Review for Algebra Test

Here are a few resources to help you study for the algebra retest. the test will be Monday, December 15.

• A video from Khan Academy (Note: when Khan gets to 3x = 12, he multiplies both sides by 1/3 to get x = 4. We have been dividing each side by 3 to get the same results. But as Khan explains, multiplying the number by 1/3 and dividing a number by 3 are the same thing).
  
• Math is fun: Click on this link and scroll down near the bottom of the page and look at the real world example. They solve 3x + 9 = 45 exactly the same way I want you to for the test.
  
• Click here for a digital copy of the review booklet

History of Mathematics

Statistics and Probability

make sure you can define and find the mean, median, mode, and range for a set of data: link

make sure you can determine probabilities for rolling a single die, flipping a coin, and having a boy or a girl: link

Shape and Space

Make sure you know how to determine the area of the square, rectangle, parallelogram, and a circle: link

Make sure you know the diameter, radius and circumference of a circle. Make sure you know how to calculate the circumference of the circle: link

make sure you can define perpendicular and parallel lines:
link 1
link 2

make sure you can plot ordered pairs on our Cartesian graph and that you can also perform:

Cartesian Coordinates

Note: we did to the items below. I informed Mr. VC. There is one question about this on the assessment, but we won't  worry about it. Save studying the items below till last if you get to it at all.
Reflections

Transformations

Rotations

Translations

Grade 8 assessment review

Make sure you can order fractions decimals and percents: link

Make sure you can add and subtract fractions with like and unlike denominators: link

Make sure you can simplify fractions: link

Make sure you can add and subtract integers: link

Make sure you can solve linear equations (3x + 2 = 14): link

Fractions, Decimals, and Percents

In grade 7, you need to be able to work with fractions decimals and percents. For review, I would start with Benchmark Fractions, Decimals, and Percents.


here is the link to the relevant Math Is Fun webpage: Fractions, Decimals, and Percents.


Make sure you can multiply and divide by benchmark decimals. Start with 0.5. Notice the following pattern:

4 x 3 = 12
4 x 2 = 8
4 x 1 = 4
4 x 0.5 = 2
4 x 0.25 = 1

Notice how as the 2nd term gets smaller (3, 2, 1, 0.5, 0.25) the product gets smaller as well (12, 8, 4, 2, 1).you can see the logic in the pattern. Just make sure you follow this logic when you make the transition from multiplying by a whole number (1) to multiplying by a decimal number that is less than one (0.5). Notice that the product is now smaller than the original term (4).

Notice that multiplying by 0.5 is the same as dividing by 2:

4 x 0.5 = 2
4÷2 = 2

Notice the opposite trend when you divide by decimals:

12÷4 = 3
12÷3 = 4
12÷2 = 6
12÷1 = 12
12÷0.5 = 24

notice that dividing by 0.5 is the same as multiplying by 2

12÷0.5 = 24
12×2 = 24
4÷0.5 = 8
4×0.5 = 2

Reflections etc

Visit each link, read and try the questions.

Reflections

Transformations

Rotations

Translations

More Grade 8 Assessment Review

Practice Mean, Median and Mode Read and Review and do the questions at the bottom.

Intro to Cartesian Coordinates Read and do the practice questions. You will need to know this for the assessment.

Practice Cartesian Coordinates

Area Link

Click here for area formulas. The test will be Friday, June 6, covering Areas of Rectangles, Squares, Triangles, Parallelograms, and Circles.

Solutions for Algebra 3 p. 40

This is from the back page of our algebra 3 booklet on page 40. In this document you will see the solutions for question 2: c - j. I show you how to solve for the variable by undoing each operation in the equation. You will see the step by step process for solving for the variable in this way.

Notice that once I find the value of the variable (what x equals), I take this value and substitute it back into the original equation. If the math works, the value we found for the variable must be correct.

P. 40 question 2: c - j

Official Vocabulary Definitions for Algebra Test

Click here to download the official vocabulary definitions for the Algebra test on Tuesday. (this was the page I sent home Friday as well).

Algebra Test Review

Here is the classwork answers for Patterns and Algebra 3 You will be responsible for anything in booklets 1, 2 and 3 for the test (not booklets 4 or 5).

Smart Notebook Algebra 3

Revised Smart Notebook Algebra 3

Revised Smart Notebook Algebra 3 PDF

All answers for Algebra booklets

Use these answers to help you check your understanding this weekend. Remember, you can't cheat by copying the answers into your booklets. I am not marking the booklets. Use the answers to check your understanding as you work through the booklets ahead of Tuesday's test. Contact me through the email contact feature on the blog if you need help, or, preferably, ask your question by posting a comment.

Integers for the Test

All your life you have been adding and subtracting. Until now it has been positive numbers, as society didn't want to burden you with learning about negative numbers when you were otherwise busy with learning to walk and go to the bathroom somewhere other than in your pants. But now you are ready.

It doesn't matter where you start on the number line (positive or negative) it matters which way you move on the number line--left or right.

You move right in the following ways:

1. Adding a Positive. That makes sense right? If I give you something positive, that positive--no two ways about it. This is the way you have been adding since kindergarten.                                              3 + 3 = +3 + (+3) = 6
2. Subtracting a Negative. That makes sense too right? Right? If I subtract a negative from my life, my life just doesn't stay the same right? It becomes more positive!   3 - (-3) = 6

You move left in the following ways:

1. Subtracting a Positive: Again, eminently sensible. If I take away a positive, you lose. Your life moves to the left.  6 - (+3) = 3 (What you learned was 6 - 3. What it really is is 6 - (+3). The positive is understood). So far so good.
2. Adding a Negative: This makes sense too right? You know it does! If I add a negative, your life moves to the left, toward negative territory. 6 + (-3) = 3.

Now, go to the Math is Fun Page and study!

Here's a Integers Jeopardy game you can play for fun and learning.

You'll notice that the Jeopardy game requires a knowledge of multiplying and dividing integers. Technically this is a grade 8 outcome, but it's not illegal for you to learn how to do it, so here's the link to extra learning.

History of Numbers

This page at Math is Fun about the history of numbers--including zero, and negative numbers--is quite interesting and will be helpful for you for learning adding and subtracting of positive and negative number (aka integers). As you will see, the invention of zero and negative numbers have allowed such things as debt and, eventually, bankruptcy. As a result, Mr Peel could "buy" the boat pictured below, even though he, in no way, can actually afford it.

Answers from Classwork

Here is a link to the work we took up in class. Remember, just copying down answers to questions you don't know how to do, is like asking someone to go out and practice shooting for you (not with you) to help you get ready for a big basketball game. These are posted in case your are away, and to help you check your own understanding--if your answers match the ones posted, that's good!

Here is the document with the answers to Integers 1 p. 139

Smart file

Day 1 Computer Class

Warmup:

1. Sign up to "follow by email" at the bottom right corner of the blog page. Use the email address that you use most frequently.
2. Go to the multiplication trainer on the Math is Fun site. Set the timer for 5 min. Pick the times tables that will be challenging for you. Do as many as you can in 5 min. Show your results to Mr. Peel (your teacher) before moving on to the next step.
3. Follow the following link to the Integers page at Math is Fun. Read the page thoroughly. He has some other examples that may make adding and subtracting positive and negative numbers easier for you to understand. 
4. Do the questions at the bottom of the page, but SIGN IN TO MATHOPOLIS BEFORE YOU START QUESTION 1! (sorry for the shouting).
5. Follow t this link to Math is Fun for an explanation of  multiplying negative numbers. Maybe learning to multiply negative numbers will help cement your understanding of adding and subtracting negative numbers. There's also a video!

Algebra and Searching for Bobby Fischer

I like to use this video because, let's face it, any excuse to show a clip from Searching for Bobby Fischer is a good excuse. But the description of isolating the king serves as a good analogy--or at least introductory hook--for isolating the variable in algebra. 

Clear the lines of men in your head, one at a time and the king will be left standing alone like a guy on a street corner.

You can do it step by step on paper. But it would also be good practice to clear the constant and coefficient in your head, while preserving equality of course, until the variable is standing alone on one side of the equation like a man on a street corner.

New Trainer Added to Math Skills Page!

Follow this link to a link to the Mathopolis Math Trainers! It beats searching aimlessly for what channel they are showing Grizzlies/Thunder. I am not hopeful for the late game between the Clips and Warriors either. (Update: they did show Clips/Warriors on TSN, but it was labelled MLS Soccer on the guide. It is not always easy to be a basketball fan in Canada).

Preservation of Equality

For all of you math lovers who are spending your Saturday night watching and waiting for the blog to be updated, you're in luck. I wanted to share the following definition with you (Why? Because I care, that's why!):

Preservation of Equality

In algebra, equality is maintained when solving for a variable by performing the same operation on both expressions in an equation.

That is the provincially certified definition, so you can take that to the bank. However, it is a little abstract without a concrete example, so here is one.

x + 5 = 10
    -5     -5
x = 5
 (Also, think of our use of the balance--if i remove or add to one side of the balance/equation without doing the same to the other, it will tip. Do not tip equations; they don't like that).

Check by substituting 5 for x in the original equation: 5 + 5 = 10. Give yourself a gold star. Now we can get back to watching Grizzlies/Thunder. If it was on in Canada. Which it is not. That is depressing.

The algebra two step

What we need to practice is undoing two step linear equations in algebra. I will put a link on this post to the math is fun website that will help you practice that. It is just the next step after using guess and check to solve for the variable. Have Fun.

Intro to Algebra
Intro to Algebra 2

Algebra Pretest Wednesday!

We will have practice test on Wednesday, April 30. It will include vocabulary, identifying and extending patterns and solving algebraic equations. No worries!

Today's Test review in Computer class:

Go to the intro to algebra page at Math is Fun. Read the page carefully and do the test at the bottom.

First, join Mathopolis! Then work through the problems. Don't just guess the multiple choice answers! If you get an answer wrong, the website provides a thorough explanation of the correct procedure.

Next, go to this link in order to review and practice multiplication with algebra. Do the quiz at the bottom. You will be ready for the test!

For a couple of the questions you will see 3(x+5) = 24 or a similar question. To solve it you would use the distributive law to solve: 

• 3(x + 5)  = 24
•  3(x) + (3)(5) = 24
•  3x + 15 =24 
• Now just solve the way we have practiced 2 step equations. 

Click on the following links for an explanation about the distributive law

• Distributive law 1
• Distributive law 2

You will responsible to define the terms: expression, equation, coefficient, variable and constant. See this link.

Study the terms, then open a Word Document.

• Type the names of each of the terms as headings in the word document
• Study the definitions at Math is Fun
• Try to type the definitions into the Word Document without looking.
• Repeat

Addicted to Learning--Getting Hooked on Dopamine: The Body's Natural Drug

Here is a great passage from John Coates excellent book, The Hour Between Dog and Wolf: 

What else besides drugs of abuse* can create a dopamine-driven craving? If dopamine fuels a desire for information and unexpected reward, perhaps it also fills us with a burning curiosity. Perhaps curiosity itself, the need to know, is a form of addiction, making us race to the end of a good mystery novel, or driving scientists to work day and night until they discover insulin, say, or decode the structure of DNA, scientific breakthrough being the ultimate hit of information. When the Theory of General Relativity dawned on Einstein, he must have had the mother of all dopamine rushes.

Learning new math and science can give you this rush as a student. Dopamine: the body's natural drug. Get hooked on it!


*Drug abuse fools your brain and gets it to release extreme amounts of dopamine. Then it ruins your dopamine system and you never find that high again.

Stanley Knowles Students Overwhelmed by Algebra Fun!

As we have begun our algebra unit, I took a trip to the Millennium Library to pick up some algebra books for both you and me. So we will be teaching algebra the meaning of the word respect.

Algebra books from Millennium Library

 Remember! Algebra is designed to make math easier and to be fun! We will meet the Manitoba Provincial outcomes for grade 7 algebra!

Welcome to the Unofficial Blog of Stanley Knowles Mathematics

This is the blog that hopefully will make math fun and easy for students at Stanley Knowles. It will be a hub for discussion and links to great math sites that will help you master math.