In Unit 5, students explore concepts of geometry and perimeter. Students have gradually built their understanding of geometric concepts since Kindergarten, when students learned to name shapes regardless of size and orientation and to distinguish between flat and solid shapes. In Grade 1, students’ understanding grew more nuanced, as they learned to distinguish between defining and non-defining attributes, as well as composed and decomposed both flat and solid shapes. In Grade 2, students drew and identified shapes with specific attributes. All of this understanding gets them ready for Grade 3, in which students begin their journey of measuring those attributes, including area (addressed in Unit 4), and perimeter (explored here), as well as classification of shapes into one or more categories based on attributes.
Students begin the unit by building on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of polygons and classify examples into various categories, then explore attributes of quadrilaterals and classify examples into various categories (3.G.1). Students also draw polygons based on their attributes. Students next use tangrams to compose and decompose shapes. In Topic B, students shift to measuring an attribute of these polygons, namely perimeter. They define perimeter as the boundary of a two-dimensional shape and compare the perimeters of various shapes using concrete units. Next, they find the perimeter of polygons whose sides are marked with unit length marks, then labeled with numerals. Then, after finding the perimeter by measuring the length of each side, they find the perimeter when some information about the length of a shape’s side lengths needs to be deduced, such as when a rectangle only has one length and one width labeled. Students then solve real-world and mathematical problems, both given a figure and without one, involving perimeters of polygons (3.MD.8). With this understanding of perimeter, they are able to compare the measurement of area and perimeter of a rectangle in Topic C, seeing that a rectangle with a certain area can have a variety of perimeters and, conversely, a rectangle with a certain perimeter can have a variety of areas, connecting the additional cluster content of perimeter to the major cluster content of area. Students then solve various problems involving area and perimeter.
In this unit, students reason abstractly and quantitatively, translating back and forth between figures and equations in the context of perimeter problems (MP.2). Students will also construct viable arguments and critique the reasoning of others as they develop a nuanced understanding of the difference between area and perimeter, as well as when they classify shapes according to their attributes and justify their rationale (MP.3). Lastly, students will use appropriate tools strategically by using rulers to measure the side lengths of polygons to find their perimeter, as well as using rulers and right-angle tools to determine what attributes shapes have to determine their classification (MP.5).
Students will further deepen their understanding of these ideas in future grade levels. In Grade 4, students solve more complex word problems involving area and perimeter (4.MD.3), as well as classify shapes based on the presence of parallel and perpendicular shapes (4.G.2), which is very connected to their study of angles (4.MD.5—7). The beginning work on categorization in Grade 3 culminates in Grade 5, where students have a complete picture of the hierarchical nature of classifying shapes (5.G.3). In the middle grades and high school, increasingly complex problems rely on students’ deep understanding of attributes of shapes and how to measure them, threaded throughout this unit.
Pacing: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)