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