Scoring Guide for the Peanuts Problem
The total score will be the sum of the 5 scores below. (maximum score = 20)
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 
4 
• Understands the pattern and calculates that Robin started with 5 peanuts 
2 
• Understands the pattern and calculates that Robin started with 5 peanuts 
1 
• The task is misunderstood 
0 
• No attempt at response 
POINTS 
STRATEGY 
4 
• Choice of a valid strategy: visual representation, make a table, guess and check, working backwards, or figuring out a formula 
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 
GUESSANDCHECK 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.  

 
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:
 
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 (7742). 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 
4 
• Described strategy and solution clearly and completely, stepbystep 
2 
• Strategy was described, but steps may be missing 
1 
• Strategy was not explained according to directions or reasoning is confusing. 
0 
• No attempt to explain 
POINTS 
REASONABLE RESULT 
4 
• Review used a diffferent approach to support the result 
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 