Download Topic 16 - Milwaukee Public Schools

Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16
Standards for Mathematical Practice
Critical Area(s): Attributes of Two- and Three-Dimensional Objects
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
FOCUS for Grade 5
Supporting Work
20% of Time
5.MD.A.1
5.MD.B.2
Major Work
Additional Work
70% of time
10% of Time
5.NBT.A.1-2-3-4
5.OA.A.1-2
5.NBT.B.5-6-7
5.OA.B.3
5.NF.A.1-2
5.G.1-2
5.NF.B.3-4-5-6-7
5.G.B.3-4
5.MD.C.3-4-5
Required Fluency Standard: 5.NBT.B.5
Standards in bold are specifically targeted within instructional materials.
Domains:
Geometry
Clusters:
Clusters outlined in bold should drive the learning for this period of instruction.
5.G.B Classify two-dimensional figures into categories based on their properties.
Standards:
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.
Revised 3/2017
Property of MPS
Page 1 of 6
Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16
Foundational Learning
4.MD.C
4.G.A
5.G.A
Future Learning
6.G.A.1
6.G.A.4
Key Student Understandings


Assessments
Students understand that two-dimensional objects can be described, classified, and analyzed based on
various attributes.
Students understand that two-dimensional objects can be classified by more than one attribute, e.g.,
triangles can be classified by their sides and by their angles.

Formative Assessment Strategies

Evidence for Standards-Based Grading
Common Misconceptions/Challenges
5.G.B Classify two-dimensional figures into categories based on their properties.
 Students think that when describing geometric figures and placing them in subcategories that the last category is the only classification that can be used.
Students need opportunities to develop an understanding that figures can be classified into more than one category (e.g., a square is a special type of
rectangle).
Instructional Practices
Domain: 5.G
Cluster: 5.G.B Classify two-dimensional figures into categories based on their properties.
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.

This standard calls for students to reason about the attributes (properties) of shapes. Student should have experiences discussing the property of shapes
and reasoning. Geometric properties include properties of sides (parallel, perpendicular, congruent), properties of angles (type, measurement,
congruent), and properties of symmetry (point and line).

Possible questions to pose and discuss with students: Examples:
o Examine whether all quadrilaterals have right angles. Give examples and non-examples.
o True or False? If the opposite sides on a parallelogram are parallel and congruent, then rectangles are parallelograms.
o A parallelogram has 4 sides with both sets of opposite sides parallel. What types of quadrilaterals are parallelograms?
o Regular polygons have all of their sides and angles congruent. Name or draw some regular polygons.
o All rectangles have 4 right angles. Squares have 4 right angles so they are also rectangles. True or False?
o A trapezoid has 2 sides parallel so it must be a parallelogram. True or False?
Revised 3/2017
Property of MPS
Page 2 of 6
Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16

The notion of congruence (“same size and same shape”) may be part of classroom conversation but the concepts of congruence and similarity do not
appear until middle school.

In the U.S., the term “trapezoid” may have two different meanings; research identifies these as inclusive and exclusive definitions. (Progressions for the
CCSSM: Geometry, The Common Core Standards Writing Team, June 2012.)
o
The inclusive definition states: A trapezoid is a quadrilateral with at least one pair of parallel sides.
o
The exclusive definition states: A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Revised 3/2017
Property of MPS
Page 3 of 6
Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16
5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties.

This standard builds on what was done in Grade 4. Figures from previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral,
pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, kite. [A kite is a quadrilateral whose four sides can be grouped into two pairs of equallength sides that are beside (adjacent to) each other.]

Properties of figure may include:
o Properties of sides—parallel, perpendicular, congruent, number of sides
o Properties of angles—types of angles, congruent

Triangles can be classified by:
o Angles
 Right: The triangle has one angle that measures 90º.
 Acute: The triangle has exactly three angles that measure between 0º and 90º.
 Obtuse: The triangle has exactly one angle that measures greater than 90º less than 180º.
o
o

Sides



Equilateral: All sides of the triangle are the same length.
Isosceles: At least two sides of the triangle are the same length.
Scalene: No sides of the triangle are the same length.
Examples:
 A right triangle can be both scalene and isosceles, but not equilateral.
 A scalene triangle can be right, acute and obtuse.
Have students create a shape hierarchy tree:
o Example 1:
Revised 3/2017
Property of MPS
Page 4 of 6
Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16

o
Example 2: Create a Hierarchy Diagram using the given terms.
o
Example 3:
Students should be able to reason about the attributes of shapes by examining: What are ways to classify triangles? Why can’t trapezoids and kites be
classified as parallelograms? Which quadrilaterals have opposite angles congruent and why is this true of certain quadrilaterals? and How many lines of
symmetry does a regular polygon have?
Revised 3/2017
Property of MPS
Page 5 of 6
Mathematics 2016-17—Grade 5
Week 35—May
enVisionmath2.0—Topic 16
Differentiation
5.G.B Classify two-dimensional figures into categories based on their properties.
 Have students work in same-ability level partner teams to sort shapes by properties. Struggling students should be
given only one attribute to sort on, while students with greater depth of understanding should be given more
attributes to sort at the same time.
The Common Core Approach to Differentiating Instruction (engageny How to Implement a Story of Units, p. 14-20)
Linked document includes scaffolds for English Language Learners, Students with Disabilities, Below Level Students, and
Above Level Students.
Literacy Connections

Academic Vocabulary Terms

Vocabulary Strategies

Literacy Strategies
Resources
enVisionmath2.0
Developing Fluency
Multiplication Fact Thinking Strategies
Topic 16 Pacing Guide
Grade 5 Games to Build Fluency
Revised 3/2017
Property of MPS
Page 6 of 6