Lab Activity Manual MATH 112-113: Math for Elementary Teachers Dr. Jonathan Duncan 2014-2015 Contents 1 Logic and Foundations 1 1.1 What Makes a Good Math Teacher? . 2 1.2 Patterns in Pascal's Triangle . 3 1.3 Stacking Cereal Boxes . 5 1.4 Scoring Darts . 7 1.5 A Logic Puzzle . 9 1.6 Glicks and Glocks . 11 1.7 Using Venn Diagrams . 13 1.8 Counting with Venn Diagrams . 15 2 Numeration and Operation 17 2.1 Whole Numbers and Counting . 18 2.2 Modeling Addition and Subtraction . 20 2.3 Patterns and Circle Clocks . 22 2.4 Interpreting Remainders . 24 2.5 Playing with Operation Sense . 26 2.6 Properties of Operations . 28 2.7 Numeration Systems . 31 2.8 Modeling Numerals in Other Bases . 33 2.9 Modeling Addition and Subtraction . 35 2.10 Skeletal Arithmetic . 37 2.11 Mental Arithmetic . 39 2.12 Modeling Multiplication and Division . 41 2.13 Multiplication and Division Base Six . 43 2.14 Doubling Algorithms for Multiplication . 45 2.15 Mental Multiplication and Division Tricks . 47 2.16 String Problems . 49 3 Number Theory 51 3.1 The Locker Problem . 52 3.2 Exploring E-Primes . 53 3.3 A Prime Numeration System . 55 3.4 Factoring Games . 56 3.5 Modular Arithmetic . 58 3.6 Modeling Divisibility Tests . 61 3.7 Divisibility Tests in Other Bases . 63 3.8 Modeling the GCD and the LCM . 65 3.9 GCD and LCM Problems and Properties . 68 3.10 Circle Clocks and Greatest Common Divisors . 70 4 Extending the Number System 72 4.1 Modeling Integer Operations . 73 4.2 Absolute Value and Opposites . 76 4.3 Modeling Fractions . 78 ii 4.4 Developing Fraction Sense . 82 4.5 Interpreting Fractions . 84 4.6 Units vs. Wholes . 86 4.7 Fraction Sense on a Number Line . 88 1 4.8 Discovering Base 2 .......................................... 90 4.9 Modeling Operations on Fractions . 92 4.10 Fraction Games . 95 4.11 Decimals and Base 10 Blocks . 97 4.12 The Right Bucket . 100 4.13 Understanding Ratios . 103 4.14 Solving Proportions . 106 4.15 Percent Change . 109 5 Algebra, Functions, and Graphs 111 5.1 Developing a Calculator Policy . 112 5.2 Modeling Algebra with Tiles . 113 5.3 From Tables to Functions . 116 5.4 Interpreting Graphs . 118 5.5 Growth Patterns in Figurate Numbers . 120 5.6 Iterated Functions . 123 6 Geometry 127 6.1 Axiomatic Systems . 128 6.2 Geometric Proof . 130 6.3 Proofs of the Pythagorean Theorem . 132 6.4 Interior Angles of a Polygon . 136 6.5 Possible Polygons . 139 6.6 Tangram Puzzles . 142 6.7 Congruence . 144 6.8 Relationships Between Polygons . 146 6.9 Sketching Rectangular Prisms . 148 6.10 Building Blocks . 151 6.11 Nets . 154 6.12 Constructing Polyhedra . 157 6.13 Spherical Geometry . 158 6.14 Basic Geometric Constructions . 160 7 Measurement and Transformation 163 7.1 Unit Conversion . 164 7.2 How Is It? . 166 7.3 Relating Area and Perimeter in Rectangles . 168 7.4 Discovering Pick's Formula . 170 7.5 Area and Perimeter on a Geoboard . 173 7.6 Exploring the Perimeter and Area of a Circle . 175 7.7 Varying Surface Areas . 177 7.8 Relating Volume and Surface Area . 179 7.9 Varying Volume . 181 7.10 The Volume of Irregularly Shaped Objects . 182 7.11 Packing Efficiency . 184 7.12 Understanding Reflections . 186 7.13 Name That Transformation . 189 7.14 Groups of Symmetries . ..