Elibrary Standards-Based Learning Activity

eLibrary Standards-Based Learning Activity

A Maze Thing

Teacher Procedures

APPROPRIATE FOR:Geometry, Grades 8-12

TIME LINE:Three class periods

MATHEMATICS Standards Addressed Through This Lesson

NCTM

Standard 8 | Communication

Instructional programs from pre-kindergarten through grade 12 should enable all students to:

Organize and consolidate their mathematical thinking through communication;
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematical ideas precisely.

Standard 6 | Problem Solving

Instructional programs from pre-kindergarten through grade 12 should enable all students to:

Build new mathematical knowledge through problem solving;
Solve problems that arise in mathematics and in other contexts;
Apply and adapt a variety of appropriate strategies to solve problems;
Monitor and reflect on the process of mathematical problem solving.

Standard 3 | Geometry
In grades 9–12 all students should:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:
Analyze properties and determine attributes of two- and three-dimensional objects;
Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;
Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;
Use trigonometric relationships to determine lengths and angle measures.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems:
Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations;
Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.
Apply transformations and use symmetry to analyze mathematical situations:
Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;
Use various representations to help understand the effects of simple transformations and their compositions.

Use visualization, spatial reasoning, and geometric modeling to solve problems:
Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;
Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections;
Use vertex-edge graphs to model and solve problems;
Use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

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Learning Expectations/Objectives

Students will research mazes as puzzles.
Students will use research to bolster their understanding of the topic and create geometric models.
Students will author instructions for making their model and describe the geometric patterns discovered to be common to the kind of maze they have chosen to create.
Students will write a short report using correct geometric terminology detailing the history of the kind of maze they have created.

MATERIALS

Computer with access to eLibrary and a printer
Paper
Colored pens or pencils
Assorted materials to design the puzzle or maze, which can be brought from home

ACTIVITY Process: Directions to the Teacher

Description of Activity

Students will work in pairs or in groups no larger than four to research mazes (puzzles) on eLibrary. They’ll use the information they gather to complete several activities culminating in the creation of an original maze. Students will write a report using correct geometric terminology about the history of the maze they have created.

Background Information/Scenario

Humans have been creating puzzles since at least 2400 BC, when magic squares were popular in China. For this project, students will research the history of puzzles, explore shape puzzles and solve several puzzles. Finally, they’ll create their own puzzle and make a model to share with the class. Students should work with a partner or in a group of no more than four. Some students prefer to work alone which is allowable if they are willing to complete all the work on their own.

Outline of Procedures – Day One

Brainstorm puzzles and mazes. Ask students to think about their favorite puzzles and explain why they are their favorites.
Go over the background of these activities and describe what they will be doing for the next three days.
At this time students should choose and partner or a group to work with.
Go over the rubric you will use to evaluate their performance.
Hand out and discuss Activities 1 and 2.
Next, students will gather historical information, copy pictures and take notes that will allow them to complete the activities.

Students should log on to eLibrary and use the special BookCart created for this activity. BookCarts save classroom time spent in searching and ensure that the best learning resources are used for each activity.
Here’s how to access the BookCart for this unit, then copy/edit it to make it a part of your local BookCart collection and easily available to students.

Access the BookCart Editor and log in using your user name and password.
At the top, enter these search terms in the following fields:
title: SBLA A Maze Thing (BookCart name)
author: ProQuest
Click the search button.
The SBLA BookCart will appear. Click the small box on the right under select, then click the copy button in the upper right-hand corner.
Change the description (optional) and add any other resources you’d like (optional), then click the green save bookcart button.
The new BookCart will now be live on your local site and available to your students when they are ready to do an eLibrary search, by clicking on the bookcart button.

Outline of Procedures – Day Two

Check progress of Activities 1 & 2.
Hand out and discuss Activities 3 & 4.
Students should go log back into eLibrary to complete their research on puzzles and mazes, and on the history of geometric puzzles.
Students should complete Activities 3 & 4.

Outline of Procedures – Day Three

Check progress of the activities. Have students share with each other pentomino shapes. (If some students have not completed this task, let those who have share their work with others so the entire class can move forward.)
Students create their puzzles. Encourage them to use the correct mathematical terminology with an emphasis on geometric vocabulary.
Students should assemble their notes, pictures and activities.
Finally, students should create a historical time line for the development of puzzles using the research they have done. They should also include the puzzle they have created.
Student should hand in their work for assessment.

Conclusion/Finished Work

As a culminating activity, teachers might want to randomly distribute the puzzles so students can solve each puzzle. OR

Make a book of the puzzles so every student can share as time allows.

ASSESSMENT

Scoring Rubric

4Your solutions are correct and illustrated with clear diagrams. You used geometric language appropriately and correctly. Your models were well constructed. Your reasoning is sensible and supported with clear explanations based on research. Your display and/or model is organized, attractive and complete.

3Most of your solutions are correct. Your diagrams and research are adequate. Explanations make sense but may contain some unclear portions or gaps in reasoning. All or most geometric terms are used correctly.

2Many solutions are incorrect. Your diagrams are unclear or misleading. Explanations are inadequate, difficult to understand or logically flawed. Geometric terms are lacking or misused. Your modem and/or display is constructed neatly.

1 This project must be redone. See the teacher.

Research

Did students use eLibrary to collect information and pictures about mazes and puzzles and the history surrounding each?
Did students organize information as described in the rubric?

Writing

Did students create a time line with correct labeling?
Did students use at least 10 geometry terms in their paper?
Were student descriptions and directions accurate and well thought out?
Were student notes complete?

Optional Extended Enrichment Activities

Create a 3D (three-dimensional) puzzle. Challenge your classmates to solve it!

ANSWER KEY

Activity 1: All triangles are right isosceles; yes

Activity 2: One triangle, five quadrilaterals and three pentagons.

Activity 3: Check students work to see that each figure has adjoining sides and use all five pentominos and that there are 10 unique figures.

Activity 4: Yes; 3/1 = 15/5; 3

A Maze Thing

A Math Lesson

Student Version Handout

People have been solving puzzles since at least 2400 BC when magic squares were popular in China. For this project, you will visit eLibrary to find out more about the history of mazes and puzzles, and then you will build a puzzle or maze model. You will write a brief history of puzzles including a time line of development using correct geometric terminology. Be sure to include directions as to how this puzzle can be solved. Finally, show the solution.

You will write a short (one page) report including historical research of geometric puzzles, plus copy and solve a puzzle you have not done before. Be clear, colorful and original in the way you tell your story. Finally, you will assemble all you have done into a report to hand in, including the activities, your research notes and a list of the Web sites you visited to obtain this information, along with your puzzle or maze and its solution. Be creative and have fun!

During this activity you will…

Research mazes or puzzles.

Create a geometric maze or puzzle.
Write clear and concise instructions for making your model and the geometric patterns discovered to be common to the kind of puzzle or maze you have chosen to create.
Write a short report using correct geometric terminology about the history of kind of puzzle you have created.
You will assemble your research notes, activities, your puzzle and the historical time line into a folder or notebook to be handed in.

DAY ONE

Read activities and rubric very carefully.

Begin by deciding who will be on the computer researching and who will be taking notes.

Here’s how to access the special BookCart that will help you save searching time and give you the best learning resources for this project:

Click the bookcartbutton in the upper right-hand corner of the eLibrary
You will see a list of BookCarts in alphabetical order by title; look for SBLA A Maze Thing
If the SBLA BookCart is not listed, then click next at the bottom to navigate through screens and to your BookCart
Click the BookCart to open it
Browse web links and articles by clicking on them
Select the most significant ones by clicking on (+) add tomy list
Click on my list (upper right of screen) to see your selections
Print my list for your bibliography
Save to disk or student network account, email to your home computer, or print the selected documents (saving makes it easier to copy them into productivity software for your reports.

4. Save and/or copy pictures and notes that will be useful in completing this project.

5. Complete Activity 1 and Activity 2

DAY TWO

Complete any parts of Activities 1 and 2 you were not able to finish yesterday.
Go to eLibrary. Research the history of geometric puzzles.
Complete Activities 3 and 4.

DAY THREE

Now the fun begins! Create your own puzzle or maze. Be clever, include supporting documentation, directions, rules and above all lots of geometry. Include at least 10 geometry terms used correctly.

Create a historical time line for the development of puzzles based on the research you have done.
Assemble your notes, pictures, plus your puzzle/maze and its solution.
Turn in your creation!

ASSESSMENT

Using the rubric, what grade would you give yourself?

Scoring Rubric

5Your solutions are correct and illustrated with clear diagrams. You used geometric language appropriately and correctly. Your models were well constructed. Your reasoning is sensible and supported with clear explanations based on research. Your display and/or model is organized, attractive and complete.

4Most of your solutions are correct. Your diagrams and research are adequate. Explanations make sense but may contain some unclear portions or gaps in reasoning. All or most geometric terms are used correctly.

3Many solutions are incorrect. Your diagrams are unclear or misleading. Explanations are inadequate, difficult to understand or logically flawed. Geometric terms are lacking or misused. Your modem and/or display is constructed neatly.

1 This project must be redone. See the teacher.

RESEARCH

You will be assessed on how well you used eLibrary to collect information and pictures about mazes and puzzles and their history.
You will be assessed on the completion of the Activities.
You will be assessed on how you organized information as described in the rubric.

WRITING

Did you create a time line with correct labeling?
Did you use at least 10 geometry terms in your paper?
Were your descriptions and directions accurate and well thought out?
Were your notes complete?

ACTIVITY 1

The tangram, known in China as the ch’I-ch’iao t’u, meaning “ingenious seven-piece plan,” is one of the oldest manipulative puzzles. You can use paper folding to make your own tangram.

Fold a square of paper in half diagonally four times the then unfold it.

Draw the segments to form seven (7) tangram pieces, called tans. (See diagram below.)

Cut out the seven tans.

How many of the tans are triangles? Form other triangles by placing the tans together. Make a sketch of each. Classify each triangle. Can you make one triangle using all seven tans?

ACTIVITY 2

In 1942, two mathematicians at the University of Chekiang in China proved that only 13 convex polygons could be formed by using all seven tans. They were able to form one triangle, six quadrilaterals, two pentagons and four hexagons. Try to make these using your set of tans. Sketch each figure.

ACTIVITY 3

You can create another geometric puzzle called pentominoes by joining five unit squares. Each square shares a side with at least one square. Corners do not count.

There are 12 different pentominoes. Sketch the other 10 pentominoes on graph paper.

Make a set of pentominoes out of cardboard. Use any three pentominoes to form a 3 X 5 rectangle. Find and record as many solutions as you can.

ACTIVITY 4

Use the pentominoes you made to answer the following: How many more pentominoes will it take to complete a 3 X 15 rectangle? How do you know?

Complete the rectangle and record your solution on graph paper.

Is the 3 X 15 pentominoe similar to the rectangular pentomino piece?

If it is, explain what the similarity ratio is.