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:
 POINTS CORRECT ANSWER - See chart following this section 4 • Answer is correct: 11 peanuts 2 • Answer is how many peanuts were eaten on Sunday: 5 peanuts 0 • Answer is not correct (other than 5 or 11 peanuts)

 POINTS PROBLEM UNDERSTANDING Understand the patterns, concepts, and approach 4 • Understands the pattern and calculates that Robin started with 5 peanuts • Calculates how many peanuts Robin ate on Wednesday 2 • Understands the pattern and calculates that Robin started with 5 peanuts • Fails to calculate how many peanuts she had on Wednesday 1 • The task is misunderstood • Information is incorrectly used. For example, did not understand that 2 peanuts are added each day. 0 • No attempt at response

 POINTS STRATEGY Choose and apply a valid strategy (Some valid strategies are given in the table below.) 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 2 • A good strategy was chosen, but was partially or incorrectly completed. For example, they made a table but the table had errors. 1 • Strategy did not apply to this problem. 0 • No attempted strategy
POSSIBLE STRATEGIES:
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.
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
<--Starting values
Sun Mon Tue Wed Thurs Fri Sat MAKE A PICTUREHere is a valid picture representation: (Each circle stands for a peanut) 00000 0000000 000000000 00000000000^11 0000000000000 000000000000000 00000000000000000
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 = 77 -------------- Adding these up: 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
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.

 POINTS COMMUNICATION Explain the reasoning at each step, using pictures, symbols, labels, and correct vocabulary 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. 2 • Strategy was described, but steps may be missing • Labels may be missing or directions may not have completely followed 1 • Strategy was not explained according to directions or reasoning is confusing. 0 • No attempt to explain

 POINTS REASONABLE RESULT Review the work and show why the result is reasonable 4 • Review used a diffferent approach to support the result • Explained why the result makes sense. 3 • The problem was reworked using the same approach to check its accuracy. 2 • The check for reasonableness was not complete, or they said something like "we checked our result." 0 • No attempt was made to demonstrate the reasonableness of the result