LESSON 1.2 ORDER OF OPERATIONS

MFM1P

Homework Check & REVIEW

1. Exercise 1.1.5 & 1.1.6

2. McGraw-Hill [Ch. 5.2]: page(s) 182-183 questions 1, 3, 5, 6, 10

OPERATIONS

Four Basic Operations :

• Addition plus sign• Subtraction minus sign• Multiplication multiplication sign• Division division sign

Equal or Even Values equal sign

x

2 MORE OPERATIONS

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;

By the end of this lesson, you will be able to:

Bonjour my friends!! This expression is called a

VOCABULARY

Tells the number of times the base iss used as a factor

Numbers expressed Numbers expressed using exponentsusing exponents

Numbers Numbers expressed using expressed using exponentsexponents

Location of Exponent

An exponent exponent is a little number high and to the right of a regular or basebase number.

103

BaseExponent

Definition of Exponent

An exponent tells how many times a number is multiplied by itself.

3 4Base

Exponent

What an Exponent Represents

An exponent tells how many times a number is multiplied by itself.

34= 3 x 3 x 3 x 3

How to read an Exponent

This exponent is read three to the fourth power.

3 4Base

Exponent

How to read an Exponent

This exponent is read three to the 2nd power or three squared.

3 2Base

Exponent

How to read an Exponent

This exponent is read three to the 3rd power or three cubed.

3 3Base

Exponent

Read These Exponents

3 2 6 72 3 5 4

What is the Exponent?

2 x 2 x 2 = 23

What is the Exponent?

3 x 3 = 3 2

What is the Exponent?

5 x 5 x 5 x 5 = 54

What is the Base and the Exponent?

8 x 8 x 8 x 8 = 8 4

What is the Base and the Exponent?

7 x 7 x 7 x 7 x 7 = 75

What is the Base and the Exponent?

9 x 9 = 9 2

How to Multiply Out an Exponent to Find the Standard

Form

= 3 x 3 x 3 x 33

927

81

4

What is the Base and Exponentin Standard Form?

2 3= 8

What is the Base and Exponentin Standard Form?

3 2= 9

What is the Base and Exponentin Standard Form?

5 3= 125

Exponents Are Often Used inArea 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.

2

15ft.

30ft

Exponents Are Often Used inVolume Problems to Show the

Centimeters Are Cubed

Length x width x height = volumeLength 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. 3

10

10

10

Here Are Some AreasChange Them to Exponents

40 feet squared = 40 ft.56 sq. inches = 56 in.38 m. squared = 38 m.56 sq. cm. = 56 cm.

2

2

2

2

Here Are Some VolumesChange Them to Exponents

30 feet cubed = 30 ft.26 cu. inches = 26 in.44 m. cubed = 44 m.56 cu. cm. = 56 cm.

3

3

3

3

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;

By the end of this lesson, you will be able to:

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.

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.

SQUARE ROOTWhen a number is a

product of 2 identical identical factorsfactors, then either factor

is called a square square rootroot. A rootroot is the opposite of the exponent.

Square Root

These are all called perfect squares because the square root is a whole number.

2 = 4

10 = 100

5 = 25

13 = 169

A number which, when multiplied by itself, results in another number.

Also called a “perfect squareperfect square”

These are all called perfect squares because the square root is a whole number..

PERFECT SQUARE

Square Numbers

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.

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.

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

Estimating Square Roots

25 = ?

Estimating Square Roots

25 = 5

Estimating Square Roots

49 = ?

Estimating Square Roots

49 = 7

Estimating Square Roots

27 = ?

Estimating Square Roots

27 = ?

Since 27 is not a perfect square, we

have to use another method to

calculate it’s square root.

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.

Estimating Square Roots

Example: 27

25 3530

27

5 6half

Estimate 27 = 5.2

36

Estimating Square Roots

Example: 27

Estimate: 27 = 5.2

Check: (5.2) (5.2) = 27.04

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

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.

What’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

=18

1. Find two errors in Bonzi’s solution.

2. Give a correct solution.

Order 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.

B  E  D  M  A  S  

rackets

xponents

ivision

ultiplication

ddition

ubtraction

Examples:

A. 3(5-1)2

=3(4)2 Brackets first (5-1 = 4)

=316 Exponents 42 = 4x4 = 16

=48 Multiplication

B. 62+42

=36+16 Exponents 62= 6x6 = 36 and 42= 4x4 = 16

=52 Addition

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.

Unit #1: Number Sense and AlgebraLesson # Lesson1.1 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)