1. Number and operations. Counting with number words -- Thinking addition means "join together" and subtraction means "take away" -- Renaming and regrouping when adding and subtracting two-digit numbers -- Misapplying addition and subtraction strategies to multiplication and division -- Multiplying two-digit factors by two-digit factors -- Understanding the division algorithm -- Understanding fractions -- Adding and subtracting fractions -- Representing, ordering, and adding/subtracting decimals -- 2. Algebra. Understanding patterns -- Meaning of equals -- Identifying functional relationships -- Interpreting variables -- Algebraic representations -- 3. Geometry. Categorizing two-dimensional shapes -- Naming three-dimensional figures -- Navigating coordinate geometry -- Applying reflection -- Solving spatial problems -- 4. Measurement. Reading an analog clock -- Determining the value of coins -- Units versus numbers -- Distinguishing between area and perimeter -- Overgeneralizing base-ten renaming -- 5. Data analysis and probability. Sorting and classifying -- Choosing an appropriate display -- Understanding terms for measures of central tendency -- Analyzing data -- Probability -- 6. Assessing children's mathematical progress. Assessment: the received view -- Assessment from a better angle -- Types of formative assessment -- Why assess? -- Final thoughts.