Objectives/Outcomes. Introduction: If we have a set "collection" of fruits : Banana, Apple and Grapes.

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1 1 September 26 September One: Sets Introduction to Sets Define a set Introduction: If we have a set "collection" of fruits : Banana, Apple Grapes. 4 F={,, } Banana is member "an element" of the set F. But Orange is not an element of the set F. Only there is one of each member (all members unique- we couldn't repeat an element in a set). {,,, }Is not a set Definition of a set : A set is a collection of well-defined objects or symbols. The objects or symbols called the elements of the set. Use curly braces { } to represent a set. Represent a set with a capital letter. Sets can be classified as : a finite set an infinite set. Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

2 1 September 26 September One: Sets Types of Sets Definition of a finite set an infinite set. A finite set is a set that has a finite number of elements. (Its elements can be counted) For any finite set, denotes the number of elements in the set A. 4 An infinite set is a set that has infinite (continuous) number of elements. (uncounted number of elements) Examples of set Set of first seven prime numbers: Set of letters in the English alphabet: Set of Natural numbers: Type of the set a finite set a finite set 26 letters an infinite set Ending in three dots e.g.: Classify the following as finite infinite sets, then determine number of elements if possible. 1) The set of days in a week. 2) The set of a multiple of. Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

3 1 September 26 September One: Sets Mathematical expression of Sets Describe the set by: a) Roster form : Listing all the elements of a set, separated by commas enclosed within curly brackets { }. 4 b) Set builder form Writing in symbolic form the common characteristic shd by all the elements of the sets. e.g. : Write the following sets into roster form set builder form : a) The set of all natural numbers between 1 0. b) The set of all letters in the word "AUSTRALIA". c) The set of all natural numbers divisible by. Roster form Set builder form Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

4 One: Sets Set notations 1 September 26 September One: Sets Set notations Identify apply basic set notations : 1).. is an element of... (belongs to) F={,, } Banana is an element of F. Banana belongs to F ( We denote this by Banana F ). Orange is not an element of F. Orange does not belong to F ( Orange F). 4 e.g.: Let A = {1, 4, 6, 9}. Insert the appropriate symbol or in : a) 1 A b) 14 A c) 9 A d) 0 A e) 146 A 2) Universal set Empty set A universal set is the set of all elements under consideration, It is represented by U. An Empty set is the set with no elements. It is represented by { } or Ø which is read "fay". Notice: {0} is not an empty set. e.g.(1): Given that A = {, 6, 10, 12} B = {, 7, 11}. Write a universal set for A B. U = {, 6, 7, 10, 11, 12} or U = {1,, 6, 7, 10, 11, 12, 13} or. e.g.(2) : Determine whether the following sets empty or not : a) {x : x, < x < 6} Empty b) {x : x is a prime number, 4 < x < 8} Not Empty c) M = The set of all months with 32 days. Empty Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

5 1 September 26 September One: Sets Representing Sets by Venn Diagram Define, use draw Venn diagrams. Venn diagrams used to represent sets. The sets represented by shapes (circles or ovals). The elements of a set written within the circle. e.g. (1): Given the set E ={x : x is an even number, 1 < x < 2} Draw label a Venn diagram to represent the set E. 4 List out the elements of E : E = {16, 18, 20, 22, 24}. Draw a circle or oval. Label it E. Put the elements in E. e.g. (2): Draw label a Venn diagram to represent the set. U =. R = {Monday, Tuesday, Wednesday}. Step 1 : Draw a rectangle label it the universal set U. Step 2 : Draw a circle or oval. Label it R. Put the elements in R. Step 3 : Write the remaining elements outside the circles but within the rectangle. E U Saturday Sunday Thursday Friday R Monday Tuesday Wednesday Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

6 1 September 26 September One: Sets Complement of a Set e.g.(3): Draw a Venn diagram to represent the following sets: U = {1, 2, 3, 4,, 6, 7, 8, 9}, A = {1, 2,, 6}, B = {3, 9} U A B 3 9 Identify apply Complement set. 4 Definition of Complement set : If U is the universal set A is a set in U (as shown). A' A The complement of A : is the set of all elements of U which not the elements of A. U We denote the complement of A with respect to U as A'. e.g.(1): If U = {1, 2, 3, 4,, 6, 7} A = {1, 3, 7} find A'. A' = {2, 4,, 6} e.g.(3) :From the given Venndiagram, find: a) A b) B c) A' d) B' e) U Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

7 29 September 7 October two: Displaying Data Probability Displaying Data - Pie Chart Display data using pie charts (degrees percent). Introduction: A pie chart is a circular chart in which the circle is divided into sectors. A sector represents an item in a data set to match the frequency of the item as a percentage of the total data set. Angle of a sector = 1. (there 360 degrees in a circle) e.g.: The following table shows how many students got grade A, B C in mathematics subject : A B C 10 First: put the data in the following table : Grade Frequency Percentage Angle (in degree) A B 10 C Total 20 Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

8 29 September 7 October two: Displaying Data Probability Displaying Data - Pie Chart Second : Draw the pie chart ( as sectors ). Step1: Use a compass to draw a Step2: Use a ruler to draw the circle of any radius. radius (horizontal straight line). 1. Step3: Use a protractor a ruler to draw the first sector (angle ) Step4: Repeat step 3 to draw the second third sectors (angle angle ) Step: Label each sector. Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

9 29 September 7 October two: Displaying Data Probability Probability Predict the probability of simple events (in a fair game) by performing repeated experiments. Activity : Coin tossing experiment 1. Total number of trials Number of times 'Heads' has occurred = If you toss the coin 40 times, what do you expect? 1. Toss a coin 10 times Record number of times the 'heads' has occurred in the given table. 2. Repeat step 1 (Toss the coin 20 then 30 times). When increasing total number of trials, is becoming approximately. Similarly, is approximately. All simple events in a fair game equally likely to happen. Probability of a simple event in a fair game = Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

10 29 September 7 October two: Displaying Data Probability Probability Calculate the probability of simple events. The sample space is the set of all the possible outcomes of an experiment. n(s) = Total number of outcomes in the sample space e.g.(1): In tossing a coin experiment : 1. a) Write the sample space for the tossed coin. The possible outcomes 'Heads' or 'Tails'. So, the sample space is : S = {Heads, Tails} b) Write the probability of getting 'Heads'. Probability of getting 'Heads' = e.g.(2): In rolling a 6 face-die : a) Write the sample space. S = { 1, 2, 3, 4,, 6 } b) Write the probability of getting the number ' '. Probability of getting ' ' = e.g.(3): In spinning a spinner contains four regions. a) Write the sample space. S = { 1, 2, 3, 4 } b) Write the probability of getting ' 3 '. Probability of getting ' 3 ' = Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

11 8 October 17 November Three : Integers The set of Integers Recognize the concept of integers as signed numbers. Definition of integer numbers: Positive numbers : numbers greater than 0 written with or without a positive sign (+) Negative numbers : numbers less than 0. written with a negative sign ( ) An integer is a whole number that can be positive, negative, or zero. This new set of numbers is called "The set of integers" which is denoted by. (which is an infinite set) Eid Al- Fetr Leave 1-17 October. Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

12 Three : Integers Comparing ordering integers 8 October 17 November Three : Integers Representing Integers on number line Locate integers on a number line. is located 2 units to the left of 0. is located 2 units to the right of 0. e.g.(1): Write the integers that represent the letters: A = B = +1 C = +3 e.g.(2): Write an integer to represent each situation: a) below zero. b) 12 meters above sea level. c) Saving of OMR 94. d) An increase of points. e.g.(3): Write the integer: a) Two units to the right of is 1 b) Five units to the left of is c) Three units to the left of is Comp order integers. (Teacher can use number line to comp order integers). Eid Al- Fetr Leave 1-17 October e.g.(1): Use > or < or = sign to comp the integers: a) 8 7 b) 4 6 c) 2 2 d) 1 6 e) 2 7 f) 0 1 e.g.(2): Arrange the numbers in descending order: Solution: Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

13 8 October 17 November Three : Integers Addition of integers Addition of integers using counters the number line. Given that represents represents. represents Using Counters Using the number line Start with the first number (3) From 3, move 2 units to the right. Your end point is the answer : Start with. From, move 2 units to the left. Answer: Start with 3. From 3, move 2 units to the left. Answer: 1. Start with. From, move 2 units to the right. Answer: 1 Hijri New Year Leave November Start with. From, move 3 units to the right. Answer: 0 Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

14 8 October 17 November Three : Integers Addition of integers Addition of integers using algorithms. represents a big number with (+) sign. represents a small number with (+) sign. represents a big number with ( ) sign. represents a small number with ( ) sign. Sign rules of Addition Example Adding integers with same signs Add the numbers Keep the sign Adding integers with different signs Hijri New Year Leave November Subtract the numbers Keep the sign of bigger number Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

15 8 October 17 November Three : Integers Addition properties of integers Properties of addition in. The property Commutative Description in symbols (for every integer numbers, ) Example : a) b) Associative [ ] [ ] Example : [ ] [ ] Commutative Associative properties useful in finding the sum of some integers. By putting positive integers together negative integers together. e.g.: Find [ ] [ ] = Additive identity Example : Additive identity is : Zero Hijri New Year Leave November Additive inverse is the additive inverse of Example : The additive inverse of is The additive inverse of is [ ] Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

16 8 October 17 November Three : Integers Subtraction of integers Subtraction of integers using counters the number line. Change subtraction problem to addition problem then solve: Subtraction problem Using Counters Using the number line Keep Change Change To the sign Addition We know that: Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

17 8 October 17 November Three : Integers Subtraction of integers Subtraction of integers using algorithms. Change subtraction sign to addition sign then solve: Changes to Changes to e.g.(1) : Find : Changes to Changes to Solution a) b) [ ] e.g.(2) : A fish was swimming 10 meters below sea level. Then it swam 8 meters further down. How far below sea level was the fish? Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

18 8 October 17 November Three : Integers Multiplication of integers Multiplication of integers using algorithms. Sign rules of Multiplication Example Multiplying integers with same signs Multiply then put (+) sign Multiplying integers with different signs Multiply then put ( ) sign e.g.(1) : In some countries, there underground buildings. One of these buildings has 4 floors. The depth of each floor is 6 meters. Find the depth of this building (in meters)? Building's depth is 24 meters underground Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

19 8 October 17 November Three : Integers Multiplication Properties of integers Properties of multiplication in. The property Commutative Example : a) b) Description in symbols (for every integer numbers, ) Associative [ ] [ ] Example : [ ] [ ] Distributive over addition Distributive over subtraction Example : Multiplicative identity Multiplicative identity is : 1 Example : Multiplicative inverse ( ) ( ) is the multiplicative inverse of Example : The multiplicative inverse of The multiplicative inverse of is is Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

20 Three : Integers Powers 8 October 17 November Three : Integers Division of integers Division of integers using algorithms. Sign rules of Division Example Dividing integers with same signs Divide then put (+) sign Dividing integers with different signs Divide then put ( ) sign Use the following exponents rules (only positive exponents): Exponents Rules: where 4. e.g.: Find : a) b) c) Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

21 18 November 26 December Four : Ratio Proportion Ratio 8 October 17 November Three : Integers Order of Operations involving the 4 operations positive exponents integers: To solve an expression using order of operations : Step 1 : Perform operations in pntheses. Step 2 : Evaluate powers. Step 3 : Multiply divide from left to right. Step 4 : Add subtract from left to right. e.g. (1) : Find : a) b) e.g.(2) : Given that,. Evaluate: Rename a ratio in lowest terms is in lowest form if e.g.: Rename the following ratio in lowest form: Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

22 18 November 26 December Four : Ratio Proportion Applications of Ratio Read interpret scale drawings. Scale drawing : is picture or diagram of a real object but is smaller or larger than the real object. e.g.(1): The real length of a car is 240 inches its length in a paper is 12 inches. Find the scale drawing of the car? 12 inches = e.g.(2) will be taking at the end of the unit (because concept of cross product will be involved) e.g.(2): If the height of the tree on paper is inches The scale drawing of this tree is, what is the height of the tree in real life? National Day Leave November Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

23 18 November 26 December Four : Ratio Proportion Rates Develop the concept of rate Definition of rate : a ratio that comps two quantities with different units of measure. e.g.(1) : A car can travel 60 km in hours. How far can the car travel in 1 hour? The rate = = 12 km / h e.g.(2): If you take 20 minutes to type 900 words. How many words can you type in 1 minute? Your rate of typing = = 4 words / minute. National Day Leave November Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

24 18 November 26 December Four : Ratio Proportion Applications of Rates Determine best buy using unit price. price : is a rate that comp a price to a one quantity. (Rials per liter, per kilogram, per pound, etc) e.g.: Calculate the unit price then determine the best buy: 7 kg 4 kg price for the first offer = = OMR price for the second offer = = OMR The best buy is the first offer because it is cheaper ( ) price for the first container = = OMR price for the second container = = OMR The best buy is the container with 7 kg because it is cheaper ( ) National Day Leave November Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

25 18 November 26 December Four : Ratio Proportion Proportion Develop the concept of proportion Determine whether a given pair of ratios forms a proportion A Proportion is an equation that shows two (or more) equivalent ratios. To determine whether two ratios form a proportion: 1) Using concept of equivalent fractions. (Method 1 Method 2) 2) By cross products ( product of means extremes). (Method 3) For the ratios : e.g. : Determine whether form a proportion. Method 1: Multiplication Method 2: Division form a proportion form a proportion Method 3: Cross product 16 8 form a proportion Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

26 Find the missing element in a proportion (using the cross products). e.g.(1): Find the missing value : Think : what number multiplied by gives you! e.g.(2) : The ratio of electric fans to rooms is. There rooms. How many electric fans needed? Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

27 18 November 26 December Four : Ratio Proportion Solve real-life problems about : a) Discount sale price A discount is an amount subtracted from the price of an item. It is the money you save when buying something. e.g.: A toy is on sale for price is OMR 1. off. If the original a) What is the discount? Discount = b) What is the sale price? Sale price = b) Service charges : is an additional paid money for a given service (added to a customer's bill). e.g.: Salim ate a dinner in a restaurant totaled OMR plus service charge. Calculate the total money that Salim paid? Service charge = OMR Total money that Salim paid = OMR Restaurant Bill Pizza 2. Salad 1. Bread 1.0 Sub Total.0 Service Charge 0.2 Total.2 Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

28 18 November 26 December Four : Ratio Proportion A commission is the amount of money earned by a salesperson for selling a certain product. e.g.: A salesperson receives a 200 at the end of the month. a) How much is his commission amount? commission on his earnings of OMR Commission = OMR b) How much is his total earnings? Total earnings = Percent increase decrease. OMR e.g.(1): A class has 2 students, it decreases by. a) How many students decreased in the class? Number of students decreased = b) How many students will be in the class? New number of students in the class = e.g.(2): Khalid earns OMR 400 monthly. He has given a his salary. a) Calculate the increase in his salary? increase in The increase in his salary = b) Calculate his new salary? Khalid new salary = OMR Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

29 18 November 26 December Four : Ratio Proportion A tax is an amount of money taken from companies' earnings that goes to the government. e.g.: A company has to pay a taxes on their earnings of OMR Calculate the amount of taxes? Amount of taxes = OMR Simple interest: how much is paid for the use of money. Interest ( I ) (principle) is amount of money deposited or borrowed. is the interest rate (expressed as a decimal). is the time in years. e.g.(1) : Dania borrowed OMR 8000 from a bank to buy a car at simple Interest for 7 years. a) How much interest he will pay? Interest = OMR Pre-exams leave December b) What is the total money he will pay back to the bank? Total money = OMR e.g.(2): Circle the correct answer : The simple interest for 2 years at a rate of on OMR 100 is (in OMR): a) 28 b) 240 c) 180 d) 10 Only minimum level of objectives given in the yearly plan more can be added further. The teacher is strongly advised to give more examples exercises (from the approved list of Math books) than the ones provided in the yearly plan.

2 + (-2) = 0. Hinojosa 7 th. Math Vocabulary Words. Unit 1. Word Definition Picture. The opposite of a number. Additive Inverse

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