NSCC SUMMER LEARNING SESSIONS NUMERACY SESSION

Transcription

1 NSCC SUMMER LEARNING SESSIONS NUMERACY SESSION Module 5 Order of Operations

2 Acknowledgement Large portions (pages 8-25) of these modules were created using Level III and Level IV ALP locally developed math resources. These ALP resources are the intellectual property of the NS Department of Labour and Advanced Education (LAE). David Pilmer, the author and LAE Curriculum Consultant, has given permission to NSCC for the use of his materials in the creation of these learning modules. SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 2

3 Welcome! The Numeracy session has six modules. This is module number 5 Order of Operations. In this package you will find everything you need to complete this module. SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 3

4 Contents Acknowledgement... 2 Welcome!... 3 LEARNING OUTCOMES What will I learn?... 5 EXTRA RESOURCES... 6 Order of Operations... 8 EXPONENTS Questions Answers REVIEW SECTION All Together Now, Part II All Together Now, Part III Answers FINAL STEPS: Finishing up the module Coming up next Module 6 Problem Solving SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 4

5 LEARNING OUTCOMES What will I learn? In this module you will learn and practice Applying order of operations to solve problems Developing a math study sheet for order of operations This is an important part of working towards the session learning objectives: Use order of operations as a foundation for more advanced math concepts Complete a math study sheet to summarize the learning about order of operations SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 5

6 EXTRA RESOURCES In case you d like to explore more resources, here about some to check out: Level III Whole Number Word Problem Bridging Unit by David Palmer (School of Access). Stepping It Up. Foundations for Success in Math. Whole Numbers. Published by Pearson. First Canadian Author: Michael Delgaty. Developmental Mathematics. College Mathematics and Introductory Algebra. 7Ed. by M.L. Bittinger and J.D. Beecher. Published by Pearson Trades Math Workbook. Published by Human Resources and Skills Development Canada. Worksheets: Games: SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 6

7 ORDER OF OPERATIONS BEDMAS B E D M A S EXAMPLES NOTE ON EXPONENTS SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 7

8 Order of Operations There is a specific order one must follow when calculating the value of an expression. 1. Perform all operations within grouping symbols like brackets [ ], and parentheses ( ). 2. Evaluate expressions with exponents. 3. Perform multiplications and divisions in order from left to right. 4. Perform additions and subtractions in order from left to right. People often remember this order using the acronym, BEDMAS. B - brackets E - exponents DM - division and multiplication AS - addition and subtraction SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 8

9 Example 1: Evaluate 3 5( 8 2) +. Example 2: Evaluate 5 2 ( 7 4) ( 2) ( 6) parentheses multiplication addition ( 7 4) parentheses exponents multiplication 22 addition then subtraction Example 3: 2 3 Evaluate ( 17 8) ( 17 8) parentheses exponents division 84 subtraction then addition Example 4: Evaluate Here the fraction bar is like a grouping symbol. We simplify above and below the fraction bar separately. The last step is to divide top by bottom SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 9

10 EXPONENTS First let s do a little review of exponents! Exponents are really just repeated multiplication. Example 1: 4 3 In this example the 4 is the base and the 3 is the exponent. This means we are going to multiply the base by itself repeatedly. The exponent tells us how many exponents we will have. Therefore: 4 3 = 4 X 4 X 4 =64 Example 2: 3 2 = 3 x 3 = 9 Example 3: 2 4 = 2 x 2 x 2 x 2 = 16 There are some great You Tube videos available to see BEDMAS in action. SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 10

11 Questions 1. Evaluate each expression (a) ( ) (b) ( 3 + 4) (c) (d) 10 ( 7 2) (e) 7 ( 2 + 3) (f) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 11

12 3 (g) 2 ( 3 + 1) 4 + (h) 3( ) 1 (i) ( ) 2 (j) ( 5 + 6) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 12

13 2 (k) ( ) (l) 30 ( 6 4 1) (m) 2( 16 13) ( 4 + 1) (n) 4 ( 5 2) + 3( 2 + 6) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 13

14 ****HINT: for the following 4 questions do all of the top, do all of the bottom and the last step will be to divide the top by the bottom (o) (p) ( 2 3) (q) ( 9 6) (r) ( 10 8) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 14

15 You sometimes have more than one set of brackets. (known as nested brackets). Be sure to work the inner most brackets first. Challenge yourself! Give these a try! (s) [ 2(5-3) + (2+ 3) 2 ] (t) [5- (3+1)] + [ 6 2 (5 X 4)] SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 15

16 SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 16

17 Answers Order of Operations 1. (a) 5 (b) 43 (c) 82 (d) 6 (e) 81 (f) 16 (g) 9 (h) 20 (i) 5 (j) 4 (k) 34 (l) 37 (m) 13 (n) 36 (o) 4 (p) 6 (q) 3 (r) 11 (s) 29 (t) 17 SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 17

18 REVIEW SECTION All Together Now, Part I Complete all of the calculations without using a calculator. Show your work. (a) ( 13) ( 5) + (b) (c) Find x. (hint cross multiply 5 times 12, then divide by 3) x 5 12 = 3 (d) 3 2 ( 11 6) (e) Take 40% of 120. (f) (g) (h) ( ) 3 2 (i) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 18

19 (j) ( 6) ( 5) (k) (l) (m) (n) ( 13) + ( 7) (o) 35 ( 2 + 3) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 19

20 All Together Now, Part II Complete all of the calculations without using a calculator. Show your work. (a) Take 20% of 70. (b) (c) ( 4) (d) (e) ( 5) 2 (f) ( + 8) ( 4) (g) ( 9 ) + ( + 7) (h) Find x. (i) 2 6 = 7 x SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 20

21 (j) (k) ( 10 3) (l) ( 3 ) ( + 8) (m) (n) (o) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 21

22 All Together Now, Part III Complete all of the calculations without using a calculator. Show your work. (a) (b) ( 11) ( 7) (c) (d) ( + 11) + ( 2) (e) 2 ( ) (f) (g) Find x. 5 x = 4 12 (h) Take 30% of 220. (i) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 22

23 (j) ( 1) 4 (k) (l) (m) (n) ( 9) ( 3) ( 8 2) 30 (o) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 23

24 Answers All Together Now, Part I (page 18-19) (a) 18 (b) (c) 20 (d) 6 (e) 48 (f) 16 7 or 1 9 (g) (h) -8 (i) 3.9 (j) (k) 9 21 (l) (m) 4 28 (n) -20 (o) 1 All Together Now, Part II (page 20-21) (a) 14 (b) (c) (d) 5 18 (e) 25 (f) -32 (g) -2 (h) 21 (i) (j) (k) 4 (l) -11 (m) (n) 2 16 (o) All Together Now, Part III (page 22-23) (a) 25 1 or 3 (b) -4 (c) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 24

25 (d) 9 (e) 7 (f) 2.7 (g) 15 (h) 66 (i) (j) 1 (k) (l) (m) 4 (n) 27 (o) SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 25

26 FINAL STEPS: Finishing up the module Well done! You ve made it to the end of this module. In this module you ve: Applied order of operations to solve problems Developed a math study sheet for order of operations This is an important part of your work towards these session learning objectives: Use order of operations as a foundation for more advanced math concepts Complete a math study sheet to summarize the learning about order of operations Coming up next Module 6 Problem Solving SUMMER LEARNING SESSIONS NUMERACY Module 5 Order of Operations Page 26