In Module 1, students explored the relationships of adjacent units on the place value chart to generalize whole number algorithms to decimal fraction operations. In Module 2, students apply the patterns of the base ten system to mental strategies and the multiplication and division algorithms.
Topics A through D provide a sequential study of multiplication (Standards 5.NBT.1, 5.NBT.2, 5.OA.1).
In topic A, students use number disks to model multi-digit multiplication of place value units, e.g., 42 × 10, 42 × 100, 42 × 1,000, leading to problems such as 42 × 30, 42 × 300 and 42 × 3,000 (5.NBT.1, 5.NBT.2, 5.MP.4). In Topic B, place value understanding moves toward understanding the distributive property via area diagrams which are used to generate and record the partial products (5.OA.1, 5.OA.2) of the standard algorithm (5.NBT.5). Topic C moves students from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products (5.NBT.7). In Topic D, students explore multiplication as a method for expressing equivalent measures. For example, they multiply to convert between meters and centimeters and between ounces and cups (5.MD.1).
Topics E through H provide a similar sequence for division. Topic E begins concretely with number disks as an introduction to division with multi-digit whole numbers (5.NBT.6).
In Topic G, students use their understanding to divide decimals by two-digit divisors in a sequence similar to that of Topic F with whole numbers (5.NBT.7). In Topic H, students apply the work of the module to solve multi-step word problems using multi-digit division with unknowns representing either the group size or number of groups.
Topics A through D provide a sequential study of multiplication (Standards 5.NBT.1, 5.NBT.2, 5.OA.1).
In topic A, students use number disks to model multi-digit multiplication of place value units, e.g., 42 × 10, 42 × 100, 42 × 1,000, leading to problems such as 42 × 30, 42 × 300 and 42 × 3,000 (5.NBT.1, 5.NBT.2, 5.MP.4). In Topic B, place value understanding moves toward understanding the distributive property via area diagrams which are used to generate and record the partial products (5.OA.1, 5.OA.2) of the standard algorithm (5.NBT.5). Topic C moves students from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products (5.NBT.7). In Topic D, students explore multiplication as a method for expressing equivalent measures. For example, they multiply to convert between meters and centimeters and between ounces and cups (5.MD.1).
Topics E through H provide a similar sequence for division. Topic E begins concretely with number disks as an introduction to division with multi-digit whole numbers (5.NBT.6).
In Topic G, students use their understanding to divide decimals by two-digit divisors in a sequence similar to that of Topic F with whole numbers (5.NBT.7). In Topic H, students apply the work of the module to solve multi-step word problems using multi-digit division with unknowns representing either the group size or number of groups.