Problem:  Each year, the Sky View Country Fair holds hot air balloon races on Saturday morning and a band concert on Saturday evening.  The bar graph below shows the number of people that have attended these events during the last 3 years.

 
 

This year, 400 people attended the balloon races on Saturday morning.  The events Director wants to have chairs set up for the people who attend the concert.  If he is able to set up a chair for each person expected to attend, haw many chairs will he most likely need?  Explain how you got your answer.
 

Math Topic/Concept:  Interpreting Data, proportional reasoning.

Materials: You will have to download this activity, then print one copy.  After you have printed a copy,  delete from line down and you will have a worksheet.  Be sure to leave lots of space for the explanation.

Classroom Use: Introductory

Classroom use comments*:  Introduce interpreting data and the rubric scoring procedure.  Make an overhead of the problem and graph.  Ask students if they notice a pattern from the first year to the second?  From the second year to the third?
Predict what will happen in the forth year.  How will the graph have to be changed?

Grade:  Third

Grade Cluster: Early Elementary

Illinois Goal:  Mathematics State Goal 10

Standard:  10.A1a.

Applied? (1-4):  3

Source: Explain it! Grades 3-4   (Answering Extended – Response Math Problems)
 Louis Lepore   Creative Publications 2001   ISBN 0-7622-1597-6

Answer:  If they follow the pattern, each year gains 150 more people from the last years number of people going to the band concert?  If in the third year they had 450 people at the concert, then in the fourth year they should have 650 people.

Strategies Listed:  Use a graph

Solution:  After going over strategies, they should be able to figure out 650 people.

Intended rubric or assessment method: The rubric I will use is the scoring rubric for short answer questions for all grade levels.  It has clear BUZZ WORDS that will remind my students of what they will need to look for when doing graphs.  For this introductory level, I would mainly observe to check to see if they had the main concept.

Write-up submitted by:  Cheri Stanton

Problem: Jon and Lan made pumpkin faces on cookies for a Halloween Party.  It took Lan a long time to make pumpkin faces.  In the time it took Lan to put a face on one cookie, Jon made faces on two cookies.  The boys kept putting pumpkin faces on cookies in the same way until all the cookies had faces on them.  Lan finished 7 cookies.  How many cookies did Jon do?

Math Topic/Concept:  Organizing data, Counting by 2’s, Doubles

Materials:  paper and pencil, manipulatives

Classroom Use: Evaluation

Classroom use comments*:  Students must have had prior experience in creating tables from story problems.

Grade:  1

Grade Cluster: Early Elementary

Illinois Goal:  8 and 10

Standard:  8 B.1 10 A.1a

Applied? (1-4):  Level 3

Source:  The Problem Solver 1, page T59, Creative Publications, 1987

Answer:  14 cookies

Strategies Listed:  Making a table, looking for a pattern,

Solution:  The students must set up a table with Jon and Lan’s names.  They must draw the correct number of cookies under each name until they reach Lan’s goal of seven cookies.

Other solution methods (if any)*: The students could use manipulatives to act out the problem and find the solution.

Extensions or related problems*:  The number of cookies decorated could change.

Write-up submitted by: Cyndi Fisher and Jodi Johnson

Problem:  Dan and Delia are going to buy a toy.  They both like toys that have wheels.  They are looking at a racecar, a motorcycle, a fire truck, a lumber truck, and a van.  They both like one of the toys very much.  Dan and Delia want to buy this toy.  It has four wheels.  It does not have a ladder.  It has a back seat.  Which toy do Dan and Delia want to buy?

Math Topic/Concept:  Eliminating options, logic

Materials:  Teaching page (below) and a pencil

Classroom Use: Developmental

Classroom use comments*:  Students tend to like these “mystery like” problems.  They should catch on to the process of elimination easily.

Grade:  1

Grade Cluster: Early Elementary

Illinois Goal:  10

Standard:  10 A.1

Applied? (1-4):  Level 2

Source:  The Problem Solver 1, T5, Creative Publications, 1987.

Answer:  van

Strategies Listed: logical reasoning, working backwards

Solution:  The students will check each picture for the clue as the teacher reads it.  They will eliminate the possibilities as they listen.

Extensions or related problems*:  Change the clues so one of the other vehicles is the answer.  Let the students bring similar toys to school and make up clues based on the toys they bring.

Intended rubric or assessment method:  Observation

Write-up submitted by:  Jodi Johnson and Cyndi Fisher

A worksheet follows:

Problem:  Four animals live in a tree.  The owl lives at the top of the tree.  The raccoon lives below the lizard.  The lizard lives below the squirrel.  Where does each animal live in the tree?

Math Topic/Concept: Order

Materials:  Paper and pencil.  A worksheet can be prepared with the problems and the graphic, if desired.

Classroom Use: Introductory

Grade:  1

Grade Cluster: Early Elementary

Illinois Goal:  10

Standard:  10 A.1a

Applied? (1-4):  Level 1

Source:  The Problem Solver 1, Page T53, Creative Publications, 1987

Answer: The owl lives at the top with the, squirrel, lizard, and raccoon living underneath in that order.

Strategies Listed:  Act it Out, Use a diagram, Use a model.

Solution:  The students can each play a role and place themselves in order as the teacher reads the problem.

Other solution methods (if any)*:  If students are more familiar with these types of problems, they can draw a picture and figure it out on paper.

Extensions or related problems*:  Change the order of the animals or add more animals to the tree.

Intended rubric or assessment method: Observation

Write-up submitted by:  Cyndi Fisher and Jodi Johnson

Problem:  Lolly likes the capital letter L at the beginning of her name.  She likes it so much that she made an L with blocks.  She made her first L with 4 blocks.  She added 2 blocks to her first L to make her second L.  She added 2 blocks to her second L to make her third L.  Lolly keeps using her number pattern.  How many blocks will Lolly use to make her fifth L?

Math Topic/Concept: Patterning, Organizing data, Determining the results

Materials:  The teacher may want to provide blocks and/or drawings of the L’s (or have the students make them).

Classroom Use: Developmental

Classroom use comments*:  How do you think the first L looked?

Grade:  1

Grade Cluster: Early Elementary

Illinois Goal:  8 and 10

Standard:  8 B.1    10 A.1a

Applied? (1-4):  Level 1

Source:  Problem Solver 1, page T 61, Creative Publications, 1987

Answer:  12 blocks

Strategies Listed:  Use a table, look for a pattern, modeling.

Solution:  The students will build the L with blocks adding a block to each end for each  new L.  They will fill the number of blocks used into a table.

Extensions or related problems*:  Larger L

Write-up submitted by: Jodi Johnson and Cyndi Fisher

James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated June 27, 2001