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Scoring Guide for the Peanuts Problem
The total score will be the sum of the 5 scores below. (maximum score = 20)
Scores will be based upon the following:
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POINTS |
CORRECT ANSWER - See
chart following this section |
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4 |
Answer is correct: 11 peanuts |
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2 |
Answer is how many peanuts were eaten on Sunday: 5 peanuts |
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0 |
Answer is not correct (other than 5 or 11 peanuts) |
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POINTS |
PROBLEM UNDERSTANDING
Understand the patterns, concepts, and approach
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4 |
Understands the pattern and calculates that Robin started with 5 peanuts
Calculates how many peanuts Robin ate on Wednesday
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2 |
Understands the pattern and calculates that Robin started with 5 peanuts
Fails to calculate how many peanuts she had on Wednesday
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1 |
The task is misunderstood
Information is incorrectly used. For example, did not understand that 2 peanuts are added each day.
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0 |
No attempt at response
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POINTS |
STRATEGY
Choose and apply a valid strategy (Some valid strategies are given in the table below.)
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4 |
Choice of a valid strategy: visual representation, make a table, guess and check, working backwards, or figuring out a formula
Applied the strategy correctly and completely
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2 |
A good strategy was chosen, but was partially or incorrectly completed. For example, they made a table but the table had errors.
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1 |
Strategy did not apply to this problem.
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0 |
No attempted strategy
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Possible Strategies
Strategy #1: GUESS-AND-CHECK
I will guess that Robin started out eating 2 peanuts on Sunday.
Then the total number of peanuts that she ate all week would be:
2+4+6+8+10+12+14 = 56 peanuts. Too low!
This is too low, so I will guess that she ate 3 peanuts on Sunday:
3+5+7+9+11+13+15 = 63 peanuts. Too low!
This is still too low, so I will guess that she ate 6 peanuts on Sunday:
6+8+10+12+14+16+18 = 84 peanuts. Too high!
This is too high, so I will guess that she ate 5 peanuts on Sunday:
5+7+9+11+13+15+17 = 77 peanuts. The right answer!
So if she ate 5 peanuts on Sunday, she must have eaten 5 + 6 = 11 peanuts on Wednesday. Horray!
Additional pattern insight:
I now see that every time I added a peanut on Sunday, it resulted in 7 more peanuts eaten all week.
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Strategy #2: MAKE A TABLE
The following table shows the patterns.
The correct column is the middle
column
where Robin begins with 5 peanuts.
The correct answer is 11 peanuts
eaten on Wednesday.
| Sun | 4 | 5 | 6 |
| Mon | 6 | 7 | 8 |
| Tues | 8 | 9 | 10 |
| Wed | 10 | 11 | 12 |
| Thurs | 12 | 13 | 14 |
| Fri | 14 | 15 | 16 |
| Sat | 16 | 17 | 18 |
| TOTAL | 70 | 77 | 84 |
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Strategy #3: MAKE A PICTURE
Here is a valid picture representation:
(Each circle stands for a peanut)
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Sun
0
0
0
0
0
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Mon
0
0
0
0
0
0
0
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Tue
0
0
0
0
0
0
0
0
0
|
Wed
0
0
0
0
0
0
0
0
0
0
0
^
11
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Thurs
0
0
0
0
0
0
0
0
0
0
0
0
0
|
Fri
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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Sat
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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Strategy #4: SOLVE WITH AN EQUATION
Admittedly, the following solution is NOT easy, but here it is:
Let S stand for the number of peanuts Robin ate on Sunday.
Then the number she ate on Monday was S+2, Tuesday was S+4 and so on.
Then the total equation becomes:
| Sunday | S |
| +Monday | S+2 |
| +Tuesday | S+4 |
| +Wednesday | S+6 |
| +Thursday | S+8 |
| +Friday | S+10 |
| +Saturday | S+12 |
| 7S+42 = 77 |
| 7S = 35 | <--Simplifying |
| S = 5 | <--Started with this many on Sunday |
| Since the number eaten on Wednesday was S+6, this is 5 + 6 = 11 |
Stragegy #5: WORKING BACKWARDS
All the "added" peanuts (2 more every day after Sunday) add up to 42 peanuts (2+4+6+8+10+12).
Subtracting those 42 added peanuts from 77 gives me 35 peanuts (77-42).
These 35 peanuts were spread out over 7 days, so the number she ate on Sunday must be a factor of 35.
Since she ate the 35 peanuts over 7 days, she must have eaten 5 (35/7) peanuts each day, plus all the "added" peanuts (42). So she started on Sunday with 5 peanuts. Since she ate 6 more than this on Wednesday, she ate 6 + 5 = 11 peanuts on Wednesday. |
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POINTS |
COMMUNICATION
Explain the reasoning at each step, using pictures, symbols, labels, and correct vocabulary
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4 |
Described strategy and solution clearly and completely, step-by-step
Correct presentation of solution, including appropriate labels, terminology, and symbols. For example, if they made a table, the table has column descriptions.
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2 |
Strategy was described, but steps may be missing
Labels may be missing or directions may not have completely followed
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1 |
Strategy was not explained according to directions or reasoning is confusing.
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0 |
No attempt to explain
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POINTS |
REASONABLE RESULT
Review the work and show why the result is reasonable
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4 |
Review used a different approach to support the result
Explained why the result makes sense.
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3 |
The problem was reworked using the same approach to check its accuracy.
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2 |
The check for reasonableness was not complete, or they said something like "we checked our result."
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0 |
No attempt was made to demonstrate the reasonableness of the result
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