Strategic Math: Multiplication with Regrouping: Partial Products

Multiplying two-digit numbers can be intimidating, especially if the numbers are large. All that regrouping can be confusing. Which number goes where? And better yet, why?

Help students master multiplication with regrouping using the two latest books from KUCRL: Multiplication With Regrouping: Partial Products and Multiplication with Regrouping: Standard Algorithm.

Based on the concrete – representational – abstract (CRA) teaching sequence from the Strategic Math Series, this manual applies the same procedures to multiplication with regrouping. The Partial Products book shows students how to break numbers into parts, multiply those parts, and then add the partial products to find the final product. . Students not only master multiplication, but come to understand exactly what they are doing and why.

The manual contains 18 lessons with step-by-step instructions for teaching students how to multiply numbers containing two digits (e.g., 36 x 24). The manuals present multiplication problems using simple word problems, emphasizing problem-solving and mathematical thinking as well as computation. Instruction begins with the concrete phase, where students use base ten blocks to solve the multiplication problems. Next, in the representational phase, students use drawings (i.e., squares, lines, and tallies) to solve the multiplication problems. And finally, in the abstract phase, students solve the problems without blocks or drawings. Along the way, students acquire special mnemonics to help them remember the process. Additionally, students obtain practice in solving word problems that involve multiplication, addition, and subtraction.

Researched and written by Margaret Flores and Bradley Kaffar, the manual is available either as an electronic PDF or a spiral-bound printed copy through the KUCRL online store($30 for PDF; $36 for printed copy). Both formats contain progress charts, place value mats, student learning sheets, and ideas for dice games to promote maintenance Dice and blocks not included.   

Resources:

• An Introduction to Multiplication with Regrouping: Partial Products (.pdf), including Students Who Need This Manual, Results of Field Tests, Prerequisite Skills, and the Instructional Sequence
• manual Table of Contents (.pdf)
• Copyright Information (.pdf) outlining information about reproducible sections of the manual
• list of Lesson Materials (.pdf)
• Related Article:
  • Bouck, E. C., Satsangi, R. & Park, J. (2017). The Concrete-Representational-Abstract Approach for students With learning disabilities: An evidence-based practice synthesis.  Remedial and Special Education, 39(4) - Summary: As researchers and practitioners have increasingly become interested in what practices are evidence based and for whom in education, different sets of quality indicators and evidence-based practice standards have emerged in the field of special education. Practices are commonly suggested as evidence based, even without a best evidence synthesis on the existing research, such as the case with the concrete–representational–abstract (CRA) instructional framework to support students with disabilities in mathematics. This study sought to support the classification of the CRA instructional framework as an evidence-based approach for students with learning disabilities by applying quality indicators and standards of evidence-based practice by Cook et al. (2014). Based on the application of the indicators and standards, the CRA instructional framework was determined to be an evidence-based practice for students with learning disabilities who struggle in mathematics relative to computational problems, such as addition, subtraction, and multiplication, largely with regrouping.

More in the Strategic Math Series

An accessible version of the documents on this site will be made available upon request. Please contact the KU CRL Professional Development Research Institute, at simpd@ku.edu to request the document be made available in an accessible format.