8.2 Perpendicular Lines

Focus: Use different methods to construct and identify perpendicular Line segments Materials: Ruler, triangle, protractor, compass, graph paper. Activity (with a partner) 1. Draw a line segment (7-8 cm long) on graph paper. 2 Using the tools provided(and your imagination), construct a second line segment perpendicular to the first. Complete 1 and 2 above in as many ways as you can. Try to find (at least) 3 different methods. Notes: 2 line segments are perpendicular if they intersect (meet) at a right angle(90 degrees) How can we construct Perpendicular Lines? 1. Use a plastic triangle. 2. Use paper folding. 3. Ruler and a protractor. 4. Use a mira. 5.Use a ruler and a compass. (see page 304) List Pairs of Lines which are Perpendicular:

Squares are also sets of perpendicular lines. Homework page 305....1 to 5

8.1 Parallel Lines

Focus - Use different methods to construct and identify parallel lines. Parallel Lines are lines on the same flat surface that never meet...they are the same distance apart, no matter where you measure. 3 different methods... 1) Ruler…Put a ruler down and draw a line on either side of the ruler. 2) Use a Compass… Make a line segment with a straight edge. Put a POINT at each end of this line segment and name these points….A and B. Put 2 points on the line about 4 cm apart. Name these 2 Points….E and F. Using your compass and a radius of 3 cm….. make 2 circles on your line segment….using points E and F as your circle centers. Strike a line from the top of 1 circle to the top of the other. Where this line contacts the circle……label the points…..H and I 3) Use a Protractor… Construct Line Segment AB. Place the protractor on the line segment. Mark 90° on the paper. Slide your Protractor 3-4 cm down the line segment and place a second point at 90°. Connect these two points with a ruler……name this new line segment MN

7.6 Tree Diagrams

Focus: investigate outcomes of probability experiments Explore: p. 284 (build a chart that will organize all your information below) List all possible combinations when you spin a five-colour spinner and flip a coin: Calculate the theoretical probability of each combination : Carry out an experiment of 100 spins/flips to determine the experimental probability of each combination you determined previously:

If you determine probability with cards, spinners, coins, dice, etc....you are performing EXPERIMENTAL PROBABILITY. If you calculate probabilities using a mathematical formula...you are performing THEORETICAL PROBABILITY. If you are calculating the probability of two separate events, where the results of one event have nothing to do with the other, the events are...INDEPENDENT EVENTS. We can use a tree diagram to show all possible outcomes for an experiment with two separate events. All the possible outcomes can be listed in what is called a SAMPLE SPACE. Eg. P(Green and Heads) - spinner and penny...

Remember the formula for probability is P(event) = # of favorable outcomes/(divided by) total # of possible outcomes So, the ratio is 1:10, the probabiltiy is 1/10. Practice - pg. 287 #1-6

7.5 Different Ways to Express Probability

Focus: express probabilities as ratios, fractions and percent As a mathematical formula, we can express probability: P(event) = # of Favourable Outcomes # of Possible Outcomes So, the Probability of an event can be calculated as the # of favorable outcomes, divided by the total # of all possible outcomes. Explore - p. 279: Complete the chart using the information in the textbook and the examples given: Probability can be expressed as a: - ratio - fraction - percent

A certain event is one that will always happen and is expressed as 1 or 100% - rolling a number on a regular six-sided die is a certain event An impossible event is one that will never occur and is expressed as 0 or 0% - rolling the number 7 on a regular six-sided die is an impossible event All probability is between 0.0 and 1.0 (the decimal form of the calculated percentage) or 0% and 100% *Complete the Example on p. 281 *Practice - Page 282-283 - #1-7

7.4 Application of Averages

Focus: understand which average best describes a set of data. Explore - page 271

Question to Ponder... Which measure best describes the average number of siblings? Mode, mean and median are all types of averages; they are called...Measures of Central Tendency the Mean is usually the best average if numbers in the data are not significantly different from one another the Median is usually the best measure if there are numbers in the data that are significantly different from one another the Mode is usually the best measure of average if the data is about measurements or sizes Eg. Shoes, Clothing, Windows Connect - page 271

The mean is 30.7 - not an actual pant size, so not very useful The median is 30 - tells us half bought bigger sizes, half bought smaller sizes The modes are 28 and 30 - tells us which sizes were bought most In this case, the mode is best as it tells us what sizes we need more of as they are most popular... Practice page 273-274, #1-3 and 6 Stem and Leaf Plot Required!!!!

7.3 - Outliers

7.3 The Effects of Outliers on Average Focus: understand how mean, median, and mode are affected by outliers. Create a stem and leaf chart using the data in Explore - p. 267: Then, Calculate the...mean ...median ...mode Now remove the outlier(s) and recalculate the ...mean ...median ...mode *An outlier is any number(s) in a set of data which is significantly different than the others *An outlier is much larger or much smaller than the other data *Some outliers occur as a result of an error in recording or measurement; these values should be ignored in any calculations *Sometimes outliers must not be ignored...they may provide important information...eg. really high or low test score!!!!!! *Not all outliers are obvious *Selecting outliers is sometimes a matter of choice. Example - the outliers in our data above are 8, 47, and 97 Practice page 269-70, #1-4 and 6 Stem and Leaf Plot Required!!!!

7.2 - Range and Median

Focus: Given some data, calculate the Range of the data and calculate the Median Score. The following scores came from a Grade 7 Social exam: 65 89 51 82 57 98 48 59 78 78 91 77 65 77 85 87 77 90 77 91 100 70 88 50 60 83 76 Organize these into a stem and leaf chart: Stem Leaf 4 8 5 0179 6 055 7 06777788 8 235789 9 0118 10 0 Range The Range in the data (or test scores) is the difference between the Highest value in the data and the Lowest score in the data. In our data, the Range is...100 - 48...or 52 Median The Median of a data set (or test scores) is the middle number when the data are arranged in order. In our data, there are 27 scores, so the middle score is the 14th value...77 is the Median If there was an even number of values, we would take the mean (or average) of the two middle scores to determine the median... Example: 3, 5, 9, 13, 17, 18 In this set of data, 9 and 13 are the "middle numbers" so we take their mean to determine the median... (9 + 13) divided by 2 = 11 Practice page 264-65 #1-4

7.1 Mean and Mode Focus: Given some data, calculate the Mean and Mode. The following test scores were assigned to students on their Chapter 6 Final Exam: 65 89 51 82 57 98 48 59 78 78 91 77 65 77 85 87 77 90 77 91 100 70 88 50 60 83 79 76 Organize the data into a Stem & Leaf Chart

Mean....Another word for "Average". Mean....Find the mean by adding all 28 test scores together, and divide by 28. The total of all scores is 2128....divided by 28 Mean score is 76% The Mode is the most common score in the data. In this case the mode is 77%. It occurs 4 times on this test. If more than one number appears the most, there would be more than one mode. Example: If 77 appeared 4 times and 100 appeared 4 times on this test, the modes would be 77 and 100. If all numbers appear only once, we would say that there is no mode. Homework..... Page 260-261 Numbers 1-6

6.5 Using Different Methods to Solve problems.

Focus: Decide which method to use to solve an equation. What Methods have we used so far........ 1 - Inspection 2 - Systematic Trial 3 - Balance Scales 4 - Algebra Tiles 5 - Use Algebra (no model) Inspection.... Use for simple equations... Read, think, then respond (no work is necessary) Systematic Trial Means....Guess and Check Use easy numbers to start, then refine your guesses. Use when you don't know where to start.

In all of these different models, verify your answer using substitution before moving on. Homework Page 243 1,2,3,4,6 and 7 Adapted..... 2,3 and 4 Unit 6 Test is Monday!

6.4 - Solving Equations Algebraically

Focus: Solve a problem by solving an equation Algebraically (no models) My mother's age is 4 more than 2 times my brother's age. My mother is 46 years old. How old is my brother? 2a + 4 = 46

Solve: 7g - 8 = 62 Homework Page.... 238-239 1, 2, 3, 4, 6 and 7