Problem: These are tables with square tops. The tables have chairs
around them. Imagine that this pattern of tables and
chairs continues.
How many chairs are there when there are?:
1. 5 tables?
2. 2 tables?
3. 10 tables?
4. Write a rule for telling the number of chairs when you know the
number of tables.
Math Topic/Concept: Patterning
Materials: Paper and pencil and 1 inch graph paper
Classroom Use: (Developmental)
Classroom use comments*: I would have the children work in partners or groups to do this activity. This would be used in my unit on area and perimeter.
Grade: 4
Grade Cluster: (LateElem)
Illinois Goal: 6,8
Standard: 6C2a, 8A2a and 8A2b
Applied? (1-4): 2
Source: Groundworks, Algebra Puzzles and Problems Grade 4 by Carole Greenes and Carol Findell
Answer:
1. For 5 tables, there are 24 chairs.
2. For 6 tables, there are 28 chairs.
3. For 10 tables, there are 44 chairs.
Strategies Listed: Drawing or model
Solution: To find the number of chairs, multiply the number of tables by 4 and add 4 to the product. (4T + 4)
Extensions or related problems*: This would be a good introductory problem for the Restaurant activity I do. The students use 1 inch graph paper and tiles to design their own restaurant. Each tile represents a table in the restaurant and I give them 16 tiles to use.
Intended rubric or assessment method: Informal observation or if used as an assessment, I would use the student friendly ISAT Rubric.
Write-up submitted by: Kathy Erlandson
Problem: Write numbers in the shapes to make the equations true.
Same shapes must have same numbers.
Different shapes must have different numbers.
1. What number is Square? ______
2. What number is Circle?_____
3. Tell how you found the numbers.
Math Topic/Concept: Number sense, Algebra
Materials: Paper and pencil
Classroom Use: (Developmental)
Grade: 4
Grade Cluster: (LateElem)
Illinois Goal: 6, 8
Standard: 6B2, 8A2b
Applied? (1-4): 1
Source: Groundworks Algebra Puzzles and Problems Grade 4 by Carole Greenes and Carol Findell
Answer: Square = 9, Circle = 5
Strategies Listed: Guess and check, Use logic
Solution: One possible solution method: In the second equation, 2 squares are 18; 1 square is 9. Replace each square in the first equation with 9. The new equation is 9 + 9 + Circle + Circle = 28, so the circles total 28 –18, or 10. Each circle is 5
Extensions or related problems*: Students could make up their own number equations to give to other students
Write-up submitted by: Kathy Erlandson
Problem: Mr. and Mrs. Robinson bought an old house that needs
some fixing up. For example, many of the tiles that surround the fireplace
in the living room are chipped and broken. All of the tiles will have to
be replaced. It takes 14 tiles to go around the opening of the fireplace.
It will rake 18 more tiles to place a second row round the opening. How
many tiles will be required for the fifth row? If the Robinsons place 7
rows of tiles around the opening, how many tiles will the seventh row contain?
A nearby tile store is offering a huge discount to customers who buy more
than 200 tiles. How many rows of tiles would be needed around the fireplace
opening to use enough tiles to take advantage of the discount?
Math Topic/Concept: finding a pattern, addition
Materials: tiles could be used, paper, pencil
Classroom Use: (Introductory/Developmental/Evaluation)
Grade: 5-6
Grade Cluster: (EarlyElem/LateElem/MS-Jr.High/EarlyHS/LateHS)
Illinois Goal: 8
Standard: 8A2a
Applied? (1-4): 3
Source: Explain It Grades 5-6 by Creative Publications (ISBN #0-7622-1598-4)
Answer: 38 tiles, 8 rows of tiles
Strategies Listed: Make a table
Solution: For each new row, 4 more tiles are added. Extending
this pattern you will find that the fifth row will have 30 tiles, and the
seventh row will have 38 tiles. Placing this information in table form
will help students keep track and will facilitate finding answers. This
can be written as t = 4n + 10, where 10 represents the number of tiles,
and n equals the number of the row.
To answer the question about the discount, students might keep a cumulative
total as they add each row. It will take 8 rows of tiles to reach, and
in fact pass, 200.
However, depending on the savings involved, it might be prudent to
purchase 200 tiles-even if they are not all needed- in order to take advantage
of the discount. Additionally, in the event that a tile needed replacing,
the Robinsons would have tiles on hand.
Intended rubric or assessment method: ISAT rubric
Write-up submitted by: Jonna Young
Problem: “Dad, where had you been?” asked Ronnie.
“I had been to the attic, my son,” replied Dad.” And do you know what I saw there? There was a big web with 16 spiders and flies on it.”
“How many spiders were there?” asked the little boy with curiosity.
“Well, there were a total of 114 legs on the web,” answered Dad with a smile. “Now you can find out how many spiders were there by yourself. Can’t you?”
Can you help the little boy find out how many spiders were on the web
in the attic?
Math Topic/Concept: Problem Solving, Number Sense
Materials: Paper and Pencil
Classroom Use: (Developmental)
Classroom use comments*: You may need to remind students that flies have 6 legs and spiders have 8 legs.
Grade: 4-6
Grade Cluster: (LateElem)
Illinois Goal: 6, 8 and 10
Standard: 6C2a, 8A2a, and 10A2c
Applied? (1-4): 3
Source: http:www.syvum.com/
Answer: 8 spiders
Strategies Listed: Drawing or model, Chart
Solution: Assuming 6 legs for each insect, 25 insects will have 150 legs. But, there are 166-150= 16 extra legs.
It is important to note that spiders have 8 legs and flies have 6 legs. So, there are 2 extra legs per spider on the web.Thus, the 16 extra legs belong to 8 spiders.
Intended rubric or assessment method: ISAT Rubric
Write-up submitted by: Kathy Erlandson
Problem: Mrs. Spears started Round 1 of a game of “Telephone”
with her class. She
told the same message to two students.
Those two students each repeated the
message to two classmates for round
2. For Round 3, each student that got the
message in Round 2 repeated it to two
classmates, and so on. The rule was that each time the message had
to be told to a person who had not heard it before. There are 30
students in Mrs. Spears’ class. How many rounds will be needed for
all of them to have heard the message?
Math Topic/Concept: number patterning,
Materials: paper, pencil
Classroom Use: (Developmental)
Grade: 4th grade
Grade Cluster: (LateElem)
Illinois Goal: 8
Standard: 8A2a
Applied? (1-4): 3
Source: Explain It! (Grades 3-4) By Creative Publication – ISBN 0-7622-1597-6
Answer: 4 Rounds
Strategies Listed: Make a chart or a tree diagram
Solution: I made a table to show what happened. For the
first round, only 2 students had
heard the message. Each of them told 2 more,
so 4 students got the message
on the 2nd round. If those 4 each told 2 more,
that would be 8 more on the 3rd
round because 4 x 2 = 8. Those 8 each told 2, so
for the 4th round, 16 more got
the message (8 x 2 = 16). To find out how many altogether, I
added up the
number of students that got the message, 2 + 4 + 8 + 16 = 30. There
were 30
students at the end of round 4.
Table
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Other solution methods (if any)*: You could also use a
tree diagram. It shows that for
each round, the number of students who heard
the
message doubles. After 4 rounds, 30 students had
heard the message.
Tree Diagram
Extensions or related problems*: Make a telephone tree for your class.
Intended rubric or assessment method: ISAT rubric
Write-up submitted by: Donna Spears
Problem: The School Board of King Middle School has ruled that
starting next school year, all students will be required to wear school
uniforms. Slacks and skirts will have to be navy blue. Shirts or blouses
can be light blue, white, or blue and white striped. Button down or pullover
sweaters can be worn over a shirt or blouse. The sweaters can be light
blue, navy blue, or plum.
Chantell’s mother bought Chantell a skirt, a pair of slacks, 3 blouses
(one of each color), a button down sweater in each color, and a plum-colored
pullover. How many different outfits can Chantell create with these clothes?
Math Topic/Concept: counting, multiplication
Materials: paper, pencil
Classroom Use: (Developmental)
Grade: 5-6
Grade Cluster: (LateElem)
Illinois Goal: 8
Standard: 8A2a
Applied? (1-4): 3
Source: Explain It Grades 5-6 by Creative Publications (ISBN # 0-7622-1598-4)
Answer: 24 different outfits
Strategies Listed: Make a list
Solution: Students might make a list or draw a tree diagram to find the answer. Or, they might simply multiply 2 x 3 x 4.
Intended rubric or assessment method: ISAT rubric
Write-up submitted by: Jonna Young
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001