| Problem Title | Benchmark | Topic(s) |
| Average 6.1 | 10.A.3b | Mean |
| Skeleton Studies | 10A3c, 6D3 | Ratio, proportion, and use of data |
| The Mix-up | 6.C.3b and 10.A.3a | Logical Reasoning and Computation |
Problem: What number should be removed from the list
1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11 so that the average of the remaining numbers is 6.1?
Math Topic/Concept: Statistics (Mean)
Materials: Calculator
Classroom Use: (Introductory/Developmental)
Classroom use comments*: They should know how to find average, maybe provide a little reminder with a simple problem. This will help them understand the affects a number has on the average of the set.
Grade: 6-8
Grade Cluster: (MS-Jr.High)
Illinois Goal: 10
Standard: 10.A.3b
Applied? (1-4): 1
Source: Teaching Mathematics in the Middle School (September 99)
Answer: 5 will be the number to be removed
Strategies Listed: Algebraic reasoning or Guess and Check
Solution: Removing one number from the list leaves ten numbers. If the average of these ten numbers is 6.1, the sum of the numbers is 61. The sum of the original list is 66, so removing 5 from the list leaves a sum of 61.
Intended rubric or assessment method: Solve the following related problem. Name ten numbers that have a mean of 7.
Write-up submitted by: Jenni Robinson and Denise Mann
Problem:
In her study of prehistoric birds, Sue checked bone measurements from
skeletons of two birds against the information for the comparison group shown
in the table below. The body length of the first skeleton measured 12
cm, and its wingspan was 28 cm. The body length of the second skeleton
was 15 cm, and its wingspan was 48 cm.
Based on the bone measurements, do you think that either of these birds
might be members of the comparison group? Explain why or why not and give
data to support your thinking.
Comparison Body Wingspan
Group Length (cm) (cm)
Skeleton A 15
35
Skeleton B 17
39
Skeleton C 10
24
Skeleton D 19
44
Skeleton E 7
17
Math Topic/Concept: ratio, proportion, and use of data
Materials: calculator
Classroom Use: (Developmental/Evaluation)
Classroom use comments*:
This problem could be used for evaluation at the end of a unit of study of use
of proportion to solve problems.
If used as a developmental problem, the teacher may wish to ask if there
appears to be a relationship between the wingspan and body length of the skeletons
in the comparison group.
Grade: 7 - 8
Grade Cluster: (MS-Jr.High)
Illinois Goal: 6, Number Sense and 10, Data
Standard: 6D3, 10A3c
Applied? (1-4): 3
Source: Explain It! Answering extended-response math questions grades 7-8. 2001, Wright/McGraw-Hill, Creative Publications. ISBN: 0-7622-1599-2
Answer: The first bird could be a member of the comparison group; the second bird does not seem to fit the group.
Strategies Listed: Analyze the data, note proportions.
Solution: The skeleton of the bird with a 12 cm length has a ratio of wingspan to body length that is 2.3 to 2.4, consistent with the birds of the comparison group. However the skeleton of the other bird has a wingspan that is 3.2 times the body length.
Intended rubric or assessment method: ISAT ‘student friendly’ rubric
Write-up submitted by: M. K. Robbins
Problem: Chris, Lisa, and Alan each ordered cookies at the bake sale, but the clerk mistakenly put all their treats together in a single bag. There were 60 cookies, 20 of each type, in the bag. The clerk needed to separate the cookies correctly.
Chris had ordered 25 cookies—chocolate chip and oatmeal.
Lisa had also ordered 25 cookies—oatmeal and peanut butter.
Alan had just ordered 10 chocolate chip cookies.
After the cookies were separated, how many of each type of cookies did each person have?
Math Topic/Concept: Logical Reasoning and Computation
Classroom Use: (Introductory)
Classroom use comments*: What do you think helped you decide how to get you answer? Which clue was the most helpful to start ?
Grade: 7
Grade Cluster: (MS-Jr.High)
Illinois Goal: 6 and 10
Standard: 6.C.3b and 10.A.3a
Applied? (1-4): 2
Source: “Explain It!” (Creative Publications) Grade 7-8 ISBN 0-7622-1599-2
Answer: Alan (10 chocolate chip) Chris ( 10
chocolate chip and 15 oatmeal)
Lisa (5 Oatmeal and 20 Peanut Butter)
Strategies Listed: Make a table or Work Backwards
Solution:
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Other solution methods (if any)*: Since Lisa is the only one to order P.B. she gets all 20, so her remaining 5 must be oatmeal. The only other person to order oatmeal was Chris so she receives the other 15, her remaining 10 must be chocolate chip.
Intended rubric or assessment method: Teacher observation of students work.
Write-up submitted by: Denise Mann and Jenni Robinson
Page by Andrea Gillett and James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
January 30, 2003