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Module 3
Using Place Value Understanding and Properties of Operations
to Perform Multi-Digit Multiplication and Division


Throughout this module students will:
  • use place-value understanding and visual representations to solve multiplication and division problems with multi-digit numbers
  • investigate the formulas for area and perimeter
  • solve comparison problems including the language of times as much with a focus on problems using area and perimeter as a context
  • multiply single-digit numbers by multiples of 10, 100, and 1,000 and two-digit multiples of 10 by two-digit multiples of 10
  • use the partial products method, the standard algorithm, and the area model to compare and connect the distributive property
  • solve multi-step word problems and multiplicative comparison problems using a combination of addition, substraction, and multiplication
  • focus on understanding remainders
  • explore factors, multiples, and prime and composite numbers within 100 to gain valuable insights into patterns of divisibility
  • practice using the standard algorithm to record long division, including solving word problems and making connections to the area model


Terminology Definition Illustration
Associative Property
of Multiplication
Changing the groupings of three or more factors does not change the product.
Composite Number A number greater than 0 having three or more whole number factors.
Distributive Property When one of the factors of a product is a sum, multiplying each addend before adding does not change the product.  
Divisor The number by which another number is divided.
Partial Product A method of multiplying in which the value of each digit in a factor is multiplied separately, and then the partial products are added together.  
Prime Number  A positive integer only having whole factors of one and itself.
Remainder The number leftover when one integer is divided by another.
Algorithm A step-by-step method for computing.
Area The measure, in square units, of the inside of a plane figure.
Area Model A model of multiplication that shows each place value product.
Equation A mathematical sentence with an equal sign.  The amount on one side of the equal sign has the same value as the amount on the other side.
Factor The whole numbers that are multiplied to get a product.
Product The answer to a multiplication problem.
Quotient The answer to a division problem.


Additional Resources

area model from JD K-4 Math on Vimeo.


partial products from JD K-4 Math on Vimeo.


Fourth grade Division Basics from JD K-4 Math on Vimeo.

Fourth grade Division part 2 from JD K-4 Math on Vimeo.

Fourth grade Division part 3 from JD K-4 Math on Vimeo.



Dr. Peter Smith, Superintendent

P.O. Box 606
DeWitt, NY 13214

Phone: (315) 445-8300

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