IntroductionLow Floor, High Ceiling TasksYoucubed Summer CampMemorization vs. Conceptual EngagementMathematical Thinking, Reasoning and ConvincingBig IdeasStructure of the BookActivities for Building NormsEncouraging Good Group WorkPaper Folding: Learning to Reason, Convince, and Be SkepticalBig Idea 1: Solving Problems with DataVisualize: Tongues, Tails, and In BetweenPlay: Inspector Graph-ItInvestigate: Data Tells Us About OurselvesBig Idea 2: Thinking Around ShapesVisualize: Get Your Arms Around ItPlay: Shapes on a PlaneInvestigate: Shape and Not a ShapeBig Idea 3: Thinking in Equal GroupsVisualize: Sharing CrackersPlay: Dozens of DiceInvestigate: Playing with PairsBig Idea 4: Tiling to Understand AreaVisualize: Cover UpPlay: A Whole New AlphabetInvestigate: Sharing an AreaBig Idea 5: Seeing Multiplication as AreaVisualize: Rods AroundPlay: Squares and Near-SquaresInvestigate: Connecting Area and PerimeterBig Idea 6: Understanding HalfVisualize: I Spy 1/2Play: Spotting 1/2Investigate: The Many Shapes of 1/2Big Idea 7: Seeing Fractions, Parts, Wholes, and FormsVisualize: Seeing Parts and WholesPlay: Cover, Cut, and SortInvestigate: Taking a Fractional WalkBig Idea 8: Being Flexible with NumbersVisualize: How Many Do You See?Play: How Close to 100?Investigate: Tile and Table PatternsAppendixCentimeter Dot PaperIsometric Dot PaperGrid PaperDot PaperGrid Paper