Monday, February 6, 2017

Inferential Division

Last week, we discussed pulling information out of your head to solve math problems and noticing extra or missing information. Sometimes, we need to know things like how many days their are in a week or year, minutes in an hour, or cups in a pint... or recognize that we need to figure it out what we do need. This is often frustrating when we are trying to do our work because it becomes an extra step. This week, we will celebrate finding word problems we need to do just that!

Try going to IXL, Math Goodies, KwixNet, more IXL. Find a word problem here or write your own. Tell us what was tricky. What did you need to do? You first need to explain how you solved it, then tell us what was extra, missing, or needed for information. Then solve the problem.

We will do something with this in class Friday. So, do your best work to help us with a fun Friday.

1. Word Problem:

Cesidia is saving up for a car. She has been saving \$100 a week every full week since December 14. If she started with \$473 and keeps saving until April 3, how much money will she have toward her new car? How much would she have if she could calculate out the days including the first and last day?

How I Solved It in Weeks:

First, you need to look at a calendar to figure out how many full weeks there are. December 14 is a Wednesday and April 3rd is a Monday so the last days won’t earn her any extra money. There are 15 weeks from her start to her end date.

If I multiply out 15 times the \$100, I will get \$1500. Then I need to add \$1500 and \$473 to get \$1973.

What was Tricky:

Determining how many full weeks there are between the two dates. I had to look at the calendar and count them out.

In full weeks, Cesidia was able to save \$1973 toward her car.

How I Solved It in Days:

To figure this problem out in days, I started by dividing \$100 by 7. I came out to a very long decimal so I decided to go out to the thousandths place which is one place more than dollars and cents. This gave me 14.286. The actual answer was 14.2857143. Using rounding, I was able to use the answer 14.286.

Next I had to determine the number of days. I started by looking at the number of days in the full months of January, February and March. Then I added the exact days remaining in the two partial months of December and April. There are 31, 28 and 31 days respectively in the full months. April is easy because it is the 3rd, so there are 3 days. I had to look at the calendar for December and count the 18 remaining days to save. I also had to make sure February is not a leap year. I then added 31+28+31+3+18 and got 111 days. Then I needed to multiply my 111 days by the 14.286 to get 1585.746. Finally I need to round again to get a real dollar amount 1585.75 + 473 = 2058.75.

What was Tricky:

I had to look at the calendar to know how many days there are in each month. I also needed to count the days in December. I even needed to remember to count the first and last days. Although this wasn’t hard, I also needed to remember to round out to the thousandths to make sure I had one extra place value to consider.

In full weeks, Cesidia was able to save \$2058.75 toward her car.

****************Could you have solved this another way? Extra credit if you turn it in on paper Friday!****************

2. Andrew has a basketball practice every other day starting from January 1 to May 29 (It is a leap year). How many practices does Andrew have?

Answer: You have to count how many days there are from January 1 to May 29 which is 150 days, and than divide that by 2 to find how many practices there are. 150/2=75 This means that Andrew has 75 practices.

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4. Evan gets \$8 a day for doing chores. How many dollars will he get in 12 weeks. Evan wants to buy an ipad and the ipad is \$488. Does he earn enough money to buy one?

You need to know how many days are in a week and then multiply by the number of weeks

Then you need to multiply that times \$8 to get the total amount of the money earned. Then subtract the total amount of the money by \$488 to see if Evan has enough money.

Tricky
The number of days in a week are not pervided

The number of days in a week =7

7 x 12 =84

84 X \$8 =672

672 > 488
672 - 488 = 184

5. By Grace

Owen and his family, with 5 people including him, want to adopt a dog between May 3rd and September 21st. The dog they want is \$423. If everyone pitches in \$5 every full week will they have enough money to get a dog?

How I solved it:

I looked at the calendar to
determine how many weeks in between May 3rd and September 21st. May 3rd is a Wednesday and September 21st is a Thursday and there are 18 full weeks in between. Multiply the number of family members by how much money is getting pitched in to get
5x\$5=\$25. Then I multiplied the \$25 by the 18 full weeks to get \$25x18=\$450. \$450 is greater than \$432 so Owen's family can get a dog.

What was tricky:

I had to look at the calendar to determine the number of weeks between May 3rd and September 21st. -Grace

6. Keshob's total allowance in a year is \$231.86. He is saving up for a IPad that costs \$599.99. He also wants to buy a LEGO set that costs \$63.46 and a hover board. The cost of the hover board is found by adding up the costs of the IPad and the LEGO set and multiplying it by 0.2

how much money does he need and how many years will it take?

First, you have to add up the cost of the LEGOS and IPad, I called the answer L.

Next, find the cost of the hover board, do L/0.2 = H or the cost of the hover board

Tricky
I didn't include the cost of the hover board you had to find it yourself!

7. Jeff is saving up for a hot yogurt, snow cone, and gumball machine. He has been saving \$95 every 5 days from December 19 to March 14 (It is a leap year). Include the first and last day. How much money will Jeff save?

How to solve:

Look at a calendar to find that there are 87 days. Then divide by 5 to get 17.4 which is rounded to 17 or 17R2. We don't need the remainder so we can now solve.
The equation is (95x17)+329=1,944

What was Tricky:

I had to look at a calendar to see how many days there were between December 19 and March 14. Then I had to add an extra day because it was a leap year. I also had to add a day because I included the first and last day.

Jeff will save \$1,944

8. Xavier has been saving 75 cents every day for the whole month of January. How much money will he save by the end of the month?

How I solved it in days:

First, I thought of the poem Mrs.Mason taught her reading class ."30 days has September,April,June, and November. All the rest have 31 except February which has 28 and sometimes 29." So January has 31 days.

Then, I multiplied 31x.75=4.25\$. So Xavier saved \$4.25.

What was tricky:

Having to remember the poem I learned in 3rd grade.

In days he saved \$4.25

How I solved it in weeks:

By looking at the calendar I figured out that there was 4 weeks 3 days. So I multiplied 4x7=28+3=31 days and 31x.75=4.25.

What was tricky:

I had to look at the calendar to figure out how many weeks there are in January,and then find away to calculate the weeks in to the right answer.

In weeks \$4.25

9. Mack wants to get a room makeover for \$980. If she saves \$50 from January 1 to March 4 will she have a enough money to get a room makeover.

How to solve it: first I counted how many weeks are are in between January 1 and March 4. There are nine weeks in between January 1 and March 4. So 50×9=\$480. She will not have enough money to get a room makeover.

What was tricky: By Looking at the calendar I had to figure out how many weeks there by looking at the calendar.

The answer: she will not have enough money \$450 < \$980.

10. Dillan is signed up for indoor soccer. There is a practice every 5 days the season lasts for 8 weeks. How many practices does Dillan have this season.

First, you need to figure out how many days in 8 weeks. 8x7=56 days. Next, you need to divide 56 by 5.
56/5=11 Dillan will have 11 soccer practices this season.

What was tricky:
Well first off, you need to figure out how many days in 8 weeks. And secondly, 56 does not divide evenly into 5, so you have one left. This confused me and I didn't know what to do with it at first.

11. Johnny wants to buy a phone for \$875. He is going to earn \$45 a week from September 1st to January 1st. Will he have enough money to buy a phone by January 1st?

How to solve it: Figure out about how many weeks there are between September 1st and January 1st. There are about 17 weeks between September 1st and January 1st, now you need to multiply 45 by 17 to get 765. So he will have \$765 between September 1st and January 1st.

What was tricky: Trying to count about how many weeks there are between September 1st and January 1st.

Answer: 875 is greater than 765 so Johnny will not have enough money to buy a phone between September 1st and January 1st.

12. Joe plans to make 17 liters of blackberry punch and 8 liters of lemon-lime punch for the class party. He also plans to make 12 batches of cookies. How many students will Joe's punch serve?

This problem has missing information, in order to solve this, you need to know how many students are in his class and how much punch each student will consume. So there is no way to solve this, therefore, no way to explain how to solve it. There is also extra information, the amount of cookies is not needed to solve.

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14. It is February 1st ,2017 and Alphys has a scientist job that she gets paid \$8 a day because she works 8 hours. She wants to buy a big computer that costs \$999 for her office. It is on sale until June 30th. Will Alphys have enough before it gets off sale? If so, how much will Alphys have left?

What was tricky:
How to figure out how much money Alphys would have ; what month to start at and end at.

There is about 4 whole weeks in a month. Usually there is 30 or 31 days in a month. In February 28. Since not a leap year, still 28 days in February.

The order from February to June this year on the calendar in days is ,February ,28 ,March ,31 ,April ,30 , May , 31 , and June has 30 days. I took out 1 day from JUne the added 28+31+30+31+29. I got 149. There is 149 days between Feb. 1st and Jun. 30th. Then i did
149 x 8 = 1192. So she has \$1192 which means she has enough money to buy the big computer.
But Alphys will only have \$193 left.

-Alec.

15. Shadman wants to get a computer that costs \$650. He makes \$25 a week from January 1 to June 1. ( Not a Leap Year) Will he have enough money to buy the computer?

How to Solve: First, you need to figure out how much money will he earn over the weeks with the \$25, and how many weeks there are from January 1 to June 1. There are 21 weeks from Jan. 1 to June. 1. Then you have to multiply the weeks which is 21 by \$25. That is \$525 so he does not have enough.

What was Tricky: To find how many weeks there were from January 1 to June 1.

Answer: He would have made \$525 which is less than \$650 for the computer. So he can not buy the computer.

16. Vincent want to buy a 3DS for \$300. He saves up \$30 from February 1st to May 2nd. Does he have enough money to buy the 3DS?

How to solve: Find out he amount of weeks from Feb.1 to May 2. Then, multiply that by 30. Vincent will have \$390. That is enough.

What was tricky: Finding all the days from Feb. to May because some months have 30 days and some have 31 days.

17. Word Problem:

Reagan is saving up for a giant duck stuffed animal. She has been saving \$10 a week every full week since December 31. If she started with \$21 and keeps saving until January 28, how much money will she have toward her new giant stuffed duck? How much would she have if she could calculate out the days including the first and last day?

How I Solved It in Weeks:

First, you need to look at a calendar to figure out how many full weeks there are. December 31 is a Saturday and January is also on a Saturday . There are 4 weeks from her start to her end date.

If I multiply out 4 times the \$10, I will get \$40. Then I need to add \$40 and \$21 to get \$61.

What was Tricky:

Determining how many full weeks there are between the two dates. I had to look at the calendar and count them out.

In full weeks, Reagan was able to save \$61 toward her giant stuffed duck.

How I Solved It in Days:

To figure this problem out in days, I started by dividing \$10 by 7. I came out to a very long decimal so I decided to go out to the thousandths place which is one place more than dollars and cents. This gave me 1.428. The actual answer was 1.42857142. Using rounding, I was able to use the answer 1.428.

Next I had to determine the number of days. I started by looking at the number of days in the full months of December and January . Then I added the exact days remaining in the two partial months of December and January. There are 28 days respectively in the full months. January is easy because it is the 28th, so there are 28 days. I didn't have to look at a calendar for December because it was December 31. I then added 28+1 and got 29 days. Then I needed to multiply my 29 days by the 1.428 to get 41.412. Finally I need to round again to get a real dollar amount 41.412 + 21 = 62.412.

What was Tricky:

I had to look at the calendar to know how many days there are in each month. I even needed to remember to count the first and last days. Although this wasn’t hard, I also needed to remember to round out to the thousandths to make sure I had one extra place value to consider.

In full weeks, Reagan was able to save \$61 toward her stuffed duck.

18. Word Problem:

Julia R. is saving up money to buy a cat and all its supplies. She will need about \$500 in all. If she has been saving 10 dollars every week, will she have enough money over the course of a year?

How I Solved It:

First, figure out how many weeks are in a year. There are 52 weeks in all, so multiply 52 by 10 to get 520.

She will have 520 dollars by the end of the year.

What was Tricky:

Figuring out how many weeks in a year. This information is not listed in the problem.

Over the course of a year, Julia was able to save \$520. 520>500, so Julia will have enough money.

19. Example 3:
Rick's car gets 29.7 miles per gallon on the highway.
If his fuel tank holds 10.45 gallons, then how far can he travel on one full tank of gas?

Analysis:
To solve this problem, we will multiply 29.7 by 10.45

Multiply:

Rick can travel 310.365 miles with one full tank of gas.

WHAT I FOUND TRICKY:
In the problem it does not say if you are on the high way.

WHAT I WOULD WHAVE DONE:
Rick's car gets 29.7 miles per gallon on the highway.
If his fuel tank holds 10.45 gallons, then how far can he travel on the high way, on one full tank of gas?

20. Word Problem:
Shreya has 7.11 lbs of candy. If she puts the candy into 9 jars, how many ounces of candy will each jar contain?

How I Solved Part of the Problem in Pounds:
I did 7.11/9=0.79 lbs. So there are 0.79 lbs. of candy in the jar

What was Tricky:
Determining how ounces were in a pound. I remembered that I had searched it up a while ago and remembered.

How I Solved the Other Part of the Problem in Ounces:
I remembered that 16 ounces were in a pound. 0.79*16=12.64

12.64

21. Bella is saving up for soccer camp. She saves \$9.00 a week from December 18 to March 18. Before she started saving, she had \$120. How much money will she have towards her soccer camp?

How I solved it in weeks:
First I need to look at a calendar and see how many weeks December 18 to March 18 is. December 18 is a Sunday and March 18 is a Saturday. March 12 is a Sunday so she will not make any money for the extra 6 days. There are 12 weeks from her start date to her end date.

If I multiply 12 weeks x \$9 and get \$108 and I add it to the \$120 I already have, I get \$228.

What was tricky:
I thought that finding how many weeks between my start date and my end date was hard because if I miscounted the whole problem would be wrong.

Answer: In full weeks I was able to save \$228 for my camp.

How I solved it in days:
To figure this out in days, I start by dividing \$9 by 7 days. I came out with a long number so I decided to go to the thousandths place, which is one place more than the dollars and cents. This gave me 1.285. The original answer was 1.28571426

Next I need to determine the number of days. I started looking at the number of days in the full months of January and February and added them together. Then I added the exact days remaining in the two partial months of December and March. December had 14 days and March had 18 days for a total of 32 days. Then I added the two full months, January, which had 31 days, and February which had 28 days. Then I added them all up 14+18+31+28 to get 91 days. After I had to multiply 91 x 1.285 to get 116.935. Finally, I need to get a real dollar amount by rounding, \$116.94. \$116.94+\$120= \$236.94

What was tricky:

I thought that finding how many days that were left in December starting on the 18th was tricky. Also having to round to a dollar amount at the end was tricky too.

In full weeks I was able to save \$236.94 towards soccer camp.

22. Jorge found a pipe in his basement that is 2.5 feet long. He wants to store balls in it that are three inches each. How many balls can he fit in there?

How I solved:

First I need to know how many inches there are there are 12 inches in a foot.
So I do 2.5 x 12 =30 inches. 30/3= 10 balls

What was tricky:

Converting 2.5 feet into inches.

Answer: Jorge can store 10 balls in the pipe.

23. Frankie had to save 250 dollars for a trip. How many weeks will it take if she saves 15 dollars each week?

Answer : You need to divide 250 by 15
250/15=16 r10
What was tricky is 1.You have to know how many days are in a week which is 7 days and 2.since there is no such thing as 16r10 weeks you need to have a total of 18 weeks because there are 7 days in a week.

The information I left out was how many days are in a week

The final total is 18 weeks

24. Emma S.

Emma wants to purchase a flat screen TV that costs \$1,000. Starting from Nov.26-Jan.1, Emma will save \$100 a week. Will Emma have enough money by Jan.1 to get her flat screen TV?

HOW I SOLVED: First I figured out how many weeks are in Nov.26-Jan.1
Then I multiplied that number of weeks by the \$100 to get 600, which is \$600.

WHAT WAS TRICKY: It was hard when I had to find out how many weeks were in Nov.26-Jan.1 because Nov.26 was on a Saturday, so I had to count them from Saturday to Saturday.

THE FINAL TOTAL: The final total was \$600 so no she dose not have enough money to buy the flat screen TV.

25. woah we used to always do these :D