TWO-DIGIT MULTIPLICATION, PART TWO—USING NEGATIVE UNITS

Prerequisites:

Students decompose one or both of the factors of two-digit multiplication problems into subtraction expressions with tens and ones. For example, students might decompose 27 × 39 as (30 – 3) × (40 – 1). Students represent this approach geometrically with an array of base-ten blocks. Unlike physical base-ten blocks, which are awkward at best for representing negative areas, the blocks used in the Sketchpad model allow for a clear, intuitive representation of negative area.

OBJECTIVES
• Students will find products of two-digit numbers by decomposing each number into tens and ones, rewriting one or both numbers as subtraction statements.
• Students will use a rectangular array model composed of base-ten blocks to explore two-digit multiplication problems.
• Students will understand the relationship between a multiplication problem represented in numerical form and the same problem represented with an array.

COMMON CORE CONNECTIONS
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure. 