Title: Labels for the Tables
Problem: Enrique is going to make cards to label the tables at the science fair. He will cut rectangles that are 4 inches wide and 6 inches long from rectangular poster board that is 2 feet wide and 3 feet long. Enrique is measuring and drawing lines to cut along in order to make the greatest number of cards without wasting any of the poster board. How many cards should he have when he is finished? Explain how you find your answer.
Math Topic/Concept: measuring in inches, converting feet to inches, drawing rectangles
Materials: rulers, paper, pencil
Classroom Use: (Developmental)
Grade: 5-6
Grade Cluster: (LateElem)
Illinois Goal: 7 & 9
Standard: 7A2a & 9A2
Applied? (1-4): 3
Source: Explain It Grades5-6 by Creative Publications (ISBN # 0-7622-1598-4)
Answer: 36 cards
Strategies Listed: Draw a picture
Solution: Draw the poster board. Change 2 feet to 24 inches and 3 feet to 36 inches because the cards would be measured in inches. Then I divided the side that was 36 inches long into 6 inch sections to make cards that were 6 inches long. Each card had to be 4 inches wide, and 24 divided by 4 = 6, so 6 cards would fit across. 6 rows of 6 made 36 cards in all.
Intended rubric or assessment method: ISAT rubric
Write-up submitted by: Jonna Young
Problem: After an introductory review of geometric solids and a discussion or visual presentation of geometric structures in the local landscape, pose this three-step task for students to accomplish individually:
1. Select a real-life structure and analyze the geometric forms which
are the basic elements of its structure. Sketch its design, focusing
on these basic geometric forms.
2. Plan and construct the model with several different 3-dimensional
geometric forms.*
3. When the model is complete, describe your building process, and
tell all the ways you can think of that the selected geometric forms are
best suited to the function of the structure (both in the model and in
real life).
Math Topic/Concept: geometric solids in practical use
Materials: tag board, pencil & paper, scissors, and tape (note: *provide pre-drawn 2-dimensional shapes for students to select or provide review of the 2-D shapes which can be formed into 3-D solids so students may create shapes suited to their designs)
Classroom Use: (Developmental/Evaluation)
Grade: 4 (developmental) 5 (evaluation)
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9.A.2a, b, & c (Language Arts ILS 3.C.2a)
Applied? (1-4): 3
Source: Trudi Shepard and Rebecca Cummins
Answer: various, according to students’ products
Strategies Listed: use logical reasoning, create design, build model
Solution: Students may select and make 3-12 pieces using basic geometric shapes (limited to cubes, cones, rectangular and triangular prisms, and cylinders). Models should reflect the design of a real-life structure. In describing the process, students should be able to identify the stages of development in proper sequence. In describing the functionality of the structural design, students should be able to identify reasons why one geometric shape is more suitable than another for the specific structure.
Other solution methods (if any)*: students might work in a group to place several models together in a complex. Each student contributes by constructing an equal number of structures. Written responses (expository paragraphs) should be individual, not group.
Extensions or related problems*: computer-generated sketches
Intended rubric or assessment method: Analytical Scoring Scale (Jim Olsen WIU)
Write-up submitted by: Rebecca Cummins (Westmer CUSD 203)
Problem: Mrs. Erlandson asked the fourth graders to explore ways to cut a cake into four equal pieces. She gave the children 8½ x 11 inch sheets of paper to use as “cakes,” and she asked them to sketch the different ways they found to divide them.
She extended the task by asking the children to respond in writing to the following direction: “Take one piece from each cake you cut. Compare the pieces to see if each one gives the same amount of cake as the others. Explain your reasoning.”
Math Topic/Concept: Geometry/Area, Fractions
Materials: Paper and pencil, scissors
Classroom Use: (Developmental)
Grade: 4
Grade Cluster: (LateElem)
Illinois Goal: 6, 9
Standard: 6A2, 9A2c
Applied? (1-4): 4
Source: 50 Problem-Solving Lessons by Marilyn Burns
Answer: All the children quickly found three ways to cut the
cake into fourths:
Some children explored further and found additional solutions:
Strategies Listed: Drawing or model
Solution: One student explained how he verified his thinking about the pieces. He wrote: “Yes, I do think they are all the same amount of cake. Why I think that is because I measured them or in other words I investigated. I cut one to measure the other one so that if it right.”
Another student wrote: “Yes, I do think they are the same because all of the objects or shapes are 1/4. No matter if you stretch and pull they are still the same size. But if you cut the cakes into smaller pieces of course they will not be 1/4 any more.”
Other solution methods (if any)*: Students could be provided with additional investigations with geometric shapes to see that different shapes can have the same area.
Have students make rectangular “cakes” with 24 color tiles to see if it’s possible to build different shapes of rectangles with the same area.
Extensions or related problems*: This can be done on a geoboard and more answers are possible.
Intended rubric or assessment method: Teacher observation
Write-up submitted by: Kathy Erlandson
Problem: Recently the kids watching videos in the Mini-Movie
Theater at school have
been so rowdy that the teacher in charge
decided he would allow no more than
two kids in any one row, including horizontal,
vertical, and diagonal rows in
the seating chart shown here.
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
X X X
Math Topic/Concept: Logical reasoning, 2-dimensional spatial visualization
Materials: Cubes (2 colors) – one representing the seats
and the other representing the
students.
Classroom Use: (Developmental)
Grade: 4th grade
Grade Cluster: (LateElem)
Illinois Goal: It does not fit any goal specifically, but definitely fits the Applications of Learning for Math in the Illinois State Goals. Goal 9
Standard: 9.a.2
Applied? (1-4): 4
Source: www.stclair.k12.il.us/makethelink/mlgrid
Answer: 12
Strategies Listed: model or drawing
Solution: The is more than one way to place the 12 students.
One solution:
@ X X X X @
X X @ @ X X
X @ X X @ X
X @ X X @ X
X X @ @ X X
@ X X X X @
Intended rubric or assessment method: Teacher observation
Write-up submitted by: Donna Spears
Problem: The Yorkwood School Council would like to have a new design for the school flag. They want the flag to be square in shape and to have four colors. The Council has asked that equal amounts of each color be used in the design of the flag.
Draw six different designs that can be considered for the school flag. Choose one of your designs and explain how you know it meets the requirements.
Math Topic/Concept: Geometry, Patterns
Materials: Drawing or model
Classroom Use: (Developmental)
Grade: 3 - 4
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9A2c
Applied? (1-4): 3
Source: Explain It Grade 3 –4 by Creative Publications
Answer: There are at least 6 designs that meet the criteria set.
Many other designs are possible.
Strategies Listed: Drawing or model, graph paper
Solution:
Extensions or related problems*: Questions to consider:
· Is it possible to divide a square into equal – sized triangles?
· Must the square be divided into 4 equal sections?
· Could dividing a square into 6 or 8 equal parts help you to
find a different design?
Intended rubric or assessment method: Student friendly ISAT Rubric
Write-up submitted by: Kathy Erlandson
Problem: The Good Food Restaurant party room has 24 square tables
that can be arranged in different ways. Since only one person can
sit at a side of a table, most guests ask to have the tables put together
to form a rectangle. How many different rectangular arrangements can the
restaurant make using all 24 tables?
Which rectangular arrangement will seat the greatest number of people?
How many people will that arrangement seat?
Which rectangular arrangement will seat the fewest number of people?
How many will that arrangement seat?
Math Topic/Concept: analyze geometric properties
Materials: could use square tiles or small square pieces of paper
Classroom Use: (Developmental)
Grade: 5-6
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9A2
Applied? (1-4): 3
Source: Explain It Grades 5-6 by Creative Publications (ISBN #0-7622-1598-4)
Answer: Greatest number of people – 50 seated at an arrangement with 1 row of 24 tables. Fewest number of people- 20 seated at 4 rows of 6 tables.
Strategies Listed: Use objects or draw a picture
Solution: Four rectangular arrangements can be made: 1 row of
24 tables, 2 rows of 12 tables, 3 rows of 8 tables, or 4 rows of 6 tables.
The greatest number of people, 50, can be seated at an arrangement
with one row of 24 tables. The fewest number of people, 20, would be seated
at the arrangement with 4 rows of 6 tables.
Extensions or related problems*: Change number of tables, or number on each side of a table.
Intended rubric or assessment method: ISAT rubric
Write-up submitted by: Jonna Young
Problem: If you are given five different colors of LinkerCubes, how many different pentominos can you make?
Math Topic/Concept: Geometry
Materials: 60 LinkerCubes , 2 centimeter grid paper, paper, pencils, crayons
Classroom Use: (Introductory)
Classroom use comments*: Were the students able to find
all 12 Pentominos?
Were they able to record each Pentomino?
Grade: Third
Grade Cluster: (LateElem)
Illinois Goal: 9
Standard: 9.A.2, 9.C.2
Applied? (1-4): 1
Source: 20 Thinking Questions for LinkerCubes, Creative Publications
Answer: 12
Strategies Listed: Make the shapes and record shapes on the Grid Paper. Then check for duplicates because of flipping or turning.
Solution:
Intended rubric or assessment method: informal assessment
Write-up submitted by: Beth Reedy, Third Grade, Harding
Elementary, Monmouth, Illinois
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001