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District School Board of Collier County Elementary Math Grade Five

Next Generation Sunshine State Standards Aligned to Florida’s Frameworks for Gifted Learners

With Extension Activities

An Overview of the Math in Fifth Grade Number and Operations: Whole Numbers Students practice and refine the strategies they know for addition, subtraction, multiplication, and division of whole numbers as they improve computational fluency and apply these strategies to solving problems with larger numbers. They expand their knowledge of the structure of place value and the base-ten number system as they work with numbers in the hundred thousands and beyond. By the end of the year, students are expected to know their division facts and to efficiently solve computation problems involving whole numbers for all operations. Number and Operations: Fractions, Decimals, and Percents The major focus of the work with rational numbers is on understanding relationships among fractions, decimals, and percents. Students make comparisons and identify equivalent fractions, decimals and percents. They order fractions and decimals, and develop strategies for adding fractions and decimals to the thousandths. Geometry and Measurement Students develop their understanding of the attributes of 2-D shapes, examine the characteristics of polygons, including a variety of triangles, quadrilaterals, and regular polygons. They also find the measure of angles of polygons. In measurement, students use standard units of measure to study area and perimeter and to determine the volume of prisms and other polyhedra. Patterns and Functions Students examine, represent, and describe situations in which the rate of change is constant. They create tables and graphs to represent the relationship between two variables in a variety of contexts and articulate general rules using symbolic notation for each situation. Students create graphs for situations in which the rate of change is not constant and consider why the shape of the graph is not a straight line. Data Analysis and Probability Work focuses on comparing two sets of data collected from experiments developed by the students. They represent, describe, and interpret this data. In their work with probability, students describe and predict the likelihood of events and compare theoretical probabilities with actual outcomes of many trials. They use fractions to express the probabilities of the possible outcomes. (Investigations in Number, Data and Space, 2008)

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Big Idea1: Develop an understanding of and fluency with division of whole numbers.

Sunshine State Standards

MA.5.A.1.1 Describe the process of finding quotients involving multi-digit dividends using models, place value, properties and the relationship of division to multiplication.

MA.5.A.1.2

Estimate quotients or calculate them mentally depending on the context and numbers involved.

MA.5.A.1.3 Interpret solutions to division situations including those with remainders depending on the context of the problem.

MA.5.A.1.4 Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm and checking the reasonableness of results.

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FL Frameworks for K-12 Gifted Learners

Goal 4, Obj. 3: Use problem-solving methods Trait: Creative Methodology (Accomplish) Designs original problem solving models for use in

specific situations

Goal 6, Obj. 1: Accept challenges to maximize learning. Trait: Acceptance of Challenge (Understand) Identifies strategies and resources to overcome obstacles Goal 4, Obj. 2: Analyze data to draw conclusions and forecast effective solutions Trait: Critical Thinking (Accomplish) Analyzes, interprets, and synthesizes details and facts to examine relationships, infer meanings, and predict outcomes

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Big Idea2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.

Sunshine State Standards FL Frameworks for K-12 Gifted Learners MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.

MA.5.A.2.2 Add and subtract fractions and decimals fluently and verify the reasonableness of results, including in problem situations. MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding. MA.5.A.2.4 Determine the prime factorization of numbers.

Goal 4, Obj. 2: Analyze data to draw conclusions and forecast effective solutions Trait: Forecasting Solutions (Understand) Organizes facts and information using various methods to predict potential outcomes

Goal 4, Obj. 1: Identify and investigate a problem Trait: Multiple Perspectives (Understand) Compares and contrasts multiple perspectives of a problem

Goal 4, Obj. 3: Use problem-solving methods Trait: Creative Methodology (Accomplish) Designs original problem solving models for use in specific situations

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Big Idea3: Describe three-dimensional shapes and analyze their properties, including volume and surface area.

Sunshine State Standards FL Frameworks for K-12 Gifted Learners

MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. MA.5.G.3.2 Describe, define and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools.

Goal 1, Obj. 2: : Foundational concepts Trait: Data analysis (Perform) Uses a variety of tools and techniques to organize data to draw conclusive statements

Goal 4, Obj. 1: Identify and investigate a problem Trait: Multiple Perspectives (Understand) Compares and contrasts multiple perspectives of a problem

Goal 4, Obj. 3: Use problem-solving methods Trait: Creative Methodology (Accomplish) Designs original problem solving models for use in specific situations

Supporting Idea 4: Algebra

Sunshine State Standards FL Frameworks for K-12 Gifted Learners

MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations. MA.5.A.4.2 Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.

Goal 1, Obj. 2: : Foundational concepts Trait: Data analysis (Perform) Uses a variety of tools and techniques to organize data to draw conclusive statements Goal 4, Obj. 2: : Analyze data to draw conclusions and forecast effective solutions Trait: Data analysis (Perform) Uses a variety of tools and techniques to organize data to draw conclusive statements

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Supporting Idea 5: Geometry and Measurement

Sunshine State Standards FL Frameworks for K-12 Gifted Learners MA.5.G.5.1 Identify and plot ordered pairs on the first quadrant of the coordinate plane. MA.5.G.5.2 Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems. MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement. MA.5.G.5.4 Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle.

Goal 4, Obj. 3: Use problem-solving methods Trait: Creative Methodology (Accomplish) Designs original problem solving models for use in specific situations

Goal 6, Obj. 1: Accept challenges to maximize learning. Trait: Acceptance of Challenge (Understand) Identifies strategies and resources to overcome obstacles Goal 6, Obj. 3: Design plans of action Trait: Action Plan Components (Perform) Action plans include appropriate allocation of time, money, materials, and other resources

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Supporting Idea 6: Number and Operations

Sunshine State Standards FL Frameworks for K-12 Gifted Learners

MA.5.A.6.1 Identify and relate prime and composite numbers, factors and multiples within the context of fractions. MA.5.A.6.2 Use the order of operations to simplify expressions which include exponents and parentheses. MA.5.A.6.3 Describe real-world situations using positive and negative numbers. MA.5.A.6.4 Compare, order, and graph integers, including integers shown on a number line. MA.5.A.6.5 Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise”.

Goal 1, Obj. 2: Basic principles and foundational concepts Trait: Components and Methodologies (Accomplish) Experiments with a variety of methods to analyze data to develop greater understanding

Goal 4, Obj. 3: Use problem-solving methods Trait: Creative Methodology (Accomplish) Designs original problem solving models for use in specific situations Goal 6, Obj. 1: Accept challenges to maximize learning Trait: Acceptance of Challenge (Understand) Identifies strategies and resources to overcome obstacles

Supporting Idea 7: Data Analysis

Sunshine State Standards FL Frameworks for K-12 Gifted Learners MA.5.S.7.1 Construct and analyze line graphs and double bar graphs. MA.5.S.7.2 Differentiate between continuous and discrete data and determine ways to represent those using graphs and diagrams.

Goal 1, Obj. 1: Broad spectrum of knowledge Trait: Organization of Data (Know) Identifies strategies and resources to overcome obstacles

Goal 1, Obj. 2: Basic principles and foundational concepts Trait: Components and Methodologies (Accomplish) Experiments with a variety of methods to analyze data to develop greater understanding

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Extension Activities for Grade Five by Unit Order of the units follows the CCPS Grade 5 Math Quarterly Outlook General Math Extension Menus These menus cover the following concepts; Factors and Multiples, Multiplication, Rounding, Area and Problem Solving https://sites.google.com/a/pflexonline.net/www/math?tmpl=%2Fsystem%2Fapp%2Ftemplates%2Fprint%2F&showPrintDialog=1 Quarter 1 Unit 1: Number Puzzles and Multiple Towers Factors and Multiples Extension Menu http://www.pflugervilleisd.net/curriculum/math/place_value_model.cfm#enrichment_extension This math menu created by Pflugerville Independent School District offers a variety of activities to extend the thinking of your students. This menu includes activity choices such as: Create a Game, Write a Music Video Script, Create a picture book and much much more! Factor Game http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 The Factor Game is a fun, interactive game that exercises your factoring ability. You can play against the computer or against a friend. The Product Game http://illuminations.nctm.org/ActivityDetail.aspx?ID=29 The Product Game is a fun, interactive game that exercises your skill with factors and multiples. The Grid Game http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html BBC has developed a game for students to choose a level and then find the factors, multiples, powers, prime and triangular numbers shown on the grid. Students are rewarded when they give a correct response by characters “Pythagoras” and “Hypathia” who jump for joy. Literature Connections: Amanda Bean's Amazing Dream (Cindy Neuschwander) Ben Franklin and the Magic Squares (Frank Murphy) Math Curse (Jon Scieszka)

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Quarters 1 and 2 Unit 2: Prisms and Pyramids

Math Investigations Center Menu (Attachment)

Paper Polyhedra Models http://www.korthalsaltes.com/ Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia. On this site are a few hundred paper models available for free. Explore Prisms http://www.learner.org/interactives/geometry/3d_prisms.html This website explains 3D shapes including polyhedron, prisms and pyramids. This activity provides the student with the opportunity to explore and manipulate animated prisms. Quarter 2 Unit 4: What’s That Portion?

Soccer Shootout http://www.funbrain.com/fractop/index.html Students will enjoy this game of soccer when they select their level and score and save by correctly answering math problems. First you shoot, and then try to save the shot by FunBrain. The Factor Game http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 The Factor Game from “Illuminations” is a fun, interactive game that exercises your students’ factoring ability. Students can play against the computer or against a friend. Decimals and Fractions Extension Menu http://www.pflugervilleisd.net/curriculum/math/place_value_model.cfm#enrichment_extension This math menu created by Pflugerville Independent School District offers a variety of activities to extend the thinking of your students. This menu includes activity choices such as: Create a Game, writing a poem, writing a song, writing a story about a world without fractions as well as many “real world” applications of the use of fractions. Who Wants to be a Fractions Millionaire? http://www.quia.com/rr/125626.html From Quia, Students will solve fractions equations to in order to reach the top and earn a million dollars. Literature Connections Fraction Fun (David Adler) The Hershey's Milk Chocolate Fractions Book (Jerry Pallotta) Working With Fractions (David Adler)

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Unit 5: Measuring Polygons

Geometry Math Investigations Center – (See attachments for Geometry Unit)

Architecture Web Quest http://www.lakelandschools.us/cb/cgravius/geometry_architecture_webquest.htm#Intro Interior Angels of Polygons http://www.coolmath.com/lesson-interior-angles-of-polygons-2.htm Students will learn to find interior angels of polygons http://illuminations.nctm.org/webresourcelist.aspx?ref=2&std=2&grd=0

http://www.coolmath.com/lesson-interior-angles-of-polygons-1.htm

http://www.mathsisfun.com/geometry/interior-angles-polygons.html

Similarity/Triangles http://www.keymath.com/x3343.xml Literature Connections Sir Cumference & the Great Knight of Angleland (Cindy Neuschwander) (5) Sir Cumference & the Isle of Immeter (Cindy Neuschwander) (5) Quarter 3 Unit 6: Stories, Tables, and Graphs Amazing Animals http://elementarymath.cmswiki.wikispaces.net/file/view/Extension%2BProjects%2Bfor%2BMath%2BInvestigations%2BGrade%2B4%2B-and%2B5.pdf Research a favorite animal and then collect data to compare, summarize interpret and analyze. Math Projects http://www.proteacher.org/c/865_Math_Projects.html A compilation of math projects including survey and data collection. Internet Activities http://www.newton.k12.ks.us/tech/fifth_grade_internet_activities1.htm Magic Square Click on the “Math” button and scroll down to “Magic Square” This activity from Newton Public schools is created in Excel. Students will Place the numbers 1-9 in the squares so that each row and column equal 15. Each number may only be used ONE time.

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Unit 7: Finding Fair Shares Pi Day Activities/Resources http://www.nctm.org/resources/content.aspx?id=2147483830 http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html http://www.vvc.edu/ph/TonerS/mathpi.html http://www.exploratorium.edu/pi/history_of_pi/index.html Fraction, decimals and percentages http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/ This BBC/UK website offers a compilation of activities at various levels of challenge. Quarters 3 and 4 Unit 8: Growth Patterns Algebra-Fun with Calendars http://math.rice.edu/~lanius/Lessons/calen.html A fun mathematical puzzle to figure out with classmates. Exponential Growth Patterns http://www.figurethis.org/challenges/c07/challenge.htm How much is your time worth? Students will discover how rates of change are important when making choices about salary options. Quarterly Extension Projects These quarterly projects from Minneapolis Public Schools provide activities including; Architecture, Grocery Store Challenge, Checkbook Challenge, and collecting data on Amazing Animals http://elementarymath.cmswiki.wikispaces.net/file/view/Extension%2BProjects%2Bfor%2BMath%2BInvestigations%2BGrade%2B4%2B-and%2B5.pdf Algebra Extensions http://illuminations.nctm.org/WebResourceList.aspx?Ref=2&Std=1&Grd=0 Review and Bridge to 6th grade

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MIC Menu for Geometry Unit

Integrating Mathematics

and Science

Landscape Architects

Watch a short video and create a

plan for your own outdoor space

that would flourish in Southwest

Florida.

Problem Solving

Callie’s Cake Capers

Investigate the “deals” at Callie’s

Cake Creations to find out if you

are getting the most cake for your

money.

Writing about

Mathematics

Tessellations

WebQuest

Explore the exciting world of

M.C. Escher and tessellations.

This activity requires a

minimum of 2 people to

complete the task.

Mathematics Game

Mission: Impossible -

Geometric Scavenger

Hunt

Grab a digital camera and search

around your school campus to find

examples of the geometric terms

on your list!

Student Choice

With teacher approval

Logic Problem

Toothpick Puzzles

Manipulate toothpicks to

create the geometric figures

and follow the directions to

solve the 6 puzzles.

Mathematics and Social

Studies

Plan a Park

Design a park and create a

proposal to submit to the

Tallmadge City Council.

Building Project

Designing Bumper Cars

Discover the mathematical thinking

that goes into designing bumper-car

floor plans!

Literature and

Mathematics

Geometry and Poetry

Read and illustrate “Shapes”

by Shel Silverstein (1981)

then write and illustrate your

own geometric poem.

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Materials for MIC Menu for Geometry Unit

Integrating Mathematics

and Science

Landscape Architects

Drawing paper

Colored pencils

Computer access

Problem Solving

Callie’s Cake Capers

Scissors

Callie’s Cake Capers

packet

Writing about

Mathematics

Tessellations WebQuest

Computer access

Mathematics Game

Mission: Impossible -

Geometric Scavenger

Hunt

Digital camera

Computer access

Student Choice

Logic Problem

Toothpick Puzzles

Baggie containing 20

toothpicks

Mathematics and Social

Studies

Plan a Park

Graph paper

Computer access for

typing report

Building Project

Designing Bumper Cars

Designing Bumper

Cars packet

Color tiles

Graph paper

Literature and

Mathematics

Geometry and Poetry

Shapes Art

Worksheet

A Light in the Attic

by Shel Silverstein

(optional)

Drawing paper

Colored pencils

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All of the cakes at Callie’s Cake Creations are exact squares. That means a 6” cake has sides of

six inches all the way around. Callie’s cake costs are fairly common, but her specials seem somewhat

suspect. Use your sleuthing skills to find the flaws and determine the drawbacks of each “deal.”

Assume that it is always best to get the most cake for your money.

Callie’s Cake Creations

Cut out the scale models of the cakes and fill in the table below to help you with your answers.

The table shows how many of each smaller cake it takes to make one larger cake. Some of the answers

have been filled in for you. Show your work

in the space below or on another sheet of

paper. Be sure to address each special.

# of smaller cakes in each larger cake

Cake Size 6” 12” 18”

12” square

18” square

2.25

24” square

1.78

Prices

6” Basic Cake……..$5.00

12” Large Cake…..$10.00

18” Family Cake…$15.00

24” Party Cake…..$20.00

Save $5 Specials

4 Basic Cakes.…….$15.00

2 Large Cakes …..$15.00

3 Large Cakes…….$25.00

1 Large Cake &

1 Family Cake….. $20.00

Save $10 Specials

4 Large Cakes.…….$30.00

2 Basic Cakes 2 Large Cakes &

2 Family Cakes….. $20.00

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For each question, determine which of the two options gives you the most cake for your dollar

using the standard prices from the first student page. Use the regular prices – not the specials! Show

your work.

Which is a better deal:

1. One family cake, or one large cake and one basic cake? Why?

2. One basic cake and one party cake, or one large cake and one family cake? Why?

3. Two family cakes, or one large cake and one party cake? Why?

4. Two family cakes or two basic cakes and one party cake? Why?

5. Two party cakes, or one party cake, one family cake, and one basic cake? Why?

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Cut out these cake models to help you think about your answers.

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Your mission, should you choose to accept it - grab a digital camera and search around your school

campus to find examples of the geometric terms on your list. Once you have found good examples, print

off the pictures and add them to your classroom’s Math Vocabulary Word Wall!

Note: You may not have learned about all these terms. If you are unfamiliar with a term, find the

definition first, then look for a real-world example.

Point Acute Angle Hexagon

Line Right Angle Heptagon

Line Segment Obtuse Angle Octagon

Mid-point Straight Angle Pentagon

Plane Equilateral Triangle Decagon

Ray Scalene Triangle Perimeter

Parallel Lines Isosceles Triangle Area

Intersecting Lines Quadrilateral

Perpendicular Lines Trapezoid

Angle Parallelogram

Vertex Rectangle

Sides Rhombus

Supplementary Square

Interior Convex

Exterior Congruent

Degrees Similar

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Meet two landscape architects who tell the story of competing against top firms in the world to win the

opportunity to design a one-of-a kind botanical garden for the city of Chicago: the Lurie Garden at

Millennium Park. Watch the short video about their planning process:

http://www.thefutureschannel.com/dockets/hands-on_math/landscape_architects/index.php

Part 1: Researching Your Design

Conduct research to answer the following questions:

How would you design an outdoor space in Southwest Florida?

What would you call your space?

Where would you like to see your space located?

What would you consider when selecting plant life to go in your outdoor space?

Specifically, what type of plants would you use in your outdoor space?

Why did you choose the plants for the space?

Part 2: The Sketch

Create a color sketch of your outdoor space. Be sure to include any plants, flowers, trees, structures,

walkways, benches, etc.

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An Internet WebQuest on Tessellations

created by Tricia Ann Cahalan

Introduction

Imagine you are just awakening for school, but you realize that you are not in your bed and not

even in your own home. You find yourself in a dormitory setting with three other students also

just awakening. You notice how they are putting on their school clothes, which happen to be

robes like in Harry Potter.

As you follow the rest of your dorm mates you become curious. So you join them donning your

robe. You walk out the door, down the hallway and find staircases everywhere going up and

down, even left and right. You follow the others and are on a descending staircase. It suddenly

becomes an ascending staircase to an upper floor and changes its direction from left to right.

You grab onto the railing and notice that all the staircases are changing. How can you get off

this stair way and find your way back home?

Who would possibly think of making a stairway that continues to move or to go around in

patterns of up and down and all around? We know that this would be impossible to draw right?

So how could it be built in real life?

In the following WebQuest, you will use the power of teamwork and the abundant resources on

the Internet to learn all about Tessellations. Each person on your team will learn one piece of

the puzzle and then you will come together to get a better understanding of the topic.

The Quest

How can a staircase be created that moves continuously whether it moves left or right and up

and down? How could a plan be drawn out for this to work?

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The Process and Resources

In this WebQuest you will be working together with a group of students in class. Each group will

answer the Task or Quest(ion). As a member of the group you will explore Webpages from

people all over the world who care about Tessellations. Because these are real Webpages we're

tapping into, not things made just for schools, the reading level might challenge you. Feel free

to use the online Webster dictionary or one in your classroom.

You'll begin with everyone in your group getting some background before dividing into roles

where people on your team become experts on one part of the topic.

Phase 1 - Background: Something for Everyone

Use the Internet information linked below to answer the basic questions of who? what? where?

when? why? and how? You need basic information about what a Tessellation is? Be creative in

exploring the information so that you answer these questions as fully and insightfully as you can.

World of Escher - Website dedicated to M.C. Escher

Tessellation Tutorial - The Basics: what is a Tessellation? Is it Math? Is it Art?

Phase 2 - Looking Deeper from Different Perspectives

INSTRUCTIONS:

1. Individuals or pairs from your larger WebQuest team will explore one of the roles below.

2. Read through the files linked to your group. If you print out the files, underline the passages

that you feel are the most important. If you look at the files on the computer, copy sections

you feel are important by dragging the mouse across the passage and copying / pasting it into a

word processor or other writing software.

3. Note: Remember to write down or copy/paste the URL of the file you take the passage from

so you can quickly go back to it if you need to prove your point.

4. Be prepared to focus what you've learned into one main opinion that answers the Big

Quest(ion) or Task based on what you have learned from the links for your role.

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Examiner of Tessellations

Use the Internet information linked below to answer these questions specifically related to

Who was MC ESCHER?:

1. Where was MC Escher from?

2. Why did he create Tessellations?

3. Was he the first to ever create Tessellations or was he just a more well known person?

4. Who has Escher been compared to?

5. How did he create his work?

6. What materials did he use?

7. How does he specifically do this?

8. What elements of Math and Art are specifically used?

Tessellations - Creative combinations of math, art and fun!

What is a Tessellation?

Mathematician

Use the Internet information linked below to answer these questions specifically related to the

question: How does MC ESCHER combine Math and Art?

1. What specific Math Elements would be used to create a staircase?

2. What types of materials would you need for this idea of a moving staircase?

3. Where could you find information or people to create this staircase?

The Mathematical Art of M.C. Escher

Geometry and Tessellations

Convex Pentagons that Tile the Plane

Strathclyde Spirals - Staircases

Edward Brown Staircases

Architechture of Staircases

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Computer Generated Designs

Use the Internet information linked below to answer these questions specifically related to

computerized Tessellations:

1. Are computerized Tessellations harder to create than handmade Tessellations?

2. Do you think using the computer is a benefit to or ruining the process of creativity?

3. Is the process multitasking?

4. What is the process you would use to create a tessellation on the computer?

The Topic: Tessellations

Hyperstudio and Tessellations

Crompton Tessellations

Artist of Hand-Created Designs

Use the Internet information linked below to answer these questions specifically related to

Hand-Created Designs:

1. Hand-Created Designs like MC Escher's have certain qualities which suggest time, hard work,

and a large amount of problem solving. How would you go about creating a handmade

tessellation?

2. Is there more than one process to make a tessellation by hand?

3. Is the process difficult?

Art Part M.C. Escher

Islamic Patterns and M.C. Escher

Phase 3 - Debating, Discussing, and Reaching Consensus

You have all learned about a different part of Tessellations. Now group members come back to

the larger WebQuest team with expertise gained by searching from one perspective. You must

all now answer the Task / Quest(ion) as a group. Each of you will bring a certain viewpoint to the

answer: some of you will agree and others disagree. Use information, pictures, movies, facts,

opinions, etc. from the Webpages you explored to convince your teammates that your viewpoint

is important and should be part of your team's answer to the Task / Quest(ion). Your

WebQuest team should write out an answer that everyone on the team can live with.

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Phase 4 - Real World Feedback

You and your teammates have learned a lot by dividing up into different roles for your research.

Now is the time to put what you have learned into a presentation which you will share with the

class. You can use any of the following formats for your presentation.

1. Create a PowerPoint Presentation citing basic information each of you found. Share your

conclusions as a group as to which type of Tessellations are better aesthetic-wise:

computerized or hand drawn. Examples backing up your position are expected. Be sure you have

answered The Task / Question.

2. You may choose to use another format like Microsoft Publisher as part of your presentation.

Same information on each part of the assignment is required and you need to show an example

of each for your position.

Conclusion

Stairs up and down, left to right, moving in at random times…just like the stairs in Harry Potter

and in M.C. Escher's Tessellations. Tessellations can be in any shape and any form. Try to find

other places that Tessellations appear. Keep exploring and remember that Art involves

everything!

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Grab some toothpicks and create the models shown in the puzzles. Follow the directions to see

if you can solve these brain teaser puzzles!

Puzzle #1

Use 17 toothpicks to construct this figure:

a. Remove 5 toothpicks and leave 3 squares.

b. Remove 6 toothpicks and leave 2 squares.

Puzzle #2

Make this figure with 12 toothpicks:

a. Remove 4 toothpicks and leave 3 triangles.

b. Move 4 toothpicks and form 3 triangles.

Puzzle #3

With 9 toothpicks, make this figure:

a. Remove 2 toothpicks and leave 3 triangles.

b. Remove 3 toothpicks and leave 1 triangle.

c. Remove 6 toothpicks and get 1 triangle.

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d. Remove 4 toothpicks and get 2 triangles.

e. Remove 2 toothpicks and get 2 triangles.

Puzzle #4

Use 8 toothpicks and 1 button to form a fish:

Move 3 toothpicks and the button to make this fish swim in the opposite direction.

Puzzle #5

Two farmers have land this shape:

a. The first farmer wants to divide her land evenly among her 3 daughters. Add 4 toothpicks to

form three parcels of equal size and identical shape.

b. The second farmer wants to divide her land evenly among her 4 daughters. Use 8 toothpicks

to form four parcels of equal size and identical shape.

Puzzle #6

Use 6 toothpicks to form 4 equilateral triangles.

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Puzzles taken from:

The Franklin Institute: Resources for Science Learning

http://www.fi.edu/sln/school/tfi/spring96/puzzles/puzzle1.html

Answers to puzzles:

http://www.fi.edu/math/toothpick_answers.html