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.
Sun456
Mon678
Tues8910
Wed101112
Thurs121314
Fri141516
Sat161718
TOTAL707784
<--Starting values
MAKE A PICTURE
Here is a valid picture representation:
(Each circle stands for a peanut)
Sun Mon Tue Wed Thurs Fri Sat
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
^
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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:
  SundayS
+MondayS+2
+TuesdayS+4
+WednesdayS+6
+ThursdayS+8
+FridayS+10
+SaturdayS+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