Generic Rubric for Session I Problem

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

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:

  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

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

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