Monday, May 22, 2006

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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14 Comments:

At 3:56 PM, Blogger michelle said...

where did you get the t-chart from?

 
At 5:29 PM, Blogger angelic72 said...

i made the tchart

 
At 2:21 PM, Blogger Mr. Reece said...

Once again a wonderful post, its very easy to follow due to the use of colours and fonts, your explanations are clear and precise. Your T-Chart is beautiful.
Another post to be added to the hall of fame.

Question 4 isn't due till next week but it looks great.

 
At 4:15 PM, Blogger michelle said...

This is a good post. Can you teach me to make a good growing post like this?

 
At 4:26 PM, Blogger angelic72 said...

sure

 
At 4:13 PM, Blogger Mr. Reece said...

Angelic you have earned 18/17 for your second scribe post, congradulations.

 
At 10:01 PM, Blogger Mr. Reece said...

Angelic your forth post is great, but there are a few small problems. You never showed how to solve the question involving farm animals. You gave the formula (D+1)D = 992, but you never said how you created this formula, or at least how someone else could create it looking at the T-chart, based upon what we have learned.

The other problem is with your solution to part 2 of the first question. You did not use a variable in your equation i.e. it should have been 200 + 20w = total money. You could then make w = 52 week.

Your mark is 21/25

 
At 8:05 PM, Blogger angelic72 said...

I'm going to do the correcrions tomorrow

 
At 2:20 PM, Blogger Mr. Reece said...

You made a small mistake on question #3. You created the formula 4 + n = 9, and then solved for n, but had n = 9, when it should be 5.

Otherwise the answers were great, the T-charts looked amazing and everything was completed to a high level of quality.
You mark is 29/30

 
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