Number Line Rectangles: Teaching Primes to Elementary School Students
Rika Yatchak
San Francisco State University
Jan. 28 2012
Learning Objectives
Lesson Plan
Mathematical Background
• Geared towards students in the younger elementary age
group (1st-3rd grade).
• Show students a geometric justification for multiplication:
the area of rectangles made up from unit squares.
• Introduce the idea of the prime number to students by
using the concept of area.
• Students will learn to associate numbers that can only
make one unique rectangle with primes.
• Also introduces the idea of square numbers: which
numbers can be represented using a square rectangle?
These are precisely the square numbers 1, 4, 9, ....
1. Review rectangles with students.
A few definitions:
• A prime is a number divisible only by itself or 1. Examples:
2,3,5,7,11,13,...
• A square is a number that can be expressed as the square of another
number. For example, 121 is a square since 112 = 121.
• Understanding of prime and square numbers is an essential part of
elementary math education.
Illustration of primes using number line rectangles
• Squares are special rectangles!
2. Introduce the unit square object. If you like, call them building blocks.
3. (Re)introduce area.
• For students who have seen area: reintroduce the concept, and explain how unit squares fit into the definition
they have already seen for area.
• For students who have not seen area: Explain that for today, area will mean counting the number of unit squares
a rectangle contains.
• For both of these area introductions, it is vital that the teacher illustrate a few examples using the board, a
projector, props, etc.
4. Discuss symmetry.
• For the purposes of this lesson, a 1x7 and 7x1 rectangle are considered the same.
5. Using the worksheet, students will create as many rectangles as they can of each given area
using unit squares that are provided.
• Students can work in groups or individually, as is desired.
After creating as many rectangles as they can think of of any given area up to 12, the
worksheet will ask students some questions about what they’ve found.
6. Group Discussion: After completing their worksheets, students will be eager to discuss their
results.
• A prime number only has one rectangle.
• A square number can be represented using a square.
Materials Required
• Worksheets or grid paper.
• Unit squares (paper or plastic)
• Pencils and markers
• Glue
Acknowledgements
The number line rectangles up to 7
• This work was supported by San Francisco State University’s (CM)2 program, a branch of the
NSF GK-12 program (Grant DGE-0841164)
• This lesson was developed in partnership with Marilyn Ong of George Washington Carver
Elementary in San Francisco, CA.
• I’d also like to thank my partner teacher Robert Pablo, an algebra instructor at Thurgood
Marshall Academic High School and my advisor Federico Ardila.
This is not a rectangle
References
Stenmark, Thompson, and Cossey. ”Number Line Rectangles.” Family
Math. Place Published: Publisher, Year. Page range.