Math Matters

Playing with Area and Perimeter

Visualizing Area

You might know that as a teacher, I try to make math hands-on and concrete for students to help increase depth of understanding. I think the more we can build in multiple sensory experiences, the quicker students can get to mastery. This might be because when we engage more than one learning style, and we build the bridges for students from concrete, to pictorial, to abstract, they have the links in the brain needed to ensure successful application of that concept later.

In my career I mostly taught secondary students (6th and up) and worked only with elementary teachers in curriculum support. But I do know that early in elementary school we start helping students build geometric reasoning by first understanding properties of basic shapes, and then applying measurement to those shapes such as perimeter and area. The area formulas can often get abstract for students quickly if we don't take the time to help them visualize how area develops using unit squares and ways to break a shape into spaces that can be filled using these unit squares.

The focus of this newsletter is to provide some ideas on how to make area finding, and formulas, more visually evident for students using manipulatives and engaging students in math made fun. And be sure to check out some of the area and perimeter Math Cut Ups pre-made activities for your grade level on my website at

A Few Teaching Thoughts

  • Start with the concrete, no matter what level students are in, including high school.
  • Allocate time for physical to pictorial modeling. This is an important step to getting students to form images in their mind when the models are gone.
  • Include connections to the procedures behind the formulas for the area. If we don’t show and talk about the connections, students may not make them. For example, visually showing how the triangle is 1/2 of a square or rectangle.
  • Link the pictorial to the abstract mathematics going on behind the scenes, such as how the trapezoid formula is based on an average length base.

Ways to extend to upper grades

Expand upon area & perimeter in middle school to composite shapes.

Use my pre-made shapes (see links to templates), pattern blocks or tangrams to have fun building the shapes. Students can use rulers (practice in cm and in) to measure side lengths of each smaller shape and make a legend. Then they can build their own composite shape pictures and find the total area and perimeter of those. What ownership they have! And building the composite figures helps students better visualize how to break a larger composite into smaller familiar shapes when they need to. Assess this by providing the outline of a composite shape picture with some measurements provided so they can divide up the outline and solve for area. Scaffold struggling students by letting them use the basic block shapes to fit inside the outline.

Thank you!

I appreciate that you took the time to do some hands on math with me today. Be sure to check out other newsletters and my pre-made Math Cut Ups activities at And reach out anytime!

Kelli D. Mallory, Ed.D.

Math Cut Ups by Integral Mathematics

I offer ready-to-use, pre-printed math activities as well as Professional Learning. Contact me for details and questions.