Curriculum / Math / 5th Grade / Unit 3: Shapes and Volume / Lesson 12
Math
Unit 3
5th Grade
Lesson 12 of 16
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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.
The core standards covered in this lesson
5.G.B.3 — Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.B.4 — Classify two-dimensional figures in a hierarchy based on properties.
The foundational standards covered in this lesson
4.G.A.2 — Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
“In the U.S., that the term ‘trapezoid’ may have two different meanings. In their study The Classification of Quadrilaterals (Information Age Publishing, 2008), Usiskin et al. call these the exclusive and inclusive definitions:
These different meanings result in different classifications at the analytic level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. Both definitions are legitimate. However, Usiskin et al. conclude, ‘The preponderance of advantages to the inclusive definition of trapezoid has caused all the articles we could find on the subject, and most college-bound geometry books, to favor the inclusive definition.’” (Geometry Progression, p. 3). Thus, the inclusive definition is used below and throughout the curriculum.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Someone sorted some shapes as shown below.
a. What is similar about the two groups of figures? What term(s) can we use to describe all of the shapes?
b. What is different about the two groups of shapes?
Grade 5, Unit 8, Unit Plan (2016-2017) is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed Feb. 6, 2018, 12:55 p.m..
Decide whether each of the following statements are true or false. If it is false, rewrite the statement so that it is true.
a. A trapezoid is always a quadrilateral.
b. A quadrilateral is never a trapezoid.
Always, Sometimes, Never, accessed on March 8, 2017, 11:39 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Progressions for the Common Core State Standards in Mathematics (Geometry, K-6), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed May 17, 2018, 4:49 p.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.
Problem Set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
What attributes do quadrilaterals and trapezoids share?
What attributes do trapezoids have that not all quadrilaterals have?
An example response to the Target Task at the level of detail expected of the students.
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
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Lesson 11
Lesson 13
Topic A: Volume of Three-Dimensional Figures
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.3 5.MD.C.4
Find the volume of pictorial three-dimensional figures.
5.MD.C.4
Find the volume of a right rectangular prism by thinking about its layers.
5.MD.C.5
Find the volume of a right rectangular prism using its side lengths.
Represent volume using expressions related to the formulas $$V = b \times h $$ and $$V = l \times w \times h$$. Use these formulas to find the volume of pictorial rectangular prisms.
Understand standard units for measuring volume, including cubic inches, cubic centimeters, cubic feet, and cubic meters. Solve real-world and mathematical problems involving these various units.
5.MD.C.4 5.MD.C.5.B
Solve more complex real-world and mathematical problems involving volume.
Solve a three-act task involving volume.
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.
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Topic B: Classification of Two-Dimensional Shapes
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 trapezoids based on the presence of one or two sets of parallel sides. Define parallelograms as trapezoids with two sets of parallel sides.
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.
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.
Classify triangles based on side and angle measures.
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