1. LESSON 1.2 ORDER OF OPERATIONS MFM1P

2. Homework Check & REVIEW
1. Exercise & 1.1.6
2. McGraw-Hill [Ch. 5.2]: page(s) questions 1, 3, 5, 6, 10

3. OPERATIONS Four Basic Operations : Addition plus sign
Subtraction minus sign
Multiplication multiplication sign
Division division sign x
Equal or Even Values
equal sign

4. 2 MORE OPERATIONS
Exponent
Square Root

5. EXPONENTS

6. LEARNING 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;

7. base X n
exponent
power
Bonjour my friends!! This expression is called a

8. exponents powers base VOCABULARY
Tells the number of times the base iss used as a factor
Numbers expressed using exponents
powers
Numbers expressed using exponents
base

9. Location of Exponent
An exponent is a little number high and to the right of a regular or base number. 3 10
Exponent
Base

10. Definition of Exponent
An exponent tells how many times a number is multiplied by itself. 3 4
Exponent
Base

11. What an Exponent Represents
An exponent tells how many times a number is multiplied by itself. 4
= 3 x 3 x 3 x 3 3

12. 3 4 This exponent is read three to the fourth power. Base
How to read an Exponent
This exponent is read three to the fourth power. 3 4
Exponent
Base

13. 3 2 This exponent is read three to the 2nd power or three squared.
How to read an Exponent
This exponent is read three to the 2nd power or three squared. 3 2
Exponent
Base

14. 3 3 This exponent is read three to the 3rd power or three cubed.
How to read an Exponent
This exponent is read three to the 3rd power or three cubed. 3 3
Exponent
Base

15. Read These Exponents 3 2 6 7 2 3 5 4

16. What is the Exponent? 3
2 x 2 x 2 = 2

17. What is the Exponent? 2
3 x 3 = 3

18. What is the Exponent? 4
5 x 5 x 5 x 5 = 5

19. What is the Base and the Exponent?4
8 x 8 x 8 x 8 = 8

20. What is the Base and the Exponent?5
7 x 7 x 7 x 7 x 7 = 7

21. What is the Base and the Exponent?9 2

22. How to Multiply Out an Exponent to Find the Standard Form4 3
= 3 x 3 x 3 x 3 9 27 81

23. What is the Base and Exponent in Standard Form?3 2 8 =

24. What is the Base and Exponent in Standard Form?2 3 9 =

25. What is the Base and Exponent in Standard Form?3 5
125 =

26. Exponents Are Often Used in Area Problems to Show the Feet Are Squared
Length x width = area
A pool is a rectangle
Length = 30 ft.
Width = 15 ft.
Area = 30 x 15 = 450 ft.
15ft.
30ft 2

27. 10 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 Cubed
Length x width x height = volume
A box is a rectangle
Length = 10 cm.
Width = 10 cm.
Height = 20 cm.
Volume =
20 x 10 x 10 = 2,000 cm. 10 10 10 3

28. Here Are Some Areas Change Them to Exponents2
40 feet squared = 40 ft.
56 sq. inches = 56 in.
38 m. squared = 38 m.
56 sq. cm. = 56 cm. 2 2 2

29. Here Are Some Volumes Change Them to Exponents3
30 feet cubed = 30 ft.
26 cu. inches = 26 in.
44 m. cubed = 44 m.
56 cu. cm. = 56 cm. 3 3 3

30. SUCCESS 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 of
To the ____ power
Squared, cubed
I am able to display an exponent in standard form;
I am able to transfer an expression from standard form into exponent form;

31. SQUARE ROOTS

32. By the end of this lesson, you will be able to:
LEARNING GOALS
By 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 15
Estimate the square root of a number
Use a calculator to find the square root of a number.

33. Before 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 6
A 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 12
And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives (hate and hate or bad and bad) makes a positive.

34. SQUARE ROOT
When 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.

35. Square Root
A number which, when multiplied by itself, results in another number.
2 = 4
5 = 25
10 =
13 =
These are all called perfect squares because the square root is a whole number.

36. PERFECT SQUARE Also called a “perfect square”
These are all called perfect squares because the square root is a whole number..

37. Square Numbers

38. What 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.

39. ESTIMATION
As 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 money
and 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.

40. Equals = Symbol
In 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 ≈ symbol
Estimation 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 calculator
Estimation helps you focus on what is really going on

41. Estimating Square Roots
25 = ?

42. Estimating Square Roots
25 = 5

43. Estimating Square Roots
49 = ?

44. Estimating Square Roots
49 = 7

45. Estimating Square Roots
27 = ?

46. Estimating Square Roots
27 = ?
Since 27 is not a perfect square, we
have to use another method to
calculate it’s square root.

47. Estimating Square Roots
Not all numbers are perfect squares.
Not every number has an Integer for a square root.
We have to estimate square roots for numbers between perfect squares.

48. Estimating Square Roots
Example:
half 5 6 25 30 35 36 27
Estimate = 5.2

49. Estimating Square Roots
Example:
Estimate: = 5.2
Check: (5.2) (5.2) = 27.04

50. SUCCESS CRITERIA I understand the meaning of factors;
I am able to explain the meaning of and identify perfect squares up to 15
I 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

51. ORDER OF OPEATIONS

52. LEARNING 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.

53. What’s Wrong?
To claim a cash prize, Bonzi answers a skill-testing question:
64164+3-22
=644+3-22
=16+3-22
=16+12
=16+2
=18
Find two errors in Bonzi’s solution.
Give a correct solution.

55. Order of Operations
The 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. B E D M A S
rackets
xponents
ivision
ultiplication
ddition
ubtraction

56. Examples:

57. A. 3(5-1)2 =3(4)2 Brackets first (5-1 = 4) =316
Exponents 42 = 4x4 = 16
=48
Multiplication

58. B
=36+16
Exponents
62= 6x6 = 36 and 42= 4x4 = 16
=52
Addition

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+2
Division/Multiplication
=56
Addition/Subtraction

60. Simplify 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)
= 5
Divide the numerator (top) by the denominator (bottom)

61. SUCCESS 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 operations
I am able to solve problems with multiple operations and positive and negative integers.

62. Unit #1: Number Sense and Algebra
Lesson #
Lesson
1.1
Integers
Adding and Subtracting
Multiplying and Dividing
1.2
Order of Operations (square roots & exponents)
1.3
Estimation
1.4
Evaluating Expressions
1.5
Fractions
1.6
Percents and Decimals
1.7
Discounts, Markups and Taxes
1.8
Ratios, Equivalent Ratios
1.9
Rates
1.10
Proportions
1.11
Exponents (powers, exponent rules, zero and negative, scientific notation)
1.12
Polynomials (intro, adding/subtracting, multiplying, expanding/simplifying)
1.13
Solving Equations (1-step, multi-step)