Tuesday, May 30, 2006

Scribe post

Yesterday in class we learned about the Terms used in Algebra.

Variable: These are letters that represent numbers. They vary in that we substitute a variable for one or more unknowns

Constant: Their value never changes in an expression. A constant is another word for starting point.

Coefficient: These are the numbers that are teamed with the variable. A coefficient is another word for the change.



Next we reveiwed the answer for question #4 on the quis we took the other day.

Algebraic Equation: Jenny's money


Next we looked at the mathematical format for writing algebraic equations.

In class we've been doing: Start+change(variable)

In grade 8 and amd the other grades beyond that, we're going to use the Mathematical method:



The next scribe will be Melissa.




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Monday, May 29, 2006

growing post # 3

Question 1: What is the difference between an algerbraic expression and an equation (Hint: One contains this and the other doesn't)? Give an example of both an expression and an equation.

An algebraic expression is when you combine numbers, operatives, grouping symbols (such as brackets and parentheses) and/or free variables and bound variables. You get to choose the variable in an algebraic expression. An example of an algebraic expression is 20J / 5. In an algebraic equation is when you combine numbers, operatives, grouping symbols (such as brakets and parentheses) and/or free variables and bouund variables. In an equation the value of the variable is given. A example for an algebraic equation is 20J / 5 = 20. J equals 5.

Question 2: What is a variable and why do we use one in algebra?

A variable is a letter that replaces a number we are solving for. The variable stands for the unknown. We use a variable (a letter) in algebra so the equations we are solving do not become confusing. Example is we use numbers as variables instead of letters.
21 + 13 = 17 This equation doesn't make sense. Now here's the same equation except we use letters for the variable. 2A + 13 = 17. A eaquals 2. You multiply 2 by A which is 2. 2 x 2= 4. Your final equation would be 4 + 13 = 17.

Question 3: Solve for N.



I found that since 2 circles equals 1 square and a circle equals one, that a square equals 2. To solve the second question you need to figure out what a triangle equals on the first scale. I took away four circles (each square equals two circles), and it left me with five circles. Since there were five circles left the triangle equals five circles each. Then I needed to solve the N's. If each square equals 2 and each triangle equals f circles each which is 10. I added it up and got 22. that means you now have to divide 22 in half and you'd get 11. So N eqauls 11.

Question 4: Solve the following equations. Show all of the steps that are needed.

a.) 3n+4n+7=2n+12
7n+7=2n+127n-2n(+7-7)=2n-2n(+12-7)
5n=5
N=1

b) 8n-(4+9)=1
1 8(3)-(4+9)=
1124-13=11
N= 3

(c) (8-3)n+7n+8=
4n+405n+7n+8=
4n+405(4)+7(4)+8=
4(4)+4020+28+8=56
N= 4

Question 5: For this question you need to create a T-Chart and a graph to plot your data from this question onto.

You are having a race against your friend, except you are on foot and he is on his bike. Your both know that if you are on a bike you will be faster so your friend gives you a head start of 3 minutes. If you can run 400m per minute, and your friend can bike 700m per minute, who will be the first to make it to the finish line 2000m away?The runner will cross the finish line first in 5 minutes. The biker will cross the finish line second in 6 minutes




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Growing post #3

Question #1
In an
algebraic expression we get to choose the value of the variable.
example: 3+4n = "n" is the variable.
I an equation the value of the variable is already given. example: 3+4n = 19
Question #2
Variables are any letter ( a - z ) that represent numbers. In an algebraic equation you are solving what the variable represent. It already had a value in an equation. In an expression you choose what the variable represent like the example in question 1.















Question #3
First I took away four circles (each square equals two circles), and it left me with five circles. Since there were five circles left the triangle equals five circles. To solve the second question you need to figure out the value of the two Ns. First I added the squares and triangles together. The total of the squares and triangles and it was 22 circles. Then I divided the 22 circles by 2. The answer was 11. So each N equals 11 circles.
Question #4
a) 3n + 4n + 7 = 2n + 12
7n + 7 = 2n + 12 7n - 2n = 12 - 7 5n = 5 N = 5/5 n = 1
b) 8n - (4+9) = 11
8n - 13 = 11 8n = 13 + 11 8n = 24 n = 24 / 8 n = 3
c) (8-3)n + 7n + 8 = 4n + 40
5n + 7n + 8 = 4n + 40 12n + 8 = 4n + 40 12n - 4n = 40 - 8 8n = 32 n = 32/8 n = 4
Question #5
I'll do number five SOON !

ohh yeah..mr.reece..did you see my growing post #2 ?...its on the same post as my first one !




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Saturday, May 27, 2006

My growing post that is due for this week is located here.




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Friday, May 26, 2006

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Notes for the growing post


Qustion 4. you must sovle for N ie. n-10 or n-3 remember you will not get a fraction decided or negative number as your answer.


Qustion 5. you will need 2 T-charts for this question remember for your gragh the person on the bike doesn't go anywhere for the first 3 minunts.


The homework is to do page 30, 31, 32, and 33


examples for our homework if you don't get like # 10 on page 32


n divided by 3.5 = 7
then 3.5 times 3.5 will canceal it out
and then 7 times 3.5

then N = 24.5




the next scribe will be michelle




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Thursday, May 25, 2006

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At the beginning of class we did mental math. Next, our homework was checked which was the ' Solving Algebraic (Linear) Equations ' worksheet.

If you didn't get the homework, here's how you do some of the questions. If you can do these questions you shouldn't have any problems with the other ones.

17) 5A + 8 = 3A + 12
Step 1 - Since there are variables on both sides you the find smallest number which is 3A.
Step 2 - You then subtract 3A with its opposite which is -3A . Looks like this :Step 3 - 3A cancels . If you subtract on one side you must subtract from the other.Step 4 - You still have the 8 which we don't want. So we do the same thing we did with 3A. Subtract 8 from its opposite, remember if you subtract from one side you subtract on the other too.
Step 5 - Last thing you do is divide 2A to 4 and you'll get the answer. A = 2

Here's another equation that deals with brackets.

13) (4-2)A + 3 = 13
Step 1 - First of all, you do the brackets.
2A + 3 = 13
Step 2 - You then subtract 3 and 13 from 3. 3 because its the smaller than 13.
2A = 10
Step 3 - divide 2A to 10.
A = 5

* We'll be having a test on this unit later on next week.


The graph for homework: remember that the lines are the perimeter. It's the outside not inside. on question 1 Figure 1 it's not 5 lines. If you don't get counting the lines, heres a diagram to help you understand.
Homework:
- growing post is due on May 29th
- graph worksheet due tomorrow

- questions (Pg26) 10, 11,12,15,16,17 due tomorrow

The next scribe is Sarika.




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Tuesday, May 23, 2006

Growing Post

#1.a) t-chart

2) a=25
180+a
205+a
230+a
255+a
280+a

c) He would have 800 baseball cards by the time he is twelve years old.

#2.a) She will have to order two pizza's because if there is six slices and four people. For 4 people there is 12 slices and six plus six equals twelve so she would order two pizza's.

b) She needs to order one more pizza. Then her total pizza's will be three pizza's.

#3.a) In one year Kathy will have 200 dollars.

b) you are only changing one number.
25+15n= savings account




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Monday, May 22, 2006

Abdul's Growing Post #2

Question #1
a)



b)180+25c c=4
180+
25(4)=280

c)180+25c
180+25(48)=1380

Question #2
a)12 slices
12 divided by 6=2
If pizza has 6 slices, Jackie should order 2 pizzas.

b)18 slices
18 divided by 6=3
If one pizza has 6 slices, Jackie should order 3 pizzas.

Question 3)
a)$20+$15n n=12
$20+$15(12)=$200

b)$25+$15n n=12
$25+$15(12)=$205






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growing Post

#1 T-CHART
a) number of cards months
180 1
205 2
230 3
255 4
280 5
b) 180 + 25(3) = 255
c) 12 - 8 = 4 12 x 4 = 48
25 x 48 = 1200
He will have 1200 cards by the time he turns 12.
#2
a) 4 = 12 slices
12 % 6 = 2 pizza's
Jackie should order 2 pizza's.
b) 18 % 6 = 3 pizza's
3 - 2 = 1
Jackie should order 1 more pizza.
#3
a) 20 + 15(12) = 200
Kathy will have $200 in one year.
b)25 + 15(12) = 205
Kathy would have $205 in one year. if she really had $25.
#4
a) 3n + 4n + 7 = 2n + 12
3n + 4n = 2n + 12 - 7
3n + 4n = 2n + 5
3n + 4n - 2n = + 5
5 % 5 = 1
n = 1
b) 8n - (4 - 9) = 11
8n = -- (4 - 9) + 11
8n = 24
24 % 8 = 3
c) (8 - 3)n + 7n + 8 = 4n + 40
5n + 7n + 8 = 4n + 40
5n + 7n = 4n + 40 - 8
5n + 7n - 4n = 40 - 8 = 32
32 % 8 = 4
n = 4




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Algebra Growing Posts for the weeks of: MAY 15-20, MAY 23-26, MAY 29-JUNE 03

* note: my growing post for the week of MAY 23-26 is below the growing post for the week of MAY 15-20. Press the "ctrl" key and the "f" key at the same time and enter *Week of MAY 23 - MAY 26* so you don't have to scroll down alot. Same goes for the *Week of MAY 29 - JUNE 03*. You can enlarge the pictures by clicking on them so you can get a clearer view.

-------------------Week of MAY 15 - MAY 20-------------------
Question #1: Solve all 3 parts of the problem below

Jack collects baseball cards. Jack has 180 baseball cards in his collection. At the end of each month Jack buys 25 baseball cards to add to his collection.

a)Create a T-Chart showing how many baseball cards Jack has at the end of the next 4 months.

b)Create an algebraic formula based upon the problem above
180 + 25m = total of cards
*(m=the number of months)

c)If Jack just turned 8 years old this month and Jack continues to buy the same amount of baseball cards each month, how many baseball cards will Jack have when he turns 12?
12 months x 4 years = 48 months
m= 48a
180 + 25(48) = 1380
Jack will have 1380 baseball cards when he turns 12.

Question #2: Use the chart to figure out the questions below.


*chart taken from Mr. Reece's post on what the questions are for this growing post.

Jackie is planning on having a pizza party with some of her friends. She is trying to figure out how many pizza’s to order. She knows that each pizza has six slices of pizza.

a)If Jackie thinks that there will be four people at the party (counting herself) how many pizza’s should she order?
There are 4 people at the party so if you look at the chart, for 4 people there are 12 slices.
12 slices/6 slices = 2 pizzas
Jackie should order 2 pizzas.

b)If two more people show up at the party how many more pizza’s does she need to order?
Based
on the chart, for 6 people you need 18 slices of pizza.
18 slices/6 slices = 3 pizzas
Jackie should order 3 pizzas.

Question #3: Answer the question below based upon this information

Kathy has $20 in her savings account. Each month she adds another $15 to her savings account. In order to calculate how much money she will have in one year Kathy has created this algebraic formula: 20 + 15n = Savings amount

a) Calculate how much money Kathy will have in one year.
There are 12 months in one year.
n = 12 months
20 + 15(12) = 200

Kathy will have $200 by the end of the year.

b) Suppose Kathy counted wrong and she really has $25 in her account instead of $20. Change the algebraic formula to reflect this miscalculation.
All your changing is one number and you don't need to change anything else.
25 + 15n = Savings Amount

Question #4: Solve the following equations. Show all of the steps that are needed.

a) 3n + 4n + 7 = 2n + 12
3n + 4n - 2n = 12 - 7
7n - 2n = 5
5n = 5
n=5/5
n=1

check: 3(1) + 4(1) + 7 = 14
2(1) + 12 = 14

b) 8n – (4 + 9) = 11
8n - 13= 11
8n = 11+13

8n = 24
n= 24/8
n = 3

check: 8(3) - 13 = 11
24 - 13 = 11

c) (8 – 3 )n + 7n + 8 = 4n + 40
5n + 7n + 8 = 4n + 40
5n + 7n - 4n = 40 - 8
12n - 4n = 32
8n = 32
n = 32/8
n=4

check: 5(4) + 7(4) + 8 = 4(4) + 40
20 + 28 + 8 = 56
16 + 40 = 56

-------------------*Week of MAY 23 - MAY 26*-------------------

Question #1: What is the difference between an algebraic expression and an algebraic equation (hint: One contains this and the other doesn't)? Give an example of both an algebraic expression and an equation.

In an algebraic expression you get to choose what the variable is.
Example: 3 + 4n =
Let's exchange "n" for a 3.
3 + 4(3) = 15
In an algebraic expression you can never go wrong, unless you're dealing with a word problem and it's asking you to put a specific number in.

In an algebraic equation you have to find out what the value of the variable is.
Example: 3 + 4n = 19
n=4

Question #2: What is a variable and why do we use it in algebra?

In an algebraic expression, a variable is the part of the expression in which you can exchange it for a number in order to find out what the answer to a question is. Like if your trying to solve how many minutes are in a certain amount of hours, you can exchange the variable and replace it for the amount of hours.

In an algebraic equation, a variable is the part of the equation we are trying to solve. For example, suppose this was the question you were trying to solve 4n = 32. The variable is the letter "n".

In algebra we use variables because we don't know the value, and we want to find what it is. We also use variables to do all the algebraic manipulation (like simplifying an expression) without using actual numbers, to save work.

Question #3: Solve for N

For question 3, you have to do the first part first. Solve the value for the triangle first.

To do this, it's easier to write it out as an equation. 1 square equals 2 circles and 2 circles equals the number 1. Lets write the triangle as "n". There are 2 squares, and that equals 2 circles. The equation is 4 + n = 9. Subtract 4 from 9 and that equals 5. Now we know that n=9. Now that we know what the triangle is, we have to solve the second part of the question.

Again, it is easier to write is as an equation. This time the equation is n + n = 12 + 18. Add 12 and 18 together and you get 30. Rewrite the equation and it becomes: n + n =30. Since there are 2 n's, all you need to do is divide 30 in half. Therefore, n = 15.

Question #4: Solve the following equations. Show all the steps that are needed.

*note: for the next questions 4a, b, and c, in the diagram, S= step and A= answer.

a) 3n + 4n + 7 = 2n + 12



b)
8n - (4 + 9) = 11

c) (8 - 3)n + 7n + 8 = 4n + 40



Question #5: For this question you need to create a T-Chart and a graph to plot your data from this question onto.

You have a race against your friend, except your on foot and he is on his bike. You both know that if you are on a bike you will be faster so you will be faster so your friend gives you a head start of 3 minutes. If you can run 400m per minute, and your friend can bike 700m per minute, who will be the first to make it to the finish line 2000m away?

T-Chart For Me:


T-Chart For My Friend:


Line Graph:


I will reach the finish line first.

-------------------*Week of MAY 29 - JUNE 03*-------------------

Question 1: Formulas. We’ve learned how to write algebraic equations in the form of: mx + b = y. Convert these two sentences into algebraic equations using the above formula.

Sentence 1: Scott is 2 years older than Donald who turns 12 on June 21st 2006. Write this sentence in the format of mx + b = y, then convert it into an expression which allows us to figure out the age of Scott.

There aren't any variables, so the sentence/expression/whatever is:
11 + 2 = Scott's age

Sentence 2: Elizabeth has $200 in her savings account. She makes $40 every two weeks babysitting for her next door neighbours. If Elizabeth saves all of her money solve for how much money she will have in one year.

If she makes $40 every 2 weeks, then that means she makes $20 per week (i divided 40 in half).

365 / 7 = about 52 weeks
200 + 20 x 52 = w
w = amount of money in 1 year.

Question 2: Creation: You need to create two questions for your classmates that cover different concepts (ex: T-Charts, patterns, equations, graphs etc.) that you have learned in this unit on Algebra. You then need to show how to solve the questions. Your mark will be based upon the level of question’s difficulty, and the effort put into your answer.

My Question #1: A girl named Mika started a farm one day. If her farm can only take 992 animals, how long will it be till the farm is all full with 992 or more animals (the information is on the t-chart below, the answer has no decimals)? Look at the t-chart. Notice that it only goes up to the 6th day and that it doesn't go up to 992 animals. Your task is to use the information below to create an expressions and then create an equation and solve it to find out long it will be till the farm is full.

ANSWER: To solve this, you have to think how the person who made this problem up (me) got the y value (the # of animals) and how it is related to the x value (the day). If I didn't know how to solve this, I would try all sorts of things. One thing I would do is to think what number times the x value would equal the y value. I started noticing that if you multiply the number you are on by the number after it, it gives you the y value. So the expression is: (D + 1) D = A.

The thing that is easy now is to create the equation. All you have to do is plug in 992 into the expression. So now it becomes: (D+1) D = 992. You could answer it using the t-chart and extend it, but if you're lazy like me then you would try to do trial and error. For some odd reason I picked the number 31 and it was the answer. So D = 31.

My Question #2: Use the graph below to answer this question: Rico and Rico are brother and sister. They each own a shop. What is the
difference between the highest shop profit Rico's shop had and the lowest shop profit Rica's shop had?

ANSWER: According to the graph, the highest shop profit Rico had was $5 mil. and the lowest shop profit Rica had was 1 mil. So the answer would be $4 mil. because $5 mil. - $4 mil. = 1 mil.

Question 3: Reflection: You need to look back at the chart that we filled out during the first day of the unit. This is the chart where you coloured a topic red, yellow or green. You now need to pick one concept that you coloured yellow or red and reflect in words what new skill/idea that you have learned on this topic.

I can now use a t-chart in helping me to create an algebraic formula because I think my analysis skills have developed more. That's good because I think I can see the pattern going on in the t-chart and create a formula out of that information.

Question 4: Preparing for the final exam: You need to think about the year that has past in mathematics and decide which topic is your weakest, and what you need to learn during class review in order to prepare yourself for the final exam. It is not enough to say fractions, instead pick your weakest area of fractions, say the subtraction of fractions, and give an example of what you don’t understand.

The topic that I am the weakest in would have to be doing operations with fractions. For example in the diagram below,I don't get how to questions like those. I think we should do a few worksheets on those and some of the other things people had trouble with.




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