One of the strongest components of the Bridges in Mathematics curriculum, is how each concept is built upon and extended from, one grade level to the next. The ideas are presented conceptually, using models and objects, in a real-world context in the beginning years. In each grade that follows, models are still used, but the type of model becomes more sophisticated to represent the ideas for that grade level. In addition, they move to a more symbolic representation for the mathematical concept. Summit Elementary School students show how geometric concepts can be introduced in 4K and built upon all the way through fourth grade, to deepen understanding of shapes, their attributes, and how this relates to the concepts of area and perimeter.
In the early grades, students have hands-on experience with a variety of shapes. 4/5K students work with both two and three-dimensional shapes and notice their properties, or “attributes.” They learn vocabulary that can define various shapes as they describe and compare them. Real shapes as well as pattern blocks are used by the students. In first grade, students expand on these concepts as they visualize and build three-dimensional shapes by linking the two-dimensional sides together. These can be built using “nets,” a geometric tool that consists of plastic flat shapes that can be linked together to form a three-dimensional shape.
In second grade, students continue investigating the attributes of shapes, but the use of geoboards, boards with pegs to stretch rubber bands into shapes, as a mathematical tool helps them add the concept of area to their study of shapes. Vocabulary is also extended to include more precise terms and ideas. In third grade, students demonstrate their understanding of the attributes of shapes with an in-depth analysis of quadrilaterals. Students select a specific quadrilateral and create a “riddle book” for other students to read and solve, based on the attributes that match their shape.
In fourth grade, students apply both their understanding of the attributes of shapes and the meaning of area and perimeter by constructing shapes with a given area and/or perimeter. In addition to the shapes, dimensions and equations would be a part of their work and explanation. Their choice of tools depends on their level of understanding – some may be able to create a labeled diagram on their own, while others may use grid paper. Other students may need more opportunities to manipulate their shapes to figure out their answers, in which case square color tile pieces or geoboards may also be used.
This continuity across grade levels for all of the mathematical concepts introduced in Bridges, allows students to connect the ideas being presented to something they have already learned. Students internalize the math concepts with this approach, as opposed to just memorizing them, which is a key to their mathematical success!
Summit Elementary Students and staff who presented “Bridges in Mathematics: Geometry through the Grade Levels at Summit Elementary” at the Oconomowoc Area School District Board of Education Meeting on Tuesday, April 17, 2018.
Pictured left to right:
Back row: Brian Stuckey, Summit Elementary School Principal
Middle row: Jessica Koski, Summit Elementary 4th Grade Teacher, Alex Seraphine, Evalyn Weber (in back), Krystin Dieringer, Summit Elementary 3rd Grade Teacher, Anne Seraphine, Summit Elementary 4K Teacher
Front row: Brianna Brown, Michelle Ganser, Summit Elementary 2nd Grade Teacher, Colin Freeman, Mallory Beard, Asher Bencivenga, Greyson Collins
Summit Teacher, Anne Seraphine, along with Summit students, Greyson Collins and Asher Bencivenga, present at the OASD Board of Education meeting on April 17, 2018.
Summit Teacher, Michelle Ganser, along with Summit students Brianna Brown and Colin Freeman, present at the OASD Board of Education meeting on April 17, 2018.