Praxis Elem CKT Math cheat sheet

Mathematics Content and Pedagogical Content Knowledge for Elementary Teaching

• Place value: in 4,706, the 7 has value 700; each move left multiplies digit value by 10, each move right divides by 10.

• Algorithms: standard addition/subtraction regroup by 10; multiplication partial products rest on the distributive property, e.g., 23 × 4 = (20 × 4) + (3 × 4).

• Fraction division: a ÷ b means 'how many b's in a'; dividing by a fraction less than 1 yields a quotient larger than the dividend, so 3 ÷ 1/2 = 6.

• Fraction equivalence: multiplying numerator and denominator by the same nonzero number preserves value; 2/3 = 8/12 because both are 8 ÷ 12 in lowest terms.

• Decimal-fraction link: 0.35 = 35/100 = 7/20; comparing decimals requires aligning place values, so 0.5 > 0.45.

• Ratio and proportion: a proportion a/b = c/d holds when ad = bc; unit rate is the amount per one unit, found by dividing.

• Geometry: area of rectangle = length × width; triangle area = ½ × base × height; volume of a right rectangular prism = l × w × h.

• Data: mean = sum ÷ count; median is the middle value of ordered data (average the two middle values for an even count); mode is most frequent.

• Error analysis: classify a child's mistake as procedural (misapplied steps) versus conceptual (flawed underlying idea) before choosing a reteaching strategy.