NCDPI – AIG Instructional Resource: Background Information
Resource Title:
The Multiplication Trick
Subject Area/Grade Level (s):
Time Frame: 1 class period/possibly extended to homework
Math/5
Common Core Standard Addressed:
Number & Operations in Base Ten
Perform operations with multi-digit whole numbers and decimals to hundredths.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
Mathematical Practice
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
6. Attend to precision.
7. Look for and make use of structure.
Additional Standards Addressed: NA
Brief Description of Lesson/Task/Activity: Students are asked to analyze a new method or “trick” for multi-digit multiplication. The method is based on a
combination of decomposing numbers, functions, and the distributive property of multiplication over addition (in which the standard algorithm is based).
Type of Differentiation for AIGs (include all that apply):
Enrichment
Adaptations for AIGs:
Product
x Content
Process
x Extension
Acceleration
Explanation of How Resource is Appropriate for AIGs: This task is appropriate for students demonstrating an understanding of the standard
algorithm and those who are able to compute using the algorithm with ease. The task requires that students consider and analyze the thinking
of another student (presented in the task) before determining the validity of the student’s strategy for multiplying.
Needed Resources/Materials: Task Sheet
Sources : NA
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
TEACHER NOTES: NA
NCDPI AIG Curriculum Resource Outline
STAGE ONE: ENGAGE
The teacher should introduce the task by having students read the situation regarding Charlotte and her new method for multiplication. Although
an example problem is provided, students may need clarification on vocabulary or reproducing the steps for another problem. The students or the
teacher should identify another problem to work on using Charlotte’s method in order to make sure all students understand the steps.
STAGE TWO: ELABORATE
After reviewing the steps in Charlotte’s strategy and checking its accuracy using other methods, such as the standard algorithm, discussion
should ensue about the idea of proving that a method is valid or invalid. Students should consider the following questions…
1. What types of multiplication problems will Charlotte’s method work on?
2. How will you know if her strategy works on all multiplication situations?
Students should share their ideas about how they can determine if a method works for all situations and provide adequate proof to show that a
method works always, for certain cases, or never. Once the group agrees on the criteria for proving or disproving the validity of the method
presented in the task, students should begin working (independently or in small groups) through example problems using Charlotte’s strategy.
The teacher should monitor progress, asking probing questions (provided below) and providing feedback when needed. Students should
answer all questions posed in the task, allowing viable arguments to be constructed regarding the validity of Charlotte’s method. (Mathematical
Practice-3. Construct viable arguments and critique the reasoning of others.) Students should be encouraged to form an idea about how/why
the method works. (Mathematical Practice - 7. Look for and make use of structure.)
STAGE THREE: EVALUATE
The group should discuss the following questions…
 When does Charlotte’s method work? What types of numbers does it work for?
 Why does Charlotte’s method work?
 How does Charlotte’s method relate to the standard algorithm for multi-digit multiplication?
 How efficient is Charlotte’s method? Explain your thinking.
Students should be able to explain what is happening in each step of Charlotte’s strategy. The teacher should encourage the use of
mathematical language. Students should name the property at work whenever possible. Students should not be expected to prove what types
of numbers the strategy works for algebraically. Rather discussion should ensue regarding examples and non-examples at this grade level.
TEACHER NOTES: NA
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project