Problem: The art teacher uses 4 push pins, one in each corner, to hang a drawing on a bulletin board. If she overlaps the corners, she can hang 2 drawings with only 6 push pins. What is the minimum number of push pins the art teacher needs to hang 8 drawings?
Math Topic/Concept: number sense, 2-dimensional visualization, addition, patterning
Materials: paper and pencil
Classroom Use: (Introductory)
Grade: 5
Grade Cluster: (LateElem)
Illinois Goal: 6, 9
Standard: 6A2, 9B2
Applied? (1-4): 3
Source: Middle Grades Math – Tools for Success , Prentice Hall (ISBN # 0-13-427709-0)
Answer: 15 push pins
Strategies Listed: Draw a picture
Solution: Make a drawing that would look like this:
Extensions or related problems*: Change the number of pieces of paper
Intended rubric or assessment method: Informal assessment
Write-up submitted by: Jonna Young
Problem: Mira bought 30 roses to place on the tables in her café. Her bud vases can hold either 1 or 2 flowers. If she fills the same number of vases with 1 flower as she does with 2 flowers, how many vases will be required.
Math Topic/Concept: number sense, addition, multiplication, division
Materials: Paper, pencil
Classroom Use: (Developmental)
Grade: 5
Grade Cluster: (LateElem)
Illinois Goal: 10.A.2a and 6.A.2
Standard: 10.A.2a and 6.A.2
Applied? (1-4): 3
Source: Explain It! Grades 5-6 Creative Publications ISBN 0-7622-1598-4
Answer: Mira will need 20 vases. Ten will hold 1 flower and ten will hold 2 flowers.
Strategies Listed: draw a picture, use logic.
Solution: By drawing pictures, you could start by making vases
with one flower in the first and two in the second. Continue this
until you use all 30 roses. Two vases will be used for every 3 flowers.
30 ÷ 3 = 10. There would be 10 groups of 3 flowers.
Multiply 10 x 2 and you will find that Mira needs 20 vases. Ten holding
1 flower and ten holding 2 flowers.
Other solution methods (if any)*: If there were 2 flowers
in each vase, 15 vases would be needed and no vases would have just 1 flower.
You could make a table to show what happens when there are fewer 2-flower
vases. You will then find out that 10 vases for 2 flowers and 10
vases for 1 flower should be used.
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Extensions or related problems*: If Mira used a vase for 1 flower and a vase for 3 flowers, can she use the same number of vases? What if she used 1 flower and 4 flowers? What are some other values for the vases that will work?
Intended rubric or assessment method: Grade 5 "Student Friendly" Mathematics Scoring Rubric found at http://www.isbe.state.il.us/isat/rubric5.htm
Write-up submitted by: Ann Hulsizer, 5th Grade, Monmouth
Problem: One summer Shane kept a record of how many kilometers
he rode on his
skateboard. He won’t tell what the number is but he will give you
these clues:
· It is less than 100.
· It is more than 44.
· If you count by 4s, you say the number’s name.
· The number can be divided evenly by 5 and 8.
How many kilometers did Shane
go on his skateboard?
Math Topic/Concept: Greater than, Less than; number sense; patterning
Materials: Pencil, paper
Classroom Use: (Evaluation)
Grade: 4th grade
Grade Cluster: (LateElem)
Illinois Goal: 6, 10
Standard: 6A2, 10A.2c
Applied? (1-4): 4
Source: Problem solver 4 by Judy Goodnow and Shirley Hoogeboom,
- Creative
Publications – ISBN 0-88488-584-4
Answer: 80 Kilometers
Strategies Listed: Make a table
Solution: I made a table starting with 44 and ending with
100. Then I counted by 4s
from 44 and put those numbers
on the chart. Then I looked at all the numbers
I had
on the chart and found the one that
could be divided by 5 and 8.
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Intended rubric or assessment method: Student-Friendly ISAT rubric
Write-up submitted by: Donna Spears
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001