Teaching Subtraction Using the Concrete, Pictorial, & Abstract Representations from CCSS 2.NBT.7
By Robert van Deusen, PhD
Contents of the packet:
• 13 pages of Teacher’s Guide including a 2-page Table of Contents
• 1 page of Place Value Pieces (Master for Manipulatives—The page contains 24
ones, 24 tens, 24 hundreds and 8 thousands)
• 2 Place Value Mats (One page is the 1,000 and 100 places. The second page is the
10 and 1 places). Each column is 5 inches wide so exactly five of the Place Value Pieces fit left to right. Two rows of 5 pieces show a ten the same way as a Ten Frame represents it.
• 4 overhead or smart board masters (Take Away Model / Place Value Representation, Comparative Model / Place Value Representation, Missing Addend Model / Place Value Representation, Singapore Bar Model Instructional Steps)
• There are 3 word problems for each subtraction model (Take Away, Comparative, and Missing Addend). Each of those 9 problems is shown in three pictorial representations (Place Value, Singapore Bar Model, and Open Number Line). Those 27 problems each have an Answer Key page that can be shown on the overhead or smart board.
• There are 9 student pages (3 word problems per page—3 models—3 representations). There are 3 additional student pages for Open Number Line since I included a version for teachers who want their students to construct their own models and another version for teachers who want to teach students one efficient strategy (based on Hundreds Complements).
• There are 12 student pages with no word problems (just the representational model) so teachers and/or students can create their own problems and use the representational model to solve them.
• There are 3 pages of word problems for the standard algorithm, so students can relate the standard algorithm to each of the representations.
• Each of the nine word problems (3 of each of the 3 subtraction models) is to be solved five times (first—concretely with the Place Value Pieces and the Place Value Mats, second, third and fourth—pictorially once with each of the 3 pictorial representations—Place Value, Singapore Bar Model, and Open Number Line, and fifth, abstractly with the standard algorithm.
• Students who can utilize the language of the models, the manipulatives, the pictorial representations, and the algorithmic procedure will be expert at subtraction.