MOW Materials
Unit 0-5
Unit 0: Getting Started with Modeling
0.1 School Population
Available data that will provide students with relevant information, such as a list of
mathematics courses offered, the number of classroom teachers in the school
0.2 BINGO Card
Colored pencils
Colored papers for making squares of various sizes
0.3 Skeleton Tower
Cubes
Materials needed to draw diagrams
0.4 Coin Switcheroo
Coins or chips of 2 different colors
Copies of the board, or have students draw the boards
0.5 Something’s Fishy
Counters, cubes, or other manipulatives to represent the quantities involved
Blank paper for drawing
0.6 The Path of a Billiard Ball
Grid paper
Straight edges as needed
Materials
Data about the school
Colored pencils
Colored paper
Cubes (Unifix Cubes)
Coins or chips of 2 different colors
Copies of the Coin Switcheroo game
board
Paper
Grid paper
Straight edges
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0.6
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Unit 1: Relationships Between Quantities and Reasoning with
Equations
Lesson 1.1 Trapezoid Trains
Pattern blocks: several trapezoids and triangles per group
Paper
Pencils
Grid paper
Lesson 1.2 Paper Stacks
Calculator
Paper
Ruler
Scissors (optional)
Additional paper (optional)
Lesson 1.3 Toothpick Polygons
Toothpicks
Paper on which line segments can be drawn to model the toothpicks
Lesson 1.4 A New Look at Equations
None
Lesson 1.5 Tile Tools
Algebra tiles
Notebook paper
Lesson 1.6 The Mighty Dollar
None
Lesson 1.7 Equation Extravaganza
Calculators
Algebra tiles
Lesson 1.8 Measuring Cups
This investigation is intended for small group work. Each group will need their own set
of materials.
two unmarked containers of different sizes
fill (for example, water, uncooked rice, or sand)
bucket or tray to contain the material
sticky notes to label the intended quantity of each container
Lesson 1.9 Formulas for Success
None
Lesson 1.10 Adjusting Grades
Graphing software
Spreadsheet that can show four columns simultaneously
Lesson 1.11 Them Bones
Measuring tape
Teacher software
Materials
Pattern blocks
Paper
Pencils
Grid paper
Calculator
Ruler
Scissor
Toothpicks
Paper on which line
segments can be drawn
Algebra tiles
Notebook paper
Unmarked containers of
different sizes
Fill (for example, water,
uncooked rice, or sand)
Bucket or tray
Sticky notes
Graphing software
Spreadsheet
Measuring tape
Teacher software
1.1
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1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9 1.10 1.11
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Unit 2: Linear and Non-Linear Relationships
2.1 Make a New Puzzle
Construction paper or card stock
Scissors
Tracing paper
Rulers
Prepare the student materials using the master copy page.
2.2 Number Sequences
None
2.3 Interpreting Graphs
None
2.4 Rods and Spools
Simple manipulatives to represent rods and spools such as toothpicks or straws
Clay
2.5 Pizza Puzzler
None
2.6 Stories and Graphs
None
2.7 Grains of Rice
Chess board or 8 by 8 grid of 1" squares
Markers to represent grains of uncooked rice
Internet access to view video clip
2.8 Waiting for Rock Concert Tickets
Two-color counters may help students set up a representation of the situation to better
understand the problem.
2.9 Painted Cubes
Cubes: Some students might find it helpful to build a cube made of 27 smaller cubes,
then place stickers on the exposed faces. If students place stickers by category (for
example, on cubes with 2 painted face or cubes with 3 painted faces), they may notice the
position of each set of small cubes relative to the large cube they form.
2.10 Tables, Graphs, and Stories
Scissors
Student materials for Part II
Use the master copies on pages 124 – 127 to prepare the student materials for Part II in
advance. You may find it easier to organize the materials by using paper of one color for
stories, another color for graphs, and a third color for tables. The labels have been
randomly assigned to the stories, graphs, and tables to make referral easier during the
discussion. They do not indicate which representations form a matching set. A key to
matching sets appears in the Annotated Student Page.
2.11 Going Viral
None
2.12 Families of Lines
Graphing calculator
Teacher software
2.13 Design-a-Box Contest
Letter-size sheets of paper
Scissors
Tape
Ruler for Part I
A second sheet of paper (not 8 ½ by 11 or multiples of that size) for Part II
A chart for students to record the length, width, height, and volume of their first box
2.14 Tower of Hanoi
A Tower of Hanoi game (if a commercial game is available)
Coins or virtual manipulatives (various sources are listed below)
Materials
Construction
paper
Card stock
Scissors
Tracing paper
Rulers
Master copy
Simple
manipulatives
(e.g.
toothpicks or
straws)
Clay
Chess board or
8 by 8 grid of
1" squares
Markers
Internet access
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14
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Two-color
counters
Cubes
Graphing
calculator
Teacher
software
Letter-size
sheets of paper
Tape
Paper (not 8 ½
by 11)
Chart
Tower of
Hanoi game
Coins (or
virtual
manipulatives)
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Unit 3: Data and Decision Making
3.1 Water Spots
Several sheets of paper towel
Medicine dropper
Cup of colored water
Ruler
Grid paper
3.2 CSI (Cheerful Scene Investigations) Hawaii
Measuring tape
3.3 Open the Elevators
None
3.4 Talk versus Text
None
3.5 Chances Are
Dice
Cards
Graphing calculators (optional)
3.6 Granting Licenses
None
3.7 Sports Connections
None
Unit Project Leaky Faucets
None
3.8 Bouncing Ball
Balls
(You may decide to have students use the same type of ball and consider quality control
issues, or you may want them to use different types of balls and have them discuss why
some would be designed to bounce more than others. Golf balls bounce well, while tennis
balls do not bounce as well.)
Measuring tape
Adhesive tape
Calculator-Based Ranger (CBR) with a graphing calculator,
Video recorder (including tablets or smart phones, if allowed) or mobile device
applications to collect data.
3.9 Will Women Run as Fast as Men?
None
3.10 Knotty Rope
A different type of rope (about 1.5 m) for each group
A meter stick or metric tape
Graph paper
A length of rope about 25 m long, of the same type used by any one of the groups in the
first part, for the class to verify a representative model (optional)
3.11 Bungee Jumping
Doll action figures
Meter sticks
A box of uniform rubber bands
Scissors
Ask students to bring in action figures and/or dolls.
Materials
Paper towel sheets
Medicine dropper
Colored water
Ruler
Grid paper
Measuring tape
Dice
Cards
Graphing calculator
Balls
Adhesive tape
Calculator-Based Ranger
(CBR)
Video recorder
Different type of rope
(about 1.5 m)
Meter stick or metric tape
Rope about 25 m long
Doll action figures
Box of uniform rubber
bands
Scissors
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3.2
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3.9 3.10 3.11
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Unit 4: Expressions and Equations
4.1 Unpacking The Think-of-a-Number Game
Algebra tiles (best used with Problems 1 and 2)
4.2 Quilting Patterns
Dot paper may help students make their drawings. Tracing paper might be helpful also.
4.3 Exploring Exponential vs. Power
None
Unit 4 Project: How Is Our Environment Changing?
It is intended that students will rely primarily on the scientifically-based websites and
articles along with technology for creating and presenting their reports.
4.4 Hawai‘i’s Population Growth and Food Production
Graphing calculator
4.5 Enlightening Exponentials
None
4.6 Response Time
None
4.7 Rods and Spools Extended
If needed, students can once again use simple manipulatives to represent rods and spools,
such as toothpicks and clay, dough, or mini-marshmallows.
4.8 The Shape of a Bottle
Encourage students to bring unusually shaped bottles to enrich the analysis and
discussion. If you need a greater variety of bottles you can find some images at the
following web sites.
Chrysanthemum bottle
http://www.picsearch.com/imageDetail.cgi?id=tQm8qCyv-srDiN0uLyV-m3eeszfxsTrnmyIXTO htY8&width=1257&start=61&q=Bottles
Bottle on the left in “Small Bottles”
http://www.picsearch.com/imageDetail.cgi?id=BEMSoGkcCowCxB6CxgGYRMrswSQ_
AaBbXwPjggWeavg&width=1257&start=91&q=Bottles
Any of a number of these
http://www.picsearch.com/imageDetail.cgi?id=8zjkaID3MKILiAUfaXyBMyoIV5avd42
OqNIVSbKrf8&width=1257&start=91&q=Bottles
4.9 Hawaiian Bloodline
Calculators should be available, grid paper or graphing technology.
4.10 Twelve Days of MOW Class
Counters might be helpful to some students.
4.11 Order from Chaos
Transparencies and/or tracing paper
29-row hexagonal template (optional; see above in Opportunity to model with
mathematics)
4.12 Skeleton Tower Revisited
Cubes
Materials
Algebra tiles
Dot paper
Graphing calculator
Toothpicks
Clay, dough, or
marshmallows
Unusually shaped
bottles
Grid paper
Counters
Transparencies and/or
tracing paper
29-row hexagonal
template
Cubes
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4.5
4.6
4.7
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4.9 4.10 4.11 4.12
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Unit 5: Quadratic Functions and Modeling
5.1 Interpreting Graphs of a Rocket
None
5.2 The Perfect Arch
None
5.3 Families of Parabolas
Graphing calculator
5.4 Area Maximized
Some students may benefit from having lengths of string available to experiment with a
scaled version of the problem.
MOW Unit 5 Project: Modeling in Your World
None
5.5 Diagonals in a Polygon
None
5.6 Things That Go ‘Round
String or rope
Tape measures
Inch-cubes
Adhesive or masking tape (to either secure the cubes to a ball, or tape the ends of the rope
to make the hoop)
5.7 L-Shaped Patios
None
5.8 Pancake Palace
Students should have access to paper, pencils, a compass, and a straightedge so that when
they draw circles and segments, the drawings are fairly accurate. Having multiple copies
of a larger circle already drawn for Part II may be helpful.
5.9 The Changing Value of Money
None
5.10 Toothpick Revisited
Toothpicks
5.11 BINGO Revisited
None
5.12 Odd Square Patterns
None
5.13 Going around Again
Paper
Rulers
5.14 Rods and Spools Finale
If needed, students can once again use simple manipulatives, such as toothpicks or straws
and clay, to represent rods and spools.
Materials
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14
Graphing
x
Calculator
String/Rope
x
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Tape
x
measure
Adhesive/
x
masking tape
Inch-cubes
x
Compass
x
Straightedge
x
Toothpicks
x
x
Paper
x
Rulers
x
Straws
x
Clay
x