Thursday, June 08, 2006

Tear's Growing Post for June 6th



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.

m- This is the coefficient.
x- This is the variable.
b- This is the constant.
y- This is the answer or the solution of a formula.

Coefficient - Is the number that is teamed with the variable and in this case the variable is x.

Variable- Is the letter that represent numbers. They vary in that we can substitue a variable for one or more numbers.

Constant- It's value never changes in an expression.

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.

Solution:

Donald + 2 = Scott
D + 2 = S
11 + 2 = S
13 =S

I color coded my solution so it's easier to understand. Donald's age is in green and Scott's age is in purple and the black number is the constant. Donald's age is my starting point.

Donald's age is 11 because he didn't turned 12 yet and the problem says that Scott is 2 years older than Donald. So 11 + 3 = 13.

That's how I got Scott's age which is 13 years old.

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.
Equation: 200 + 40n= total money for one year.
Solution:

200+40n =$ In my solution every month has 4 weeks only.
200+40(24)=$ My variable is n and it's value is 48(which is in the
200+960 = $ brackets because if she makes $ 40 in every 2 weeks
1,160=$ then she makes $ 80 per month. If there are 12 months
you multiply 80 by 12 which gives 960.

I color coded my solution again. The number on green is my constant and it is my starting point. The number in golden yellow is my coefficient. The letter in sky blue is my variable. On this problem I'm solving for the value of this symbol: $ .

My starting point is 200 because that is her money in her savings acount. I got 40 as my coefficient because she makes $ 40 every 2 weeks. So this symbol: $ has a value of 1,160 which means Elizabeth will have $1,160 in one 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.

To solve this problem correctly, you have to make an equation, a T-Chart, a graph and lastly you have to explain what is the pattern.

Question 1

Solve for Step 4, step 5 , step 10 and step 50. First explain the pattern. Second, make an equation. Third make a T-Chart . Fourth make a Graph.

First: Pattern Explanation:


In Step 1, there's 3 t-shirts in total, they form the capital L shape 1 t-shirt on line 1 and 2 t-shirts on line 2. For example, when you look at it there's 2 t-shirt vertically and 2 t-shirts horizontally.
In Step 2, there's 5 t-shirts in total, 3 vertically and 3 horizontally.This 5 t-shirts also form the capital L shape.


In Step 3, there's 7 t-shirts in total , 4 vertically and 4 horizontally.This 7 t-shirts also form the capital L shape.

The pattern goes like this:
Every new step, you add 2 t-shirts, one to the vertical line and 1 to the horizontal line.

Second : Equation

3+2n=

For example:

3+2n=

3+2(4)=

3+8=11

Third: T-Chart

On the t-chart above you could see the pattern better.

Fourth: Graph

The graph above shows that the pattern is increasing not decreasing.

Problem 2


Margaret has 10 marbles more than Lisa and the total marble they have all together is 34 marbles. If Lisa keeps adding 2 marbles every other day and Margaret only adds 1 marble everyday. How many would Margaret and Lisa have after 30 days and who will have more marbles. How much is the difference?

To solve this problem you have to do it step by step.


First, solve how many marbles Lisa have. Margaret has 10 more marbles than Lisa so you have to subract 10 marbles from 34 to make is equal then you divide it by 2 to figure out how many Lisa has. For example:
34 - 10 = 24
24 / 2 = 12
12 = Lisa's marbles


Second, you figure out the pattern.
The pattern goes like this for margaret.
Margaret started with 22 marbles and she adds 1 marble everyday.
The pattern goes like this for Lisa.
Lisa started with 12 marbles and she adds 2 marbles every other day.


Third, make an algebraic equation.
Margaret: 22 + 1m= # of marbles
Lisa : 12 + 2m= # of marbles


Fourth, solve it.
Margaret:
22 + 1m =
22 + 1 (30)=
22+ 30 = 52


Lisa:
12 + 2m
12 + 2 (15)=
12 + 30=42


For Lisa, the number on the bracket is 15 because she adds marbles only every other day. So I divided 30 by 2 to figure out the number of marbles Lisa will have.


ANSWER:
Margarett has 52 marbles after 30 days and Lisa only has 42. So it shows that Margaret has more marbles. The difference between Marget's number of marbles to Lisa's number of marbles is 10. To solve that you subtract 52 from 42 and it gives 10.

I made a t-chart below to show the pattern because the pattern is easier to see here. You can also see that Margaret has more marbles from the start.

I made a graph below to show it is increasing and it is easier to see that Margaret has more marbles that Lisa.

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.

Can I create a T-chart for my pattern?

When I read that question on the chart, the question seemed familiar to me because we learned about patterns last year in grade 6.But the word t-chart is unfamiliar to me but when we talked about it in class this year I understand it now. I learned that what you put on the t-chart depends on the pattern. So to make a t-chart you have to figure out the pttern first.

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.

One topic on the exam I know I'll have a mistake on is about Integers especially Word problems about Integers. That's the topic I know I have to study hard for the exam because I get confused to what the word problem meant sometimes. One word problem I got confused on is below.

When Craig woke up this morning it was 7 below zero outside. By noon the temperature had reached 2 above and by late afternoon the temperature had peaked at 5 above. What is the total change in temperature today?

I got confused about this question. I thought the question meant was what is the temperature after all the temperature change so I put this as the answer:

(-7)+(+2)+(+5)=0

The correct answer was 12 because from -7 to +2 the temperature went up by 9 degrees and from +2 to +5 the temperature went up by 3 degrees. So 9 degrees plus 3 degrees it equals to 12 degrees.

So the total change in the temperature today is 12 degrees.




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3 Comments:

At 5:45 PM, Blogger *bOeUn said...

hi^^ you made a mistake,,
it should be because not becasue

 
At 5:26 PM, Blogger tears_77 said...

Thanx boeun for your comment. I really appreciate it.

 
At 12:30 PM, Blogger Mr. Reece said...

You have one other small mistake. There are a total of 52 weeks in a year, remember that most months have 4 weeks and 2 or three extra days left over. Otherwise the amount of effort that you put into this growing post is absolutely phenominal. The effort that you put into the 2 questions that you created truly demonstrated that you understand all of the concepts that we have learned in grade 7 patterns and equations. You mark is 24/25 + 6 bonus marks for the level of detail for your 2 created questions.

congradulations Tears77 on a phenominal post

 

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