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Mathematics for Elementary Teachers Mathematics for Elementary Teachers MICHELLE MANES Mathematics for Elementary Teachers by Michelle Manes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted Contents Problem Solving Introduction Problem or Exercise? Problem Solving Strategies Beware of Patterns! Problem Bank Careful Use of Language in Mathematics Explaining Your Work The Last Step 17 22 28 37 42 Place Value Dots and Boxes Other Rules Binary Numbers Other Bases Number Systems Even Numbers Problem Bank Exploration 47 52 56 60 68 76 80 86 Number and Operations Introduction Addition: Dots and Boxes Subtraction: Dots and Boxes Multiplication: Dots and Boxes Division: Dots and Boxes Number Line Model Area Model for Multiplication 91 93 100 106 108 120 126 Properties of Operations Division Explorations Problem Bank 132 158 161 Fractions Introduction What is a Fraction? The Key Fraction Rule Adding and Subtracting Fractions What is a Fraction? Revisited Multiplying Fractions Dividing Fractions: Meaning Dividing Fractions: Invert and Multiply 173 174 185 190 197 208 218 224 Dividing Fractions: Problems Fractions involving zero Problem Bank Egyptian Fractions Algebra Connections What is a Fraction? Part 230 233 236 247 251 253 Patterns and Algebraic Thinking Introduction Borders on a Square Careful Use of Language in Mathematics: = Growing Patterns Matching Game Structural and Procedural Algebra Problem Bank 259 261 265 273 278 283 290 Place Value and Decimals Review of Dots & Boxes Model Decimals x-mals Division and Decimals More x -mals Terminating or Repeating? Matching Game Operations on Decimals Orders of Magnitude 299 306 315 318 329 334 342 350 359 Problem Bank 365 Geometry Introduction Tangrams Triangles and Quadrilaterals Polygons Platonic Solids Painted Cubes Symmetry Geometry in Art and Science Problem Bank 373 374 378 394 399 405 408 421 431 Voyaging on Hōkūle`a Introduction Hōkūle`a Worldwide Voyage Navigation 439 440 443 446 Problem Solving Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths – Yoko Ogawa ... sentence below: • Decide if the choice x = makes the statement true or false • Choose a different value of that makes the statement true (or say why that is not possible) • Choose a different value... finally got paid at work, so he brought cash to school to pay back his debts First he saw Brianna, and he gave her 1/4 of the money he had brought to school Then Alex saw Chris and gave him 1/3 of... other dots How many pieces will you get? Lines may cross each other, but assume the points are chosen so that three or more lines never meet at a single point Think / Pair / Share After you have