# Factors and Multiples in Number Lines, Equations, and Words

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Common Core Standards
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Factor, multiple, product, dividend, divisor, quotient….. We know that these words related to multiplication and division are key to our students’ understanding of the reversibility of those two operations, and to working fluently with fractions and later with algebra. How to make the relationships explicit?

These pages start with a page of number lines, on which students mark multiples of 2, 3, 4, 5, 6, 8, and 9. The number lines are aligned so common multiples are obvious. The number lines are precisely sized to centimeters, so students can use Cuisenaire Rods to show the multiples, or simply mark the multiples with a marker or colored pencil. Two different sizes of pages are included: one on 17 by 11” paper for those with access to a printer/copier that will accommodate it, and the other on legal paper.

We then proceed to multiplication and division equations and fact families – words, phrases, and concepts that 4th graders are at least familiar with. Students practice identifying the factors and multiples in both types of equations, use those words both in English and number sentences, and relate them to the parts of a division equation: dividend, divisor, and quotient.

Students also learn a systematic procedure for listing factors. They are introduced to common factors and common multiples. And these pages will serve as an ideal jumping-off point to begin work on primes and composites.

Most of this work is for 4th graders, but the beginning pages will be useful and comprehensible to most students in late 3rd grade as well. Many 5th graders will also benefit from this, especially the writing if they cannot use and understand the vocabulary in context.

A detailed, illustrated discussion of the process is included, as is a Smartboard 10 file. The number line pages are in Word 2003 files so they will print accurately.

Common Core Standards:

4.OA.4: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors….”

Subjects: Math, Basic Operations, Mental math

Duration: 11 pages, many problems, 2-4 days if done in sequence

A Smartboard 10 file is also included. Click on the .zip file icon, and you can open the PDF, Word, and Smartboard files separately.
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Teaching Duration
4 days
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