Celebrating 40 Years of “Mathtown” at Renbrook School

Chris Ladd
Middle school children are full of questions about themselves and the world around them. What career will I have as an adult? How does what I am learning in school help me in the future? Hundreds of vital questions that deserve answers. Middle School students are reaching adulthood and will be moving on to secondary school. In a few years, they will pick a college and declare a major or find a job. Children at any age need to understand why they are learning topics, and at Renbrook, teachers intentionally bring learning to life. A hands-on approach allows students to work at their own pace and tackle challenges appropriately.
In the Mathematics Department, the teachers have long incorporated projects into their program. These projects often show applications to career paths. While textbooks, staffing, and assignments have changed over the years, the core curriculum and philosophy have remained strong. Although teachers have always made sure that students are well-prepared for secondary school, their primary goal has been to help them understand why they are learning math and feel competent in their skills. Small class sizes and close relationships also contribute to building confidence in math.
 
In the early 1980s, Christine Ladd, Mathematics Department Head, joined the Math Department at Renbrook. She worked closely with Tom Donato and Margaret Ayres, the former department chairman, and the idea of building scale model houses to form Mathtown was developed. As part of the ratio and proportion unit, students select a building plan from architectural magazines and then convert measurements using a scale of 4 ft. (in real life) = 1 inch in Mathtown. Each sixth-grade student works on their own house but can have a consultant if another student selected the same design. No more than two students can pick the same architectural blueprint.
 
All students follow the same steps to create their contribution to Mathtown:
  • Students begin by making a house floorplan on graph paper, labeling each room and wall measurement.
  • Following teacher approval, students re-create the floor plan on oaktag, using rulers and triangles.
  • Students then create walls for their structure, using the parameter that each story is ten feet and that the scale remains 4 ft = 1 inch. During this stage, they quickly learn the importance of accurate measuring so that walls fit their floor plans the first time!
  • Incorporating additional math knowledge, students construct peaked walls to hold roofs on the houses. Students must calculate the midpoint of the base on each peaked structure and understand that on a two-story house, the peak may be a three-story height, thus creating pentagonal-shaped pieces for peaked roofs. As the students begin to test whether each wall fits their floorplan, the two-dimensional floor plan comes to life as a three-dimensional house, and the joy in the room is palpable!
  • Next, students convert the doors and windows to scale and draw them on each wall.
  • Now they begin the gluing of the walls, and cheers erupt as houses are now permanent three-dimensional models.
  • To create roofs, students measure up and down peaks to find the width of their rooftops and measure walls for their length.
  • The final stage is to have a lottery for house lots. They display their finished homes on green fabric along black oaktag roads, and they create driveways to connect to the streets.
  • Students may now add optional details, such as small bushes, chimneys, patios, and swimming pools. These final additions are made with natural materials and completed during free time.
The classrooms are busy and sometimes messy, as oaktag lays around desks. Students work on tables or floors so they can spread out. When you listen to the conversations in the room, you hear that "math is so much fun," but you also hear, "I have to measure that again," "I have to use a proportion to figure that out," " This wall must be two stories in this location" or " I have to find 12   of 534 to make that peak." In the end, the question, "Why am I learning this math," is never heard because the students understand how vital it is that they are accurate with fractions, measuring, solving proportions, and geometry. The "why' is practical because the wall doesn't fit the floorplan, or the wall is too short. Teachers celebrate each student's progression with collaboration, spatial reasoning, measuring, problem-solving, and mathematical accuracy. In the end, having the room buzzing with problem-solving discussions and hands-on learning is the crowning achievement for these teachers.
 
Mathtown brings learning to life and lets students understand the "why" behind the "how." A project that started 40 years ago has become a tradition in the sixth grade and almost a rite of passage. This is learning at its best!
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