Mapping Diagrams

[amnesobel]

I am not sure which area this post belongs. I am in 6th Grade using The "Big Ideas" journal worksheet page 192. I am stuck on this one and only problem of the seven pages of math homework I had this weekend.

Activity: Interpreting Mapping Diagrams

Describe the pattern in the mapping diagram. Complete the diagram. Find two earlier lessons where you used a similar function.

D. Input, x
1 given
2 given
3 given
4 given
5 given
6 given
7 given

Output,A
4/3 given
5/3 given
2 given
need to solve
need to solve
need to solve
need to solve

The earlier lessons used were about Mapping diagrams using Area, Perimeter, Circumference and volume

I have tried Area a=x2
I have tried perimeter p= x+x+p+p
I have tried Circumference pieD or 2pieR
I have tried Volume Bh

I changed the outputs to decimals and If I look at it It would appear to maybe work out like this. If I solved it without using math.
1.33 given
1.66 given
2 given
2.33 Educated guess
2.66 Educated guess
3 Educated guess
3.33 Educated guess

But once I use a formula I cannot get it to work out to get my guessed answers to correlate with the other numbers (like all outputs going up by .33 or .42)so they must be wrong. Then I attempted to scratch my guessed answers and just work the problems with each formula and I still cannot get the outputs to correlate with eachother.

the other problems I have completed all work out but for the life of me I cannot get this one to workout and do not know what I am doing wrong. It seems that for example to get from 3 input to 2 output you would have to add or multiply to get a larger number to then be able to subtract or divide to get to 2. But I am lost because none of the formulas I have to use work. As I said I tried all of the formulas given in the book and none of them work out.

An example of a problem I have completed which I used Area where S= nx

input,n
1/2 given
3/2 given
5/2 given
7/2 given
9/2 given
Output,S
3/2 given
9/2 given
15/2 given
21/2 I solved
27/2 I solved

Similarities are input goes up by odd numbers and output goes up by 6 each time.

Maybe If I graph the points on a graph I can see how they correspond. I will try that now while I wait for help.

As for the problem that I cannot solve yet I cannot find the similarities in the output column no matter how hard I try. Thanks for your help and time.

Thanks,
Riley

 

[amnesobel]

Okay so I did a little more math while awaiting a response.

I believe the correct answers for the output would be they go up by 0.33 and the whole number by 0.34 This is my educated guess!

output,A
4/3 given = 1/33/100 =1.33
5/3 given =1/33/50 = 1.66
2 given = which would represent 6/3
7/3= 2/33/100 = 2.33
8/3= 2/33/50 = 2.66
3 = which would represent 9/3
10/3= 3/33/100 = 3.33

That being said I still do not know how to get from input to output. I tried the formulas but they aren't working for me. please help this is due 3/29/11 Tuesday.

 

[soroban]

Hello, amnesobel!

Don't look for some formula (area, perimeter, etc.).
Instead, examine the behavior of the sequence of terms.

The one you solved has this chart:

. . \(\displaystyle \begin{array}{cccc} \text{Input} & \text{Output} \\ \hline \\[-3mm] \frac{1}{2} & \frac{3}{2} \;=\; 3(\frac{1}{2})\\ \\[-3mm] \frac{3}{2} & \frac{9}{2} \;=\; 3(\frac{3}{2}) \\ \\[-3mm] \frac{5}{2} & \frac{15}{2} \;=\; 3(\frac{5}{2}) \\ \\[-3mm] \frac{7}{2} & -\;\;\; \\ \\[-3mm] \frac{9}{2} & -\;\;\; \end{array}\)

Can you see that the Output is three times the Input?

\(\displaystyle \text{The pattern is: }\:\text{Output} \:=\:3 \times \text{Input}\)


The other problem has this chart:

. . \(\displaystyle \begin{array}{ccc} \text{Input} & \text{Output} \\ \hline \\[-3mm] 1 & \frac{4}{3} \;=\;1 + \frac{1}{3} \\ \\[-3mm] 2 & \frac{5}{3} \;=\;1 + \frac{2}{3} \\ \\[-3mm] 3 & 2 \;=\;1 + \frac{3}{3} \\ \\[-3mm] 4 & - \\ \\[-3mm] 5 & - \\ \\[-3mm] 6 & - \\ \\[-3mm]7 & - \end{array}\)


This one is trickier.
We see that: .Output equals 1 plus (Input divided by 3)

\(\displaystyle \text{The pattern is: }\:\text{Output} \:=\:1 + \frac{\text{Input}}{3}\)

 

[amnesobel]

Thanks so much for your help. These are very new to me And I definitely need to practice them some more. I guess I was hung up on looking@ them the wrong way But I see how you came to your conclusions. I am going to review all of my previous pages and see if I can look at them as straight forward as you did. Thanks again!

Riley