8.4 Constructing Angle Bisectors

When you divide an Angle into two equal parts.... you bisect the angle. There are several ways to bisect an angle: • Paper Folding • Using a mira • Use a compass. • Use a protractor. • Ask a math teacher to do it for you. • Use a triangle and a ruler. Protractor: Q. How can you use your protractor to check your work? - make sure the two angles you have created are the same - make sure the two angles add up to the measurement of the original angle Practice: Page 312 and 313....3,4,5,6,and 7 You must use your protractor to construct the angles!

8.3 - Constructing Perpendicular Bisectors

Focus......Use a variety of methods to construct perpendicular bisectors of Line segments Bisect means to cut in half. When you bisect a line....you cut it in half. If you construct the bisector at right angles (90 degrees) to the line segment.....you've constructed a Perpendicular Bisector. There are several ways to construct perpendicular bisectors: a) Use paper folding. b) Use a compass. c) Use a mira. d) Use a ruler. Method 1 - Paper Folding 1. Draw a line segment AB (about 10cm) 2. Fold the line in half so that Point B is on top of point A. 3. Draw a line down the crease in your paper. This is your perpendicular bisector. Method #2 - Mira 1. Draw a line segment AB (10cm) 2. Place the mira in the middle of the line segment, the reflection of Point A should be on top of Point B (otherwise your line won't be straight). 3. Draw a line down the mira Method #3 - Use a Compass... Method #4 - Ruler 1.) Draw a line segment AB (10 cm) 2.) Place the ruler on a diagonal so that A is on one side of the ruler and B is on the other side. 3.) Draw a line segment down each side of the ruler. 4.) Turn the ruler so that A and B are on opposite sides of the ruler and draw line segments again. 5.) Label the points where the line segments meet, Point "C" and Point "D". 6.) Connect C and D to create a new line segment. CD is perpendicular to AB. Homework: pg. 308-309 # 1-7

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

6.3 Solving Equations Involving Integers

Focus :Use Algebra Tiles to solve Equations Involving Integers.

Verify... x + 3 = -6 (-9) + 3 = -6 -6 = -6 *** RHS = LHS Try this one: 2 = p - 5 How about.....b + 7 = -5 Homework.... Page...234-235: 1bde, 2abc,3,4 and 5

6.2 - Using a Model to Solve equations.

Focus : Using A Balance Approach to solve equations. Verifying Equations. Using the Balance Method In an Equation... The left-hand side is equal to the left-hand side. To maintain balance....add or subtract the same amount to each side.

6.1 Solving Equations

Focus: solve equations by inspection and by systematic trial

Equation: a mathematical statement that two expressions are equal.

What is the difference between an Equation and an Expression?

Explore: (p-220) Solve this problem any way you like:



Method #1 - Inspection
Inspection - find the value of the variable using addition, subtraction, multiplication and division.

Ex: 2y + 5 = 11

First, Find a number that can be added to 5 to get 11.

6 + 5 = 11
so, 2y, must be equal to 6.

Then, we must find a number that, when multiplied by 2, is equal to 6.

3 x 2 = 6, so y = 3


Method #2 - Systematic Trial

Systematic Trial - choose a value for the variable, then check
by substitution. Use the answer and reasoning to choose the
next value you will try and check. (Fancy name for "Guess + Check.")

Ex: 3d - 4 = 14


Use equations to solve word problems:

Connect p. 20

Every equation needs a numerical coefficient, variable, a constant term, and a total which balances the equation. (The answer!)
Which piece of information is which?

NC:

v:

CT:

Total:

So, the Equation to solve is:



Practice: pg. 223 - 225 #1-10

5.7 - Subtracting Mixed Numbers

Focus: Use models and symbols to subtract mixed numbers.

Practice - p. 207
#2-6, 8, 9, 10, 11

Responsible Government

The Reformers in BNA all agreed on one key point:

THE GOVERNOR AND THE COUNCILS DID NOT HAVE TO FOLLOW THE WILL OF THE PEOPLE

Solution? The British sent a wealthy British noble and politician to make sure more rebellions did not happen!

Discussion – What do you think Lord Durham would do?
What suggestions would he make to the King?

He decided on two key recommendations:
- Unite upper and Lower Canada
- Grant Responsible Government to the colonies

Discussion – Who would be happy? Upset?

Canada East and Canada West]

Act of Union 1841

The main provisions:
1) Elected assembly now has power! Governor Can’t Veto
2) English Language only language of government
3) Suspension of specific French Canadian institutions relating to education and civil law.

The Act naturally aroused considerable opposition. In Upper Canada, the Family Compact opposed union, and in Lower Canada religious and political leaders reacted against its anti-French measures.

Upper Canada = Canada West
Lower Canada = Canada East

The Rebellions Of 1837-38

In Lower Canada:

Some Of The Issues That Needed To Be Resolved:

- The Government in Lower Canada favored the business interests of the English over the farming interests of the French population.

- The French in Lower Canada were also concerned about losing their French culture and language, and the privileges given to the Anglican church when most of the population were Catholic.

- The Château Clique: The Château Clique was a group of wealthy Englishmen and leading English merchants in Lower Canada. They were the British landed gentry and they believed that the British should control everything.

- The Parti Canadien often quarreled with the Governor because they did not support taxes for building canals and roads. Louis Joseph Papineau was the leader. His goal was to seek a responsible Government.

Watch video clip of Lower Canada Rebellion:


In Upper Canada
Why Were There Rebellions In Upper Canada In 1837-38?

The news of chaos in Lower Canada reached the people of Upper Canada in October of 1837. Many people in Upper Canada agreed with the Lower Canadian rebels about the need for change in the government.

The Upper Canadian rebels were in favor for the American Revolution and felt a similar revolution was needed in Upper Canada.

William Lyon Mackenzie was the leader of the rebellions in Upper Canada. He shared many of the same ideas of the Patriotes in Lower Canada. He used his newspaper The Colonial Advocate, to demand change against the British Government and Family Compact. He was a supporter of the American Revolution and the republic it created, so he went out to accomplish the same thing in Upper Canada.

5.6 - Adding with Mixed Numbers

Focus: Use models and symbols to add mixed numbers.

Mixed Number: a number consisting of both a whole number and a fraction.

Steps to Solve Using Symbols:

1.) Change Mixed number to improper fraction.
2.) Find the Lowest Common Denominator
3.) Change the fractions to new fractions with the same denominator.
4.) Add the numerators together to get the numerator in your answer.
5.) The denominator does not change!
6.) Change your answer from an improper fraction to a mixed number. Make sure the fraction is in its' lowest terms!

Practice:
Page 202-203
#1-5, 7-10

5.5 Using Symbols to Subtract Fractions

Focus: Use common denominators to subtract fractions.

Estimate first, to check that your answer is reasonable.

Page 197/198 #1-6 & 8

War of 1812

Check out the following website:
There is plenty of excellent information and a video that is quite long, but definitely worth watching the first 30-40 mins.
http://www.warof1812.ca/index.html


Use the video and your textbook to answer the following questions:

1.) Why was the War of 1812 fought?

2.) Who was involved?

3.) How did the War of 1812 end?

War of 1812 – First Nations Perspective
What role did the First Nations have in the War?
- Tecumseh’s outraged with American Attack
- Fought the American’s without Britain’s help
- More First Nations died in the War than British and American’s combined (The British promised a First Nations State, but the Americans wouldn't allow it.)

War of 1812 Hero Biography Assignment due Thursday April 12.
A copy of the assignment and rubric is available to download and print off from the virtual classroom at the FMT school website.

Please also see the virtual classroom for a powerpoint presentation containing additional information about the War of 1812!

5.4 - Using Models to Subtract Fractions

Focus: Use pattern blocks, fraction strips, and number lines to subtract fractions.

Homework – pgs. 193-194 #s 1,2,3,5,6-11

5.3 Using Symbols to Add Fractions

Focus: use common denominators to add fractions.

To add fractions with the same denominator, just add the numerators and keep the same denominator; be sure to always write the fraction in lowest terms.

Practice
p. 188-189
#1-8

Social Quiz - Chapter 6A

Thursday, March 22

1.) What problems exist within the government structure?
2.) Who has the power?
3.) Who might be upset?
4.) What led to the Rebellion in the 13 Colonies?

Key Concepts:
- Loyalists
- Perspectives of the Loyalists, Canadiens, Patriots and First Nations
- Constitutional Act
- Government Structure

5.2 Using Other Models to Add Fractions

Focus: use fraction strips and number lines to add fractions

Fraction strips and number lines can be used to add fractions greater than 1
To add the fractions 2/3 and 3/6, use the number line divided into 6ths.

You will get copies of the following to cut out and use as manipulatives in class. But, if you miss this lesson, you may choose to print off and cut out the Number Lines and Fraction Strips to use as manipulatives to make this concept easier.

Practice - Page 183-185 # 1,2,4,5,7,8,9,11.