Kathleen's Math Parent Quiz Post

Ratio Rate Proportion ( My Proportion Scribepost)
Peter runs 200 m in 30s while his sister Eva runs 300 m in 36s.

• Who is the faster runner? Explain how you can tell.
• At the same rate, how far will each runner go in 2 minutes?

Percent 
A bicycle is on sale for 10% off the origional price of $420. when it does not sell, the store reduces the sale price by another 5%.  What is the final price of the bicycle?

Surface Area
Calculate the Surface Area of the net below.

Fractions (My Fraction Scribepost)
Chad likes to eat Honeycomb for breakfast every day.  He eats 3/4 of a box per week. 

• How much of the box does he eat each day?
• How many boxes of Honeycomb does he eat each year?

Algebra Equation Solving(My Algebra Unproject)

Kathleen's Algebra Unproject

Steps on how to solve a 2-step equation (multiplying)

 1.) Look at your equation and check which ones are the constant, variable, and co-efficient. In this equation, 3 is the co-efficient, x is the variable, and 2 and 8 are the constants.

2.) In order to isolate the variable, you get rid of the constants first by using a zero pair. If you're looking at it, + 2 will look like an integer (+2) and to make a zero pair you use the opposite operation. So, the opposite operation of (+2) is (-2). Once you have written that, whatever you do to one side, you have to do it on the other side. Also put a (-2) on the side of the equal sign.  

Here, it just shows you since you have made a zero pair with the (+2 -2) You use the difference of 8-2 in the next step.

3.) Since you have made the constant disappear, you put the remaining numbers together, which will look like an easier equation. Wait, you haven't isolated the variable (x) yet because the co-efficient is still there!

4.) To get rid of the co-efficient, you must do the same steps you did to get rid of the constant. On this one though, you use the opposite operation of multiplying. How do I know 3x is supposed to be multiplied? Well, since there's no order of operations between the variable and co-efficient, it automatically multiplies! Moving on, the opposite operation of multiplying is dividing so you divide 3 with 3 to make 1. Whatever you do to one side you have to do to the other so 6 divided by 3 equals 2.

AND THEREFORE X = 2! BUT WAIT! ALWAYS VERIFY BECAUSE IT MIGHT BE THE WRONG ANSWER! If you knew the answer was x=2 still please verify because it is good practice and you never know, you might be wrong!

DON'T FORGET TO VERIFY!

Re-write the original equation again

Now you change x as 2 because that was your/my(?) answer

You use the system BEDMAS/ PEDMAS  so 3(2) equals 6 (Remember the rule I said about numbers not having an operation in between them)

Definitions

Variable- A letter or a symbol that represent s an unknown number. In order to solve this problem, you will have to find what the number x's value is.

Constant- A fixed value.

Co-efficient-A number used to multiply or divide a variable

Distributive Property

I made 3 groups of x (variable) and the -2 (constant). Then, I added the the 3 groups of -2 and got -6. Which would be your next equation.

This will have similar steps from both multiplying and dividing so this step might be easy for you. In order to make a zero pair, you will have to use the opposite operation of the constant and add/subtract them. The opposite of -6 is +6, and whatever you do to one side, you do to the other. So, you also put in +6 on the side of the equal sign. making it 9+6. I then re-wrote the remaining numbers which were 3x and 15. You do the same step with this equation, so you do the opposite equation to isolate the variable x. After I did that, I got x = 5!

DON'T FORGET TO VERIFY, ALWAYS VERIFY!!

So, I re-wrote the equation again, then replaced x with what I got which is 5 and then continued on. I got it right!

How to solve a 2-step equation (dividing)

 1.) Look at the equation and look for the variable you need to isolate and the co-efficient and constants you need to get rid off.

2.) -1 is the one you need to get rid off, so in order to get rid of it you use the opposite operation of -1 (which is +1). Also put a +1 on the side of the equal sign because whatever you do to one side, you have to do to the other.

3.) Once you have finished doing the last step, you re-write the remaining numbers and symbols. It's suppose to look like the second equation on the diagram. Then, you get rid of the co-efficient by doing the same step you did to get rid of -1. You use the opposite operation of division, and that is multiplying. Don't forget to do the same thing  on the side of the equal sign (even though it doesn't show there haha.) So 4(3) is 12 and you write h = 12.

Then you VERIFY! ☺ 

Modeling

RED- POSITIVE
WHITE- NEGATIVE

1.) Look at the diagram. It's a distributive property so you have to share. First you draw the diagram.

 2.)Get rid of the constant by making a zero pair. Then, whichever number you added on the -1 side, you add it on to the equal sign side

 3.)Then, you share them equally in two groups (because there are only 2 groups there)

4.)Since you put in two groups, you have to show how many x's are there in 1 group. So you draw it again but this time you show only 1 group! X = 4!!

Also, don't forget to verify using numbers! (Just to be sure)

*Thank you for taking the time to read my post about the different equations on Algebra. I was planning to sing because I wanted to try something out of my comfort level but I guess I wasn't ready enough and it would highly be embarrassing for me to sing by myself (especially with my really weird voice). Anyways, I hope you have learnt something from my post and good luck!☺☺ -Kathleen*

Kathleen's Algebra Scribepost

9.3 Pg. 357 Questions: 5, 8, 11, 14

5.) A long-distance telephone plan can be represented as C= 6t, where C is the cost in cents and t is the time in minutes.

a)Make a table of values , using at least four whole number values for t.

b)Graph the ordered pairs.

http://www.funmaths.com/math_tutorials/tutorial_graphs_straight_lines_intercept.htm

c) If part minutes are rounded up to the whole next whole minute, is it reasonable to have points between your graph? Explain.

No because they round it up anyways. So if it's 1 min. 30 secs. It would be rounded up to 1 minute.

8.) Evaluate y= 7x + 3 using each value.

a.) x= 1 

7x + 3 =y
7(1) + 3 =y
7 + 3 =y
10 =y 

b.) x= -4

7x + 3 =y

7(-4) + 3 =y

-28 + 3 =y

-25 =y

c.) x= 0

7x + 3 =y

7(0) + 3 =y

0 + 3 =y

3 =y

d.) y= 17

7x + 3 =y         7x + 3 =y   

7x + 3 =17       7x + 3 =17 

7x + 14            7x  (17-3)

2 =x                 7x  14 -------> 14 / 7 = 2 

11.) The graph below represents part of the linear relation y= -2x.

(Check the online textbook for the graph)

a.)Use the equation to calculate the y-coordinate when x=1

y= -2x
y= -2(-1)
y=  2
b.) What is the value of y in (-4, y )?

y= -2x

y= -2(-4)

y= 8

14.) You are given part of the table of values for a linear relation.

(Check online textbook for table of values.)

a.)How could you use a pattern to find the missing y-coordinates?

Well, looking at the table of values, it seems like y is increasing by 2 and x is increasing by 1.
b.)Identify the missing y-coordinates.

Kathleen's Integer Scribepost

8.2 Page 296 Questions 1, 3, 5 and 7

1.) Darcy modeled (+7) x (+3)  on a number line by drawing seven arrows. Ishnan modeled (+7) x (+3) on a number line by drawing only three arrows. Explain Ishnan's thinking.

Darcy did 7 groups of 3 while Ishnan did 3 groups of 7. It still works because the product is the same and Ishnan just "switched" the two numbers. 

3.) Without doing any calculations, Wei said that -19 and +27 have the same product as +19 and -27. How did she know?

5.) What multiplication statement does each diagram represent? 

a.) 2 x (-6) = -12

2 groups of negative 6 equals negative 12

b.) 4 x 4 = 16

4 groups of  4 equals 16

7.) Determine each product.

a.) (+4) x (-7) = -28

4 groups of -7

b.) (+2) x (+9) = 18

2 groups of 9

Still don't get it? Click on one of  the videos below!

Kathleen's Pay It Forward

Part 1

What is "Pay it Forward". To complete this part please edit and revise the paragraphs that you wrote after watching the movie.  

Pay it Forward is doing a good deed that can help others but you ask nothing for return. By doing this, it can make an impact on someone's life and help someone else, causing a chain of kindness! It doesn't matter if you know them or not, as long as you help them and ask nothing in return, that's Paying it Forward!

Part 2

What was your Pay It Forward act of kindness?

I donated to Value Village

Why did you choose this activity? 

Because my dad always says "If you don't need something, donate it because someone else might need it and make them happy." Some kids my age don't have much 

Who did you help?

Value Village. They would give the money they earned to a local nonprofits.

What did you do?

I donated some books, activity books, school supplies, and clothes.

When did you do you act of kindness?

I did it last Saturday December 1st 2012.

Part 3

How did your act of kindness go?

It went really well, the people working there were happy that I donated and they said they were thankful because not a lot of kids offer donations, it's usually the parents.

What Happened?

When we got there, we talked to the manager if we could take a picture with some employees and we explained to her what this was for. 

How did you feel?

I felt great that I was helping people in need!

How did the person or people react?

The people that were in-charge of taking the donations were very happy.

Did you ask the person or people to "Pay It Forward"?

She already knew what Pay it Forward was about because other kids have donated there too and have told some workers about it.

How did they react to your request?

The manager that we talked to said she does volunteer when she has the time.

Part 4

Why is the idea of "Pay it Forward" important?

It's important because most of us are forgetting what being kind means. Most of us nowadays expect something in return when you do something nice for them. Being kind doesn't mean you get something in return, it just means you did something nice because you wanted to help them out! If they do something in return, thank them because they're probably paying it forward too!

Has your act of kindness made a difference?
I hope my act made a difference in someone's life. Even though it was a small act, I hope it made someone happy. 

Kathleen's Scribepost

Questions: 10, 11, 12

Page 228

*The ones that are in RED are WHOLE NUMBERS
*Reciprocal-  is the fraction that when multiplied creates a product of 1

10.) Divide

a.) 1 1/12 divided by 2 1/2

You need to turn the mixed numbers into an improper fraction. 1 and 1/2 becomes 13/12 and 2 and 1/2 becomes 5/2. Since you have to do the reciprocal on the denominator, you multiply 13/12 by 2/5 on the top (numerator). Then simplify your answer if needed.

b.) 8/11 divided by 4/5

 Do the reciprocal on the denominator then after you do that step, you put the reciprocal on the denominator and multipy those. Simplify if it is needed, in this case, I simplified it by 4.

c.) 1 3/8 divided by 2 3/4

Do the reciprocal on the denominator then after you do that step, you put the reciprocal on the denominator and multipy those. Simplify if it is needed, in this case, I simplified it by 11 then 2.

11.) In a comedy review, each performer has a 1/4-h slot. How many performers are there in a 2-h show?

My tip for words problems like this is whatever the second number is, that is what's going to be the denominator. I'm not 100% sure it will work all the time, but this is what I've been using for these kind of word problems.
2 divided by 1/4
How many times does 1/4 go into 2?

*Since 2 is a whole number, make it into a fraction by using 1 as a denominator. So it becomes 2 over 1.

12.) It takes 2 1/2 scoops of flour to make one cake. How many cakes do 15 scoops of flour make?

*My tip for words problems like this is whatever the second number is, that is what's going to be the denominator. I'm not 100% sure it will work all the time, but this is what I've been using for these kind of word problems.

If you don't get my explanation, here's a video you could watch to understnad dividing fractions more.

And the video below explains how to do the reciprocal for divind fractions.

My Test Corrections

In computer terminology, a bit is 1/8 of a byte. How many bits equal 16 bytes?

16 divided by 1/8

Tamar had 1/2 of an apple pie in her refrigerator. She ate 1/4 of this piece of pie. What fraction of a whole pie did she eat?

1/2 x 1/4 = 1/8

5/6 x 1/2

What is 1/2 of 5/6

1/4 divided by 1/3

Everything Kathleen Knows About Fractions

Kathleen's Proportion Post

Part 1

Ratio-shows the same size of two or more values. You can express is by using a fraction bar, a column bar ":" or a word ratio.

Rate- compares two quantities measured in different units.

Proportion-a relationship that says two ratios or rates are equal

Part 2

1.) 5 hours to travel 360 kilometers is about _____km/h.

5 divided by 5 = 1h
360 divided by 5 = 72km
5 hours to travel 360 kilometers is about 72 km/h

2.) Emma saves 28 cents of every dollar that she earns.  Emma earned $75 last week.  How much money did Emma save last week?

 

Part 3

What are the three ways you can prove that equivalent ratio statements are true?
1.) 3/4 = 12/16  or 2.) 4/9 = 16/32

Part 4

Here's a link explaining how proportions work

Part 5

http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg

1.) Does this seem fair?

It doesn't seem fair because Paul Allen (The CEO) only gets 3 years in prison because he did a scheme that invovled 3 billion dollars while Roy Brown (2nd article) gets imprisoned for 15 years just because he stole $100. On top of that, Mr. Allen didn't confess about his doings while Mr. Brown called the police the next day after he stole it.

2.) With what you know about proportion look and read what is in the image above. Does it seem just and fair?

No.

3.) Why have you made this choice? 

4.) What would you have done if you were the judge?
 I would have switched the prison sentences and I would've given the CEO the 180 month sentence and I would've probably gave Roy Brown the 40-month sentence.