Title:  Lolly’s Capital L

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

Intended rubric or assessment method:  Observation

Write-up submitted by: Jodi Johnson and Cyndi Fisher

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:  Making a table, 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 10 B.1c

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:  There are 4 blocks in this train.  3 cubes and a longer rod.
There are 3 cubes followed by a rod in the train.

Repeat the train pattern.

1. Draw the train with 16 blocks.
2. How many are cubes?
3. How many are the longer rods?

Think about a train that has 18  .

4. How longer rods are in this train?
5. How many cubes are in this train?

Math Topic/Concept:  Patterns, logic.

Materials:  Blocks, paper and pencil.

Classroom Use: (Introductory/Developmental/Evaluation)

Grade:  3

Grade Cluster: (EarlyElem/LateElem/MS-Jr.High/EarlyHS/LateHS)

Illinois Goal:  8

Standard:  8.B.1

Applied? (1-4):  1

Source:  Groundworks 3, Creative Publications, 1999.

Answer:
Draw the train with 16 blocks.
1. How many are cubes? (12)
2. How many are longer rods? (4)
3. How many are longer rods? (4)

How many rectangles are in the train if there are 18 cubes? (6)
How many blocks in the whole train?  (24)

Strategies Listed:  Draw a picture, Use a pattern, Use a table

Solution:  See answer.

Extensions or related problems*:  The size of the longer rod can be varied to create a different size train.

Intended rubric or assessment method:  Informal assessment.

Write-up submitted by:  Diana Kent

Problem: The sign says: JIMMY’S MAGIC SHOW.  Jimmy is behind the curtain, getting ready for the show.  He has to make up his mind what to put on.  He will wear a cape or a coat.  On his head he will wear a bright red wig or a hat.  Then he will put on his black boots or his shoes with the pointy toes.  What are the 8 different outfits Jimmy could wear for his magic show.

Math Topic/Concept: Organized list/predictions based on given data.

Materials: If a worksheet is desired, one can be made by typing the problem out and making a chart to help sort out the clothing items .

Classroom Use: Introductory

Classroom use comments*:  To introduce solving problems using symbols and predicting results.
· What is the question you have to answer?
· What can Jimmy choose to wear on his shoulders?  Would he wear both of them at the same time?
· What can Jimmy choose to wear on his head?  Then what on his feet?
Would it help solve the problem if you could keep track of all the things Jimmy could wear together?  Yes.  The symbol at the top of your paper means that you can make an organized, step-by-step list to help you solve the problem.

Grade: Third

Grade Cluster: Early Elementary

Illinois Goal: Mathematics State Goal 8

Standard: 8.B.1

Applied? (1-4):  2

Source:  1987 Creative Publications     Problem Solver 3

Answer:  There are 8 different outfits. Listed below.

Strategies Listed:  Make an organized list.

Solution: Make a chart to keep track of the outfits.  This can be done as a part of the worksheet.  Do 1, 2, 3, 4, as a group then they finish 5, 6, 7, and 8 the same way.
There are 8 different outfits they can make.
1 coat wig boots
2 coat wig shoes
3 coat  hat boots
4 coat hat shoes
5 cape wig boots
6 cape wig shoes
7 cape hat boots
8 cape hat shoes

Extensions or related problems*:  More sorting problems for practice.

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 help my students see what they will need to score well on this introductory level.

Write-up submitted by:  Cheri Stanton

Problem:  The Stanton’s  are playing music in the lunchroom.  Harry, Helen, Herman, and Harriet are in the band.
· Harry and Herman have ears.
· Herman does not have a nose.
· Harriet and Helen have hair.
· Helen has knobs on the top of her head.
What name belongs on each nametag?

 

Math Topic/Concept: Problem solving with patterns.

Materials:
You will need to print out and copy this lesson, then trace the figures on the master as well as make one for the overhead.  Also needed is a pencil.

Classroom Use: Introductory

Classroom use comments*: To introduce students to analytic methods in problem solving and predicting results.
· What is the question you have to answer?  What name belongs on each nametag?
· How many Stanton’s are playing in the band?  4
· What are their names?  Harry, Helen, Herman, and Harriet.
What do you know about Harry?  He has ears.
· What is one thing that you know about Herman?  He has ears. What else do you know about him?  He does not have a nose.
· What do you know about Harriet?  She has hair. What else do you know about her?  She has knobs on the top of her head.

Grade:  Third

Grade Cluster: Early Elementary

Illinois Goal: Mathematics State Goal Number 8

Standard:  8.B.1

Applied? (1-4):  1

Source:  1987 Creative Publications       Problem Solver 3

Answer:

Strategies Listed: You can use a special kind of thinking to solve this problem.  It is called “logical reasoning.”  You are going to answer “if. . .then” kinds of questions in this problem.  If you know one thing is true, then you can figure out what else is true.  You will have to use the pictures on your paper, too.

Solution:
· What does the first clue tell you?  Harry and Herman have ears.  Look at the picture on your paper.  Which player could be Harry and Herman?  The two players with ears.
· What does the second clue tell you?  Herman does not have a nose.  Which of the two players is Herman?  The one without a nose.  Write Herman’s name on his nametag.  Then who is the other player?  Harry.  Write his name on his tag.
· What does the third clue tell you?  Harriet and Helen have hair.  How many players have hair?  Two.  Who are those players?  Harriet and Helen.
What does the forth clue tell you?  Helen has knobs on the top of her head.  Which one of those two players is Helen?  The one who has knobs on the top of her head.  Write Helen’s name on her tag.  Then who is the other one?  Harriet.  Write her name on her nametag.
 

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 help my students see what they will need to score well on this introductory level.

Write-up submitted by:  Cheri Stanton

Problem: Mary’s cat weighs 2 pounds. Bob’s dog weighs 14 pounds.  Both pets are gaining about a pound a month. If they keep on gaining weight like that, the dog will soon weigh three times as much as the cat.  How many pounds will the cat weigh then?

Math Topic/Concept: Algebraic thinking, patterns

Materials: pencil and papers

Classroom Use: (Development/Evaluation)

Grade: Third

Grade Cluster: (EarlyElem)

Illinois Goal: 8

Standard: 8.A.1a, 8.B.1

Applied? (1-4): 2

Source: The Problem Solver, 1987 Creative Publications

Answer: 6 pounds

Strategies Listed: Use or make a table

Solution: Make a table like below and keep adding the numbers until the dog’s weight is three times the cat’s weight.

Pounds the cat weighs    2      3      4      5      6
Pounds the cat weighs    14    15    16    17    18

Extensions or related problems*: If the cat weighs 2 pounds and the dog weighs 8 pounds now, the cat will soon weigh half as much as the dog.  How much will the dog weigh then?

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