyday life a few cents here or there are not going to make much difference ... you should focus on the dollars!Approximately ≈ symbolEstimation is ...... finding a number that is close enough to the right answer.•You are not trying to get the exact right answer•What you want is something that is good enough (usually in a hurry!)• Estimation can save you time (when the calculation does not have to be exact):• Estimation can save you from making mistakes with your calculatorEstimation helps you focus on what is really going on
50SUCCESS CRITERIA I understand the meaning of factors; I am able to explain the meaning of and identify perfect squares up to 15I am able to use a calculator to find the square root of a number.I am able to estimate the square root of a number
52LEARNING GOALS By the end of this lesson, you will be able to: Understand the meaning of the term “operations”Understand the meaning of other words related to addition, subtraction, multiplication, division and equal.Understand what “BEDMAS” stands for.Apply BEDMAS to expressions with multiple operations.
53What’s Wrong?To claim a cash prize, Bonzi answers a skill-testing question:64164+3-22=644+3-22=16+3-22=16+12=16+2=18Find two errors in Bonzi’s solution.Give a correct solution.
55Order of OperationsThe correct sequence of steps for a calculation can be remembered with the BEDMAS code.Complete the following chart to help you remember the order of operations.BEDMASracketsxponentsivisionultiplicationdditionubtraction
58B=36+16Exponents62= 6x6 = 36 and 42= 4x4 = 16=52Addition
59 Brackets first (you can do the operation under the root sign as well) Brackets first (you can do the operation under the root sign as well)=(2)(27)+2=54+2Division/Multiplication=56Addition/Subtraction
60Simplify the numerator (top) and the denominator (bottom) separately, and then perform the division.Brackets:Exponents (or square roots):Division/Multiplication (top only)Addition/Subtraction (top only)= 5Divide the numerator (top) by the denominator (bottom)
61SUCCESS CRITERIA I understand the meaning of the term “operations” I understand the Order of Operations rule.I am able to solve a NUMBER problem with multiple operations.I am able to solve a WORD problem with multiple operationsI am able to solve problems with multiple operations and positive and negative integers.
62Unit #1: Number Sense and Algebra Lesson #Lesson1.1IntegersAdding and SubtractingMultiplying and Dividing1.2Order of Operations (square roots & exponents)1.3Estimation1.4Evaluating Expressions1.5Fractions1.6Percents and Decimals1.7Discounts, Markups and Taxes1.8Ratios, Equivalent Ratios1.9Rates1.10Proportions1.11Exponents (powers, exponent rules, zero and negative, scientific notation)1.12Polynomials (intro, adding/subtracting, multiplying, expanding/simplifying)1.13Solving Equations (1-step, multi-step)