Tuesday, October 26, 2010

14-1 Problem Solving

YAY WORD PROBLEMS AGAIN!
Basically, all you need to do is find the fraction/decimal in word form, and then write it into either a fraction or decimal, depending on what the question is asking for.

Hundreds Tens Ones . Tenths Hundredths

#1) Three-tenths - They want it written in decimal form.
.3

#2) Half - They want it in both fraction and decimal form.
1/2 and .5

#3) Nine-Hundredths - They want it in decimal form.
.09

Friday, October 22, 2010

8-1 Problem Solving

AHHHH Word Problems!!!

#1 There are 20 members and 47 posters. They even told you what to do when they said 'divide'!
We haven't done two digit division yet, BUT, you can still walk through this one.
COunt by 20's until you get to 47 without going over.
20, 40, 60...Stop at 40 because 60 is too big. That took us 2 counts to get to 40. Now write a 40 underneath the 47 and subtract, you should get 7. We can't count by 20's to get to 7, because 20 is too big. So there are 7 remainders. The final count will be that each member will get 2 posters and there will be 7 posters left over.

#2 SAME AS #1!
There are 43 members and they need to be DIVIDED into groups of 10. Let's count by 10's until we get to 43 or close to it without going over.
10, 20, 30, 40, 50...Stop at 40 because 50 is too big! That too us 4 counts. Write the 40 underneath the 43 and subtract. You should get 3 left over, because you cannot count by 10's to get to 3. SOOOO There will be 4 groups with 3 people extra.

#3 SAME AS #1 AND#2!
There are 20 members and they each need to do the same number of reports. If there are 53 reports we need to DIVIDE them equally among the members. Let's count by 20's until we get to 53 or close to it without going over.
20, 40, 60....Stop at 40 because 60 is too big! That too 2 counts. Now write 40 underneath 53 and subtract. You should get 13. This means that each member will do 2 reports with 13 extras!

Monday, October 18, 2010

8-5 Two-Digit Quotients



Don't forget that QUOTIENT is the answer to a division problem.


I've added a picture walk-through from tutorvista.com to solve a division problem.
















Friday, October 15, 2010

8-2 Divide multiples of 10, 100, and 1,000

This idea really only needs you to know your basic multiplication facts, the rest if just adding zeros.

#1) 300 divided by 6.
I want you to draw a line cutting the number 300 into two pieces; 30 and 0. Now that we've narrowed things down, let's count by 6's until we get to thirty. 6, 12, 18, 24, 30. That took us 5 times. Write a 5 above the thirty, and the number 30 underneath. Don't forget to subtract the 30 and 30. That's easy, you get 0. Now that poor other zero is there all by himself. You can't count by 6's until you get to 0, that's silly. Think of it this way, 3 times what gives you 0? 0! So write that 0 on top as well. And you get an answer of 50.

#16) The input output table
The directions for this one tells us to divide by 5. The first input number is 1,500. According to the directions, we need to divide 1,500 by 5. Draw this with the 1,500 under the house and the 5 outside the front door. I sure hope you understand what that means. Now draw a line cutting 1,500 into two pieces; 15 and 00. Super easy now. Count by 5's until you get to 15. 3! Add in your filler zeros above the other two, giving you the answer 300!

#17)61 divided by 3.
Re-write this problem with the 61 inside the house and the 3 outside. Now cut the 61 in half with a line. Super easy now! Count by 3's until you get to 6. 3, 6. That took us 2 times. So write a 2 above the 6, and the 6 below the 6. Now subtract the 6 and 6. We get Zero. BUT! That poor 1 is all by himself. Bring him down, now let's count by 6's until we get to 1. Uh-oh, can't do it. Now listen very carefully. You HAVE to put a 0 above the 1, because we can't leave that place value empty. So far we now have 20 as our answer, but that pesky left over 1 needs to be a remainder. So your final answer is 20 r1

Thursday, October 14, 2010

8-1 Division with Remainders


*Note: you can solve these on a seperate sheet of paper. You might find yourself running out of room on the homework sheet.
**Note: #17-22 involve double digit multiplication. We have not learned this skill yet. You may skip it if you'd like, or you can use a calculator to solve it.

Oh yes, that dreaded division. :)

We have to know our multiplication facts in order to do this properly.

Step by Step of the above problem. We are solving 10 divided by 3. Sing your three's until you get as close to 10 as possible without going over. 3, 6, 9. We stop there because if we kept going the next number would have been 12, and that's too much. So we write a 3 on top and a 9 underneath. You will then subtract the 10 and 9, giving you 1. Now you can't sing your three's until you get to 1, that's just silly. You now have the answer, 3 with a remainder of 1.

Let's try some on the homework.

#1) 56 divided by 6.

Sing your 6's until you get as close to 56 as you can. 6, 12, 18, 24, 30, 36, 42, 48, 54. We stop there because if we kept going the next number would have been 60, and that's too big. Write a 9 on top and a 54 underneath. Subtract 56 and 54. You will get 2. Now you can't count by 6's until you get to 2, that's just silly. So you'll have that 2 as a remainder. Your answer 9 r2


Wednesday, October 13, 2010

5-6 Multiplication and Division Expressions

Make sure you know your multiplication facts!

For #1-9, Remember that j = 12 and k = 6

#1) j / 3 ___
We know that j = 12, so we will now solve 12 / 3. Sing or count by 3's until you get to 12.
3, 6, 9, 12. That took us four times to get to 12. So the answer to j / 3 is 12

#4) 5 x k
We know that k = 6, so we will no solve 5 x 6. Count by 5's until you get to your fifth finger.
5, 10, 15, 20, 25, 30. The answer to 5 x k = 30

#7) 5 x (j /4)
We know that j = 12. We know to always do what is inside parenthesis first. So let's solve j/4, or 12/4. Sing or count by 4's until you get to 12.
4, 8, 12. We now see that 12/4 =3.
Now for the second step. Bring down 5 x, to make 5 x 3.
This should be fairly easy. 5 x 3 = 15

Monday, October 11, 2010

5-2 Solve Equations Mentally

To find the missing variable you need to do mental math. If you are dealing with an addition problem, subtract the number given with the answer. This will give you the variable. If you are dealing with a subtraction problem you will need to count backwards from the number given to the answer to find the variable.

#1) 3 + d = 11
Since you have an addition problem, you can easily subtract the two numbers. 11 - 3 = 8.
So d = 8

#2) 15 - r = 2
Since you have a subtraction problem, I need you to visualize the number 15. Start counting backwards and put up one finger for each number you say, until you say the number 2. Like this 14 (put up 1 finger), 13 (put up 2 fingers), 12 (put up 3 fingers), 11(put up 4 fingers), 10(put up 5 fingers), 9(put up 6 fingers), 8(put up 7 fingers), 7(put up 8 fingers), 6(put up 9 fingers), 5(put up 10 fingers)....uh-oh, we aren't to 2 yet, remember that we got to 10 ok? And start over with your fingers... 4 (put up 1 finger), 3(put up 2 fingers), 2(put up 3 fingers)...whew! Remember how we already got to 10 fingers then put up 3 more.....10+3 = 13......
So r = 13

But the finger subtraction only works if the missing variable comes second in the equation. What if it comes first? Look at #6

#6) 9 = w - 12
I hate looking at problems with the answer first, so I'll just scoot the =9 to the other side
w - 12 = 9
We cannot use the counting backwards method for this or you'll get a tiny number to put first in a subtraction problem, which we all know is a no-no.
Instead, I want you to add the two numbers given to you. 12+9 = 21
So w=21

So basically:
All addition problems with a missing variable will be solved by subtracting the two numbers given, regardless of the placement of the missing variable.
A subtraction problem with the missing variable first can be solved by adding the two numbers given.
A subtraction problem with the missing variable second can be solved by counting backwards from the given variable to the answer.

Thursday, October 7, 2010

Problem-Solving Strategy: Make a Table

#1 Rosa knits sweaters to sell. Each sweater takes 4 balls of yarn. How many balls of yarn will she use if she makes 23 sweaters? This is a simple multiplication problem. 23 x 4



#2 You will need to use the answer from #1 to help you solve this problem. The first thing you need to find, is the total amount of money Rosa will earn if she sells 23 sweaters for $35. That is 23 x 35. You can use a calculator to find that product. You will see That if Rosa didn't have to buy yar, she would have made a profit of $805. But in the real world, Rosa had to buy yarn. According to problem #1, Rosa needed to buy 92 balls of yarn (shhh yes I know I just told you the answer to number 1), and this problem told us that each ball of yarn cost Rosa $6. That's 92 x 6. That means that Rosa had to spend $552 on yarn. Now you need to take the number she would have made if yarn was free, and subtract the amount she spent at the store to find her earnings. 805 - 552



#3 This is one doozy of a question! Follow me very closely...

Step 1 - Divide the total he made selling portraits by the amount he's selling each one for

180 / 15 You can use a calculator here. He sold 12 portraits.

Step 2 - For every 7 pictures he takes, he has one portrait, so now we need to multiply 12 x 7

That will give you the answer to this problem.



#4 This is a two step problem. If Hannah practices 12 times a day for 5 days, you will need to multiply 12 x 5 to find out how many times total she practices. She practices 60 times in a 5 day week. If she pracitces for 4 weeks, how many times will she practice total? You need to multiply her 60 times by the 4 weeks. 60 x 4



For numbers 5 and 6

Please put the numbers in order from least to greatest. Remember that mode is the number you see the most, median is the middle number, and the outliers are found when you subtract the first two numbers and the last two numbers. If you need a refresher, scroll down to the blog post about median, mode, and outliers.



:)

Wednesday, October 6, 2010

Probability

For numbers 1-5, you will use the spinner at the top of the page, and the answers can be either certain, likely, equally likely, unlikely, or impossible.

Certain - It will always land there
Likely - There are a lot of that choice, so it will land there more often
Equally Likely - There is the same number of that choice as there are of ther others
Unlikely - There are not many of that choice, so you won't land on it that often
Impossible - There are no options for that choice, you will never land on it

#1 what is the probability of spinning an even number? There are 3 even numbers and 3 odd numbers, so if there is the same number of options, which probability word will you choose?

#2 what is the probability that you will land on a 2? There is one 2 on the spinner, there aren't a lot of 2's on the spinner.

#3 Spinning a 4, 5, or 6? They are asking for how often the spinner will land on those three numbers, that leaves three left over. Seems to me that you have the same chance that it will land on a 4, 5, or 6.

#4 Spinning a 7? If you look at the spinner, there are no 7's. You will never land on a 7.

#5 Spinning a 1, 2, 3, 4, 5, 6? That's all that is on the spinner, so you will always land on one of those numbers won't you?


Word Problem
#6 Jorge needs meat! He has 2 pastas, 3 rice, and 5 meats. It isn't certain that he picks meat, if that were the case everything would be meat. It isn't impossible to pick meat, because he has some. It isn't equally likely that he pick meat because there isn't exactly 5 of one other choice. So it's either unlikely, or likely. Likely means he's got more meat that any other food, and unlikely means he has less meat than any other food....
Now that I've narrowed it down for you, what do you think?

#7 Don't trust the drawing. Make a Tree diagram and pick the three shapes to start with, then your options will be the same three shapes. Doesn't make sense does it? That's because you're still looking at the picture!

_______Circle
Circle___Pentagon
_______Trianlge

________Circle
Pentagon__Pentagon
________Triangle

_______Circle
Triangle_Pentagon
_______Triangle

Now how many outcomes did you make?

Tuesday, October 5, 2010

Determine Possible Outcomes

Today you will be finding all of the possible combinations/outcomes.

#1 You need to find all of the combinations and outcomes for jackets and shoes. The chart gave us a white, black, and green jacket, and black, tan, and white shoes.
The directions ask you to make a tree diagram, you can also use a t-chart.

To make a t chart we need to pick one jacket color to focus on first. Let's pick white. Next to white, we will write the colors of the shoes.

White - Black
White - Tan
White - White

You will repeat this for each jacket color.

Black - Black Green - Black
Black - Tan Green - Tan
Black - White Green - White

Now find all of your color combinations. That number is the total possible outcome for this problem.

If you want to write it in a tree diagram you will essentially do the same thing. First, write each color jacket. Then draw three lines off of each jacket color. At the end of these lines you will write the shoe color. Lastly, you will write the actual combination you made. :)

_______Black WB
White __Tan WT
_______White WW

_______Black BB
Black __Tan BT
_______White BW

________Black GB
Green __Tan GT
________White GW

The two letter combinations represent your total possible outcomes.




Spiral Review:

#2 Two movie tickets cost $18 dollars(expensive right? that's why I don't go to the movies anymore). Thea and 3 friends want to go to the movies. That's 4 tickets, Thea plus her three friends. Since they already told us that 2 tickets cost $18, another 2 will also cost $18. Remember we need 4 total tickets. Usually when you see the word "total" it means you are going to create an addition problem. This means you need to add $18 plus $18, to find out how much it will cost Thea and her friends to go to the movies.

#3 Salma is reading a 300 page book. She's already read 60 pages, and she wants to finish it in the next 3 weeks.
Our first step is to figure out how many pages she has left to read. To do this you need to subtract the total number of pages with the number she's read. That will be 300 - 6. If you subtract properly, be careful around those zeroes, then you should get 240 as the number of pages that Salma has left to read.
She needs to read all 240 pages over the next 3 weeks. You will need to divide the pages equally over the next 3 weeks. If you're thinking what I think you're thinking, yes, I do want you do divide 240 by 3. But let me make it easier on you. Let's drop the zero. Now divide 24 by 3. If you sing your 3's song, that will help you get to the solution. Now add that pesky zero back to the end of your solution. I won't say the answer here, but you have just found the answer as to how many pages Salma needs to read each week to finish her book. :)

#4 This one is a tad more complicated. Marcus has $15 to spend on baseball cards. Each box is $2.50. First let's find out how many boxes Marcus can buy. Add $2.50, until you reach $15. You should have found out that he can buy 6 boxes of baseball cards. This is NOT the answer! The question is asking you to find the total number of cards, not boxes. They told us that there are 10 cards in a box. If Marcus has 6 boxes, with 10 cards in each box, how many cards will he have? You can either multiply 10 by 6, or draw six boxes, and write a number ten in each one. Either way, you will get to the same solution. :)

Monday, October 4, 2010

Word Problems

There is a misprint in tonight's homework!
#1 - The question should say "How many minutes does Sabrina spend doing homework in that same week?

#1. To solve this problem, you need to figure out how many minutes a night Tiffany spends a night on homework. It says that Tiffany spends 50 minutes in a 5-day week on homework. How many minutes is that a night? That problem is 50 divided by 5. So count by 5's until you get to 50. How many did you come up with? You should have found out that Tiffany spends 10 minutes a night on her homework.
Now if Sabrina spends 15 more minutes a night on her homework than Tiffany, how many minutes does Sabrina spend on homework? The word more means addition. So add Tiffany's 10 minutes plus Sabrina's 15 more. 10 + 15 = ?? What did you get? You should have found out that Sabrina spends 25 minutes a night on homework.
Lastly, you will need to find out Sabrina's total weekly homework time. If Sabrina spends 25 minutes a night on her homework, how much total time is she spending in 5 days?
Day 1 = 25min
Day 2 = 25 min
Day 3 = 25min
Day 4 = 25 min
Day 5 = 25min
I won't give you the answer here. :)

#2 Caleb is organizing his shirts into a pattern.
white, blue, white, red, white, blue .........
Look for the first pattern
white, blue, white, red is the first pattern
Caleb needs to know what color comes after blue. Look at the list, what color is written after blue?
You can find the pattern can't you? :)

#3 Corey needs to send cards to 56 people. But the cards only come in boxes of 10. To solve this, draw a box and write the number 6 inside. This is the first box Corey needs to buy. But it isn't enough is it? He needs to continue buying boxes until he has enough to send 56.
Hint~ the number of boxes he ends up buying will have more than 56 cards total.
I think you can figure it out now! :)