Getting Creative and Going Concrete with My Math Instruction

By Matthew Macca

Happy Teacher Appreciation Week! While we work to showcase the work of current practitioners all school year, this week offers us a special opportunity to feature teachers who are working to provide inclusive education for their students. A special thank you to our guest blogger Matthew Macca, a 6th-8th Grade Math Learning Specialist at Explore Upper Charter School, for highlighting some ways in which he makes his math instruction more accessible.

Teachers invest in responsive practices and data-driven lessons in order to build classrooms that meet their students’ needs, encourage growth, and foster respect for their opinions. However, there’s one pervasive student opinion that teachers cannot escape: Kids Hate Math. Many find it confusing, boring, confusing, tedious, confusing…and repetitive. For some, it’s easier to relinquish the idea of understanding math and aim instead to just “get it right.” How can we combat this overwhelming hatred and stress towards such an important subject?

As adults, we often forget that the most symbolic (and complex) version of a number is its written form. For example, seeing the symbol “3” is the most abstract version of the number “three.” Seeing three fingers, three dots on dice, or three pencils on a case all represent the number “three” more clearly than the symbol “3.” Once students memorize the symbols for each number in elementary school, we stop using concrete objects to represent symbolic ideas. If we begin to physically enact problems and creatively represent numbers, our middle school students may start, dare I say, LIKING math. Or at the very least, they won’t fear math anymore!

Below are three examples of creative and physicalized math I’ve used this year for 6th, 7th, and 8th graders. I cannot take credit for all of these ideas as many were created by others or built with a co-teacher. However, in enacting these lessons, I’ve seen student joy and understanding increase exponentially and hope my sharing will help create similar experiences for your students.

Students engaging with a large, interactive coordinate plane on the hallway floor, with one student crouching to touch the grid and another observing with papers in hand.

6th Grade – Giant Coordinate Plane

Creating a giant coordinate plane is by far the most involved and time-consuming idea n this list–as well as the most rewarding and beneficial. On a giant coordinate plane, 6th graders could walk to count the spaces between given points and physically see the absolute distance between points in different quadrants. My 8th graders also enjoyed using it to perform rigid transformations. Though this takes time to assemble and take apart, it only requires painters tape (about 4 rolls) and notecards to make! Additionally, students were amazed at the sheer size.

A white surface with groups of colored scribbles and corresponding handwritten counts in black ink: four orange and two purple stripes, and one blue stripe, with the counts ‘Orange = 4 or 2’, ‘Purple = 3’, and ‘Blue = 1’.

7th Grade – Enacting Probability

Probability incorporates two of the most hated aspects of math: word problems and fractions. However, probability word problems easily lend themselves to in class reenactments. If a problem asks for the chances of pulling a red jellybean out of a bag with 3 red and 4 green jelly beans, teachers can make this bag and act out the problem. In order to keep problems clear, it’s best to use large objects (replace jelly beans with colored notecards or larger stress balls) and use a clear bag so students can see every object. Sometimes, ditching the bag and placing all the objects on the whiteboard works best. Making multiple class sets allows students to practice on their own and check if their answers are reasonable.

A hand-drawn diagram on paper with two parallel lines AB and CD intersected by a transversal line, forming alternate interior angles. The angles on one side of the transversal are colored orange and labeled as 50°, and the angles on the opposite side are colored purple and labeled as 130°. The text ‘Orange=50°’ and ‘Purple=130°’ is written at the top left corner.

8th Grade – Coloring Angle Relationships

With colored pencils and crayons, students can visualize which angles in a figure made of two parallel lines cut by a transversal are equivalent. The colors help students visualize and remember these relationships better than simply labeling with degree sizes. Additionally, many 8th graders enjoy coloring and will love showing their thinking through colored pencils instead of numbers.

No matter the grade, it’s important to keep school accessible and fun. If we take time to make math less symbolic and more concrete, students will find a deeper understanding and find joy in their education.

About Matthew:

Matthew Macca is a 6th-8th Grade Math Learning Specialist at Explore Upper Charter School in Brooklyn. He’s previously taught Reading and Social Studies to 3rd-5th Grade students and is currently pursuing a degree in 1st-6th grade Special Education.