Students explore the volume of three-dimensional shapes, connecting it to the operations of multiplication and addition, as well as classify two-dimensional shapes hierarchically.
In Unit 3, students will explore volume of three-dimensional shapes (5.MD.3—5), connecting it to the operations of multiplication and addition (5.NBT.5, 4.NBT.4). They also use their understanding that they gradually built in prior grade levels to classify shapes in a hierarchy, seeing that attributes of shapes in one category belong to shapes in all subcategories of that category (5.G.3—4).
In prior grade levels, students explored the idea of volume informally, comparing the capacity of various containers as being able to “hold more” or “hold less” (K.MD.2). Students have also explored one-dimensional and two-dimensional measurements of figures, developing a deep understanding of length in Grade 2 and of area in Grade 3. In their exploration of area in Grade 3, students come to understand area as an attribute of plane figures (3.MD.5) and measure it by counting unit squares (3.MD.6), and they connect area to the operations of multiplication and addition (3.MD.7).
Students have also explored two-dimensional shapes and their attributes extensively in previous grades. “From Kindergarten on, students experience all of the properties of shapes that they will study in Grades K–7, recognizing and working with these properties in increasingly sophisticated ways” (Geometry Progression, p. 3). In Kindergarten through Grade 2, students focused on building understanding of shapes and their properties. In Grade 3, students started to conceptualize shape categories, in particular quadrilaterals. In Grade 4, work with angle measure (4.MD.5—7) lent itself to classifying figures based on the presence or absence of parallel and perpendicular sides.
Thus, this unit builds off of students’ well-established understanding of geometry and geometric measurement. Similar to students’ work with area, students develop an understanding of volume as an attribute of solid figures (5.MD.3) and measure it by counting unit cubes (5.MD.4). Students then connect volume to the operation of multiplication of length, width, and height or of the area of the base and the height and to the operation of addition to find composite area (5.MD.5). Throughout Topic A, students have an opportunity to use appropriate tools strategically (MP.5) and make use of structure of three-dimensional figures (MP.7) to draw conclusions about how to find the volume of a figure.
Students then move on to classifying shapes into categories and see that attributes belonging to shapes in one category are shared by all subcategories of that category (5.G.3). This allows students to create a hierarchy of shapes over the course of many days (5.G.4). Throughout this topic, students use appropriate tools strategically (MP.5) to verify various attributes of shapes including their angle measure and presence of parallel or perpendicular lines, as well as attend to precision in their use of language when referring to geometric figures (MP.6). They also look for and make use of structure to construct a hierarchy based on properties (MP.7).
In Grade 6, students will explore concepts of length, area, and volume with more complex figures, such as finding the area of right triangles or finding the volume of right rectangular prisms with non-whole-number measurements (6.G.1, 6.G.2). Students will even rely on their understanding of shapes and their attributes to prove various geometric theorems in high school (GEO.G-CO.9—11). Thus, this unit provides a nice foundation for connections in many grades to come.
Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 5th Grade Scope and Sequence Recommended Adjustments.
?
?
base | rectangular prism |
cubic units | regular polygon |
height | unit cube |
hierarchy | volume |
?
?
This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
5.MD.C.3
5.MD.C.4
Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures.
5.MD.C.4
Find the volume of pictorial three-dimensional figures.
5.MD.C.5
Find the volume of a rectangular prism by thinking about their layers, applying the formula $$v=b\times h$$.
5.MD.C.5
Solve more complex problems involving volume by applying the formula v = b x h.
5.MD.C.5
Find the volume of a rectangular prism by multiplying all of their dimensions, applying the formula $$v= l \times w \times h$$.
5.MD.C.5
Solve more complex problems involving volume by applying the formula $$v=l\times w \times h$$.
5.MD.C.5.C
Understand that volume is additive. Find the volume of composite solid figures when all dimensions are given and their decomposition is already shown.
5.MD.C.5.C
Understand that volume is additive. Find the volume of composite solid figures when not all dimensions are given and/or they must be decomposed.
5.G.B.3
5.G.B.4
Classify shapes as polygons versus non-polygons and classify polygons according to their number of sides.
5.G.B.3
5.G.B.4
Classify quadrilaterals based on the presence or absence of one pair of parallel sides. Define trapezoids as quadrilaterals with at least one pair of parallel sides.
5.G.B.3
5.G.B.4
Classify trapezoids based on the presence of one or two sets of parallel sides. Define parallelograms as trapezoids with two sets of parallel sides.
5.G.B.3
5.G.B.4
Classify parallelograms based on the presence or absence of right angles or based on the presence or absence of sides of equal length. Define rectangles as parallelograms with four right angles and rhombuses as parallelograms with four equal sides.
5.G.B.3
5.G.B.4
Classify rectangles based on the presence or absence of sides of equal length, and classify rhombuses based on the presence or absence of right angles. Define squares as quadrilaterals with sides of equal length and all right angles.
5.G.B.3
5.G.B.4
Classify triangles based on side and angle measures.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?