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 0.1 x 0.2 0.3 0.4 0.5 0.6 x x x x x x x x x x x x 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 x x x x 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 x x x x x x x x x x x x x x x x x x 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 x x x x x x x x x x x x x 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) x x x x x x x x x x 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 3.1 x x x x x 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 x x x x x x x x x x x x x x x x x x 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 4.1 x 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 x x x x x x x x x x x 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 x 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