Download Grade 4 Unit 5 Geometry Mathematics

Grade 4
Unit 5 Geometry
Mathematics
Unit Goals – Stage 1
Number of Days: 29
Traditional: March 13 – April 28, 2017; Track B: March 23 – June 8, 2017
Unit Description: In Unit 5, students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry. Students use their
understanding of equal partitioning and unit measurement to understand angle and turn measure. They apply understanding of shapes to patterns and extend their
previous understanding of number sense to geometric and numeric patterns.
Materials: protractors, fraction circles, student clocks, pattern blocks, base ten blocks (unit cubes) for building tower patterns, polygons, geoboards, dot paper,
AngLegs and Go Math! MathBoard or whiteboard
Standards for Mathematical Practice
Transfer Goals
Students will be able to independently use their learning to…
SMP.1
Make sense of problems and
• Make sense of never-before-seen problems and persevere in solving them.
persevere in solving them.
• Construct viable arguments and critique the reasoning of others.
SMP.2
Reason abstractly and
Making Meaning
quantitatively.
UNDERSTANDINGS
ESSENTIAL QUESTIONS
SMP.3
Construct viable arguments and
Students will understand that…
Students will keep considering…
critique the reasoning of others.
• Patterns are ordered sets of numbers
• Is there a pattern?
SMP.4
Model with mathematics.
or objects that can be repeated.
• Where is geometry found in your everyday world?
SMP.5
Use appropriate tools strategically.
• Geometric figures can be analyzed and • How are symmetrical figures used in artwork?
SMP.6
Attend to precision.
classified based on their properties.
• How can you relate angles and fractional parts of a circle?
SMP.7
Look for and make use of
• A line of symmetry divides a shape into
structure.
two parts that are the same size and
SMP.8
Look for and express regularity in
shape.
repeated reasoning.
Acquisition
KNOWLEDGE
SKILLS
Standards for Mathematical Content
Students will know…
Students will be skilled at and/or be able to…
Clusters Addressed
• The definitions of the academic
• Generate a shape pattern that follows a given rule.
vocabulary words such as acute angle,
• Measure angles in whole-number degrees using a protractor
Operations and Algebraic Thinking
clockwise, counterclockwise, degree (°),
and use a right angle as a benchmark angle.
4.OA.C
Generate and analyze patterns.
dimension, geometric pattern,
• Solve addition and subtraction problems to find unknown
intersecting lines, line, line of symmetry,
angles on a diagram in real world and mathematical problems.
Measurement and Data
line symmetry, obtuse angle,
•
Draw and identify points, lines, line segments, rays, angles
4.MD.C
Geometric measurement:
parallelogram, protractor, perpendicular
(right, acute, obtuse), and perpendicular and parallel lines
understand concepts of angle and
lines, ray, repeating pattern, right angle,
alone and in two-dimensional figures.
measure angles.
right triangle, rule, sequence, straight
• Classify two-dimensional figures based on the presence or
Geometry
angle, term, turn, and vertex.
absence of parallel or perpendicular lines, or the presence or
4.G.A
Draw and identify lines and angles,
•
A
right
angle
can
be
used
to
classify
all
absence of angles of a specified size.
and classify shapes by properties
angles.
•
Recognize and identify right triangles.
of their lines and angles.
• An angle that turns through 1/360 of the • Recognize a line of symmetry for a two-dimensional figure,
circle measures 1 degree.
draw lines of symmetry, and identify line-symmetric figures.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
1
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Assessed Grade Level Standards
Standards for Mathematical Practice
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Standards for Mathematical Content
Operations and Algebraic Thinking
[a] 4.OA.C
Generate and analyze patterns.
4.OA.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For
example, given the rule “Add 3” and the starting number 1 generate terms in the resulting sequence and observe that the terms appear to
alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Use the four operations with
whole numbers to solve problems.
Measurement and Data
[a] 4.MD.C
Geometric measurement: understand concepts of angle and measure angles.
4.MD.5
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle
measurement:
a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular
arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,”
and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.6
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.7
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of
the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical
problems, e.g., by using an equation with a symbol for the unknown angle measure.
Geometry
[a] 4.G.A
4.G.1
4.G.2
4.G.3
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional
figures.
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.
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into
matching parts. Identify line-symmetric figures and draw lines of symmetry.
Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
2
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Evidence of Learning – Stage 2
Assessment Evidence
Unit Assessment
Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in this guide.
[a] 4.OA.C
• The student generates shape patterns.
• The student analyzes a number pattern or shape pattern, showing understanding of the pattern rule and features other than the pattern rule.
[a] 4.MD.C
• The student uses a protractor to measure angles (composed of one-degree angles) and constructs angles to whole-number degrees.
• The student decomposes an angle into smaller non-overlapping parts and adds the measures of these smaller parts to find the measure of the whole
angle.
• The student solves addition and subtraction problems in real world and mathematical contexts using angle measures.
• The student identifies angles of specified measures.
• The student relates the concept of an angle to the number of degrees in a circle.
[a] 4.G.A
• The student identifies and draws points, lines, line segments, rays, and angles both in two-dimensional figures and in isolation.
• The student distinguishes between right, acute, and obtuse angles.
• The student distinguishes between parallel and perpendicular lines.
• The student classifies two-dimensional figures based on presence or absence of parallel/perpendicular line segments.
• The student classifies two-dimensional figures based on the presence or absence of angles of a specified size.
• The student identifies right triangles.
• The student identifies and draws lines of symmetry in line-symmetric figures.
• The student distinguishes line-symmetric figures from line-asymmetric figures. (symmetrical vs. asymmetrical)
For selected content, students will need to…
• Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
• Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
Other Evidence
Formative Assessment Opportunities
• Exit slips
• Opening Tasks
• Quizzes
• Go Math! Show What You Know
• Extension Menus
• Classroom Challenges
• It’s All About the Facts Supplemental materials
• Go Math! Performance Task
• In-class projects
• Homework (Go Math! Standards Practice Book)
• Recorded Teacher Observations
• Go Math! Getting Ready for the Smarter Balance
• Writing activities
• Go Math! Chapter 10, 11 Test (Assessment Guide)
• SBAC Interim Assessment Block (IAB)
• Go Math! Chapter 10, 11 Review / Test – Student Book
• Multiple Markers (Use this for 4.OA.C)
Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
3
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Learning Plan – Stage 3
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Days
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
(Universal Access for SPED, Struggling
Students, ELL, GATE)
Sabré las
operaciones
básicas de
matemáticas al...
•
•
•
Saying facts orally.
Writing Fact Families.
Using them to play games.
•
Puedo usar las
estrategias
matemáticas
mentales al...
•
•
Participating in daily Number Talks.
Communicating my reasoning.
•
90
minutes
per week
(Schools/
grades
with ST
Math)
Perseveraré en la
resolución de
problemas al
ayudarme a
entender las
matemáticas al…
•
•
Developing long term problem solving
skills.
Visualizing math concepts.
Making connections between concepts
and across grades.
Playing interactive games
Before the
Unit
(as
needed)
I can show what I
know about
geometry by…
•
Completing “Show What You Know”.
Daily
Daily
•
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
•
Instructional Tools - Elementary 4th Grade)
Maintaining Fluency Through
Fact Families, pp.1-10, 13-28
Go Math! Strategies and
Practice For Skills and Facts
Fluency
•
Top 10s, 11s, and 12s (Resources
- Games)
Number Talks Strategies and
Problem Sets, Grades 2-5
(also found on intranet in
Instructional Tools)
•
Multiple Marker
ST Math Objectives
• Exploring Lines and Shapes
• Lines of Symmetry
• Parallel Lines and
Parallelograms
• Angles and Triangles
ST Math Tips
• When a students’ screen is
orange use Teacher mode to
intervene.
• Review teacher mode at
trs.stmath.com
•
Ch. 10-11 “Show What You
Know”, pp. 397 & 439
**Use the Diagnostic Table if
needed for intervention options:
On-level, Strategic, Intensive, and
Independent.
4
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Learning Plan – Stage 3
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Days
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
(Universal Access for SPED, Struggling
Students, ELL, GATE)
1
Puedo explorar los
ángulos en el
entorno del mundo
real al…
OPENING TASK – G is for Googol
• Creating a Geometry Alphabet Book.
• Classifying angles.
• Locating the three types of angles.
•
•
•
G is for Googol
Ch. 10-11 “Math Detective”,
pp. 397 & 439
Ch. 10-11 “Vocabulary
Builder”, pp. 398 & 440
Instructional Tools - Elementary 4th Grade)
•
•
•
•
2–3
Puedo describir los
ángulos usando el
vocabulario
geométrico al…
•
•
•
4-6
Puedo explicar
cómo medir un
ángulo al…
•
•
•
•
•
Identifying, drawing and labeling points,
lines, line segments, rays, and angles.
Identifying, drawing, and labeling parallel
and perpendicular lines.
Identifying, drawing and labeling right,
acute and obtuse angles.
•
Placing fraction pieces to create angles
on circles.
Relating degrees to fractional parts of a
circle.
Using hands of a clock to show clockwise
and counterclockwise.
Using circular geoboards to show angles
in terms of degrees and turns.
Finding example of different kinds of
angles in the classroom.
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
5
•
Lessons 10.1: Lines, Rays,
and Angles and 10.4: Parallel
Lines and Perpendicular Lines
(Note: You can skip to the
activity on the second page of
the lessons because the first
page is what the students
complete in their Geometry
Alphabet Book.)
Lesson 11.1: Investigate –
Angles and Fractional Parts of
a Circle
Lesson 11.2: Degrees
•
•
•
•
•
•
•
See
https://www.illustrativemathematic
s.org/4 for tasks to be used
throughout the unit.
Engage, Explore, Evaluate
Problems (to use throughout the
unit)
Notice and Wonder Introduction
and Record Sheet (to use
throughout the unit, Instructional
Tools – Notice and Wonder)
String Geometry (Instructional
Tools - Normbuilding Activities)
Kudos for Geometry
Learning Target Posters
Line Relationships
LBUSD map found under “M” at
www.lbschools.net to identify lines
and angles in context
Time on Your Hands
Clock Angles Power Point
Problem Solving Grades 3 – 5 pp.
110 – 112; Task 6.3 “Categorizing
Letters of the Alphabet”
o Categorizing Letters of the
Alphabet
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Learning Plan – Stage 3
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Days
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
(Universal Access for SPED, Struggling
Students, ELL, GATE)
7–9
Puedo medir y
dibujar los ángulos
al usar mi
transportador al…
•
Using right angles to determine whether
angles are greater than, less than, or
equal to right angles.
•
Using protractors for length measure and
angle measure.
Sketching given angle measures and
check with a protractor.
Exploring benchmark angles of 90 and
180 degrees.
•
•
•
10 - 13
14 - 16
17 - 19
Lesson 11.3 Measure and
Draw Angles
Instructional Tools - Elementary 4th Grade)
•
•
•
Good Questions p. 81 # 5-6, p. 82
#1 & p. 83 #7
What is the Shape?
Problem Solving Grades 3-5 pp.
88-89; Task 5.4 “Rulers and
Protractors”
o Rulers and Protractors
Good Questions p. 83 #5
Puedo determinar
la medida de un
ángulo más grande
al usar las
medidas de un
ángulo más
pequeño al…
Puedo encontrar
los ángulos
desconocidos
usando una
variedad de
estrategias al…
•
•
•
•
•
Decomposing angles.
Adding angle measures.
Exploring angles as additive.
Cutting paper angles into two parts.
Using a protractor.
•
Lesson 11.4: Investigate – Join
and Separate Angles
•
•
•
Finding unknown angle measures.
Using a symbol to stand for the unknown
angle measure.
•
Lesson 11.5: Problem Solving
– Unknown Angle Measures
Ch. 11 Performance Task Klee
Kat pp. AG179 – 183D
•
•
Daily Homework
“For the Win” 3-Acts Lesson
o Three Acts Explained
(Instructional Tools Modeling)
o Three Acts Student Handout
(Instructional Tools Modeling)
Puedo clasificar
los triángulos
basado en líneas y
ángulos al…
•
Sorting triangles by the size of their
angles.
Sorting triangles by the length of their
sides.
•
Lesson 10. 2: Classify
Triangles by Angles
Lesson 10.3: Classify
Triangles by Sides
•
•
Exit Tickets-Triangles
Triangles to Classify
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
6
•
•
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Learning Plan – Stage 3
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Days
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
(Universal Access for SPED, Struggling
Students, ELL, GATE)
20 - 21
Puedo clasificar
los cuadriláteros
basado en líneas y
ángulos al…
•
•
•
Sorting quadrilaterals by the size of their
angles.
Sorting quadrilaterals by the number of
parallel sides.
Communicating my reasoning.
•
•
Lesson 10.5: Classify
Quadrilaterals
Mid-chapter Checkpoint pages
419 - 420
Instructional Tools - Elementary 4th Grade)
•
•
•
•
20 – 23
24 - 25
Puedo identificar
una línea de
simetría en una
figura
bidimensional al…
Puedo usar mi
entendimiento de
los atributos para
analizar las figuras
geométricas al…
•
•
•
•
•
•
•
•
Recognizing lines of symmetry.
Drawing lines of symmetry.
Identifying when a figure is symmetrical
and when it is not.
Using isometric and square dot paper.
FORMATIVE ASSESSMENT LESSON
Classroom Challenge: Tile Designs
The number and types of angles.
The parallel and perpendicular sides.
The lines of symmetry.
Communicating my reasoning.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
7
•
•
Lesson 10.6 Line Symmetry
Lesson 10.7: Find and Draw
Lines of Symmetry
•
•
•
•
•
•
•
•
FAL, Tile Designs (Intranet Assessment)
Chapter 10 Review/Test pp.
433 - 436 (You could assign
one page per night for
homework)
•
•
•
•
•
Problem Solving Grades 3 – 5 pp.
104 – 107; Task 6.1 “Shape
Riddles”
o Shape Riddles
Good Questions p. 80 # 1-4, p. 83
#9 & p. 86 #4
Sorting Shapes Task
Sorting by Attributes
Alphabet Symmetry
Polygons and Their Lines of
Symmetry
Symmetry Drawing
Stained Glass Task
Good Questions page 82 #3
Problem Solving Grades 3-5 pp.
108-110; Task 6.2 “Twin Shapes”
o Twin Shapes
Tile Designs - FAL, Differentiated
Activities
Geometry Classroom Challenge
with Pattern Blocks
Quilt Making Task
Geometry Mix Freeze Match
Tricky Trapezoids
Posted 6/14/16
Grade 4
Unit 5 Geometry
Mathematics
Learning Plan – Stage 3
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Days
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
(Universal Access for SPED, Struggling
Students, ELL, GATE)
26 – 27
Usaré mi
entendimiento de
los patrones al...
•
•
•
•
Identifying the rule to extend a pattern.
Creating a pattern of towers using baseten unit cubes.
Creating a pattern or following a rule to
extend a pattern using pattern blocks.
Communicating my reasoning.
•
Lesson 10.8: Problem Solving
– Shape Patterns
Instructional Tools - Elementary 4th Grade)
•
•
•
•
•
•
Double Plus One Task
Multiples of Nine Task
Pyramid Cup Challenge
(Instructional Tools Normbuilding)
Video Game Display
Squares and Circles Task
What is a Trapezoid? (Part 1)
Task
End of Unit Assessment
28
Ch. 10 Performance Task “Quilting Bee” (Assessment Guide: pages AG174 – AG178D)
29
At this point, all standards addressed in the Grade 4 Interim Assessment Blocks – “Operations and Algebraic Thinking” and “Geometry” have been covered.
These blocks may now be administered.
We would appreciate feedback on the following:
Unit Guide bit.ly/Grade4UnitGuide
Assessment and FAL bit.ly/Grade4Assessment
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
8
Posted 6/14/16