Grade 5
Unit 2 Addition and Subtraction of Fractions
Mathematics
Unit Goals – Stage 1
Number of Days: 23
Traditional: October 20 – November 29, 2016 Track B: October 20 – November 29, 2016
Unit Description: In Unit 2 students’ understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence. They
reason about the size of fractions to make sense of their answers. The new complexity is that if units are not equivalent, they must be changed for smaller
equal units so that they can be added or subtracted. Fraction bar models, which students began using in third grade, become increasingly useful as
students apply them to form units to solve word problems.
Materials: “Multiple Markers” for class number line, paper strips, customary rulers, fraction strips/bars, number lines, graph paper, pattern blocks, color
tiles, GoMath! MathBoard or whiteboard
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
Clusters Addressed
Number and Operations - Fractions
5.NF.A
Use equivalent fractions as a strategy
to add and subtract fractions.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
Transfer Goals
Students will be able to independently use their learning to…
• Make sense of never-before-seen problems and persevere in solving them.
• Construct viable arguments and critique the reasoning of others.
Making Meaning
UNDERSTANDINGS
ESSENTIAL QUESTIONS
Students will understand that…
Students will keep considering…
• Addition and subtraction of fractions with
• How does equivalence help us solve
different denominators (including mixed
problems?
numbers) are based on understanding
• When and why should we estimate?
equivalent fractions.
• Benchmark fractions help you make
reasonable estimates.
Acquisition
KNOWLEDGE
SKILLS
Students will know…
Students will be skilled at and/or be able to…
• The definitions of the academic vocabulary
• Add and subtract fractions with unlike
words such as benchmark fractions, common
denominators (including mixed numbers) as
denominators, equivalent fractions, mixed
equivalent calculations with like
numbers, and unlike denominators.
denominators.
• Solve word problems involving addition and
subtraction of fractions using visual fraction
models or equations.
• Use benchmark fractions and number sense
of fractions to estimate mentally and assess
the reasonableness of answers.
1
Posted 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
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
Number and Operations - Fractions
[m]
5.NF.A
5.NF.1
5.NF.2
Use equivalent fractions as a strategy to add and subtract fractions.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in
such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 =
23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing
that 3/7 < 1/2.
Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
2
Posted 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
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.
[m] 5.NF.A
• The student adds or subtracts fractions with unlike denominators (including mixed numbers) by using visual fraction models or equations to
represent the problem.
• The student identifies and explains the use of equivalent fractions when adding or subtracting fractions with unlike denominators (including mixed
numbers).
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
• Opening Tasks
• Go Math! Show What You Know
• Classroom Challenges
• Go Math! Performance Task
• Homework (Go Math! Standards Practice Book)
• Go Math! Getting Ready for the Smarter Balance
• Go Math! Chapter Test (Assessment Guide)
• Go Math! Chapter Review / Test – Student Book
•
•
•
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•
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Exit slips
Extension Menus
It’s All About the Facts Supplemental materials
In-class projects
Recorded Teacher Observations
Writing activities
Quizzes
SBAC Interim Assessment Block (IAB)
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 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet Instructional Tools – Elementary – 5th Grade)
(Universal Access for SPED, Struggling
Students, ELL, GATE)
Daily
Aprenderé a
resolver las
operaciones
básicas de
matemáticas …
•
•
•
•
•
Saying facts orally.
Writing Fact Families.
Using the Properties of Addition and
Multiplication.
Using them to play games.
•
•
Daily
90
minutes
per week
(Schools/
grades
with ST
Math)
Before
the Unit
(as
needed)
Utilizaré las
estrategias de
matemáticas
mental para
sumar, restar,
multiplicar y
dividir …
•
•
Perseveraré en la
resolución de
problemas
mientras juego
juegos
interactivos para
ayudarme a
entender las
matemáticas …
I can show what I
know about
adding and
subtracting
fractions by…
•
•
Number Talks Strategies and
Problem Sets, Grades 2-5
(also found on intranet in
Instructional Tools)
•
•
Developing long term problem
solving skills.
Visualizing math concepts.
Making connections between
concepts and across grades.
Playing interactive games.
ST Math Objectives
• Fraction and Decimal
Concepts
• Fractions on the Number Line
• Unlike Denominator Concepts
and Strategies
• Unlike Denominator Addition
and Subtraction
•
Completing “Show What You Know”.
•
•
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
•
Participating in daily Number Talks.
Communicating my reasoning.
Maintaining Fluency Through
Fact Families, pp. 1 –10, 13 –
28
Review Properties of Addition
and Multiplication, Lesson 1.3
pp. 13 – 16
Go Math! Strategies and
Practice for Skills and Facts
Fluency
•
•
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•
•
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•
“Fluency Builder,” Go Math! Ch. 6
p. 265B. You can vary the
products on multiple days.
Top 10s, 11s, 12s (Instructional
Tools - Resources - Games)
Basic Facts Game: “Get to
Zero”
https://www.youcubed.org/task/
get-to-zero/
Fraction Number Talks
(Instructional Tools – Elementary
– Number Talks)
Calendar Math (from Unit 1)
Multiple Markers for 100 Days
(from Unit 1)
Assign a minimum of five
homework objectives.
Review facilitation prompts and
processes to help struggling
students.
District will handle all student
rostering.
Ch. 6 “Show What You
Know”, p. 251
**Use the Diagnostic Table if
needed for intervention options:
On-level, Strategic, Intensive, and
Independent.
4
Posted 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
(Universal Access for SPED, Struggling
Students, ELL, GATE)
1
Determinaré si la
parte fraccionaria
es menor que,
mayor que o igual
a un entero…
•
OPENING TASK – Equal to One Whole,
More or Less?
• Using a set of fractional parts to
compare to one whole.
• Using my understanding of numbers
less than and greater than one
whole.
•
•
Equal to One Whole, More or
Less?
Ch. 6 “Math Detective”, p. 251
“Vocabulary Builder” p. 252
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet Instructional Tools – Elementary – 5th Grade)
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•
2-3
4–7
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•
Using a number line to round
fractions to the nearest benchmark:
1
0, , 1.
Using a mental math rounding
strategy of comparing a numerator to
a denominator.
Lesson 6.3: Estimate Fraction
Sums and Differences
o Note: Continue to work on
estimating with fractions
during Number Talks.
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•
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•
Jog-A-Thon Task
Benchmark Fraction Task
Number Cards Fraction Task
Cross-Curricular Fractions
•
Making a fraction kit, folding and
cutting paper into equal parts.
Playing the games Cover Up and
Uncover.
Using manipulatives such as fraction
strips, number lines, pattern blocks
and area models.
Using visual fraction models.
Multiplying the numerator and the
denominator by the same non-zero
whole number.
•
•
•
Building Equivalent Fractions
Cover Up and Uncover
Lesson 6.5: Common
Denominators and Equivalent
Fractions
•
Building Equivalent Fractions
Power Point
Problem Solving - Grades 3-5,
Task 4.3 “Purple Triangle-Gray
Rectangle Problem” pp. 66 – 68
o Black Triangle-Gray Rectangle
Task 4.3
Equivalent Fraction Task
Good Questions, p. 28 (#1) and p.
29 (#10)
How Far Apart Are The Freeway
Puedo estimar las
sumas y
diferencias de
fracciones…
•
Puedo formar
fracciones
equivalentes con
denominadores
comunes…
•
•
•
•
2
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
Ted Ed “One Is One…or is it?”
http://ed.ted.com/ lessons/oneis-one-or-is-it
One Fourth Fraction Models
See www.illustrative
mathematics.org/5 for fraction
tasks and videos 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)
•
•
•
•
5
Posted 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
(Universal Access for SPED, Struggling
Students, ELL, GATE)
•
8 – 12
Puedo sumar y
restar fracciones
con
denominadores
diferentes…
•
•
•
Dividing the numerator and the
denominator by the same non-zero
whole number.
*Suggestion: Start with “Go
Deeper” or “Think Smarter”
questions at the end of lessons
6.1 and 6.2 to frontload problem
solving. Observe students’
strategies as a formative
assessment.
• Lesson 6.1: Investigate –
Addition with Unlike
Denominators
• Lesson 6.2: Investigate –
Subtraction with Unlike
Denominators
• Lesson 6.6: Add and Subtract
Fractions
• Ch. 6 Mid-Chapter
Checkpoint pp. 277 - 278
*See note about simplest form from the
CA Mathematics Framework: "Teachers
must be careful not to overemphasize this
"simplifying" of fractions, as there is no
mathematical reason for doing so, though
depending on the problem context one
form may be more desirable. In particular,
teachers should avoid the use of the term
"reducing" fractions for this process, as
the value of the fraction itself is not being
reduced. A more neutral term such as
"renaming" (which hints to these fractions
simply being different names for the same
amount) allows for referring to this
strategy without the potential for student
misunderstanding".
New 2016 – 2017
Instructional Tools – Elementary – 5th Grade)
•
•
Using manipulatives and visual
models to find common
denominators.
Multiplying the numerator and the
denominator by the same non-zero
whole number to find common
denominators.
Solving word problems and
communicating reasoning.
LONG BEACH UNIFIED SCHOOL DISTRICT
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
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6
Exits? http://robertkaplinsky.com
/work/freeway-exits/
Fraction War
Fractions and Mixed Numbers on
Number Lines
Making S’Mores Task
Egyptian Fractions Task
Finding Common Denominators
to Add Task
Finding Common Denominators
to Subtract Task
Problem Solving - Grades 3-5,
Task 4.4 “Pizza Fractions” pp. 69
– 70
o Pizza Fractions Task 4.4
Problem Solving - Grades 3-5,
Task 4.5 “Who Drank More
Lemonade?” pp. 71 – 72
o Who Drank More Lemonade?
Task 4.5
Good Questions, p. 28 (#3)
John’s Trip to Disneyland
Performance Task
Agree or Disagree
Deck of Cards
Add Fractions
Subtract Fractions
Math Sponges
Posted 6/10/16
Grade 5
Unit 2 Addition and Subtraction of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Metas de
Aprendizaje
(Universal Access for SPED, Struggling
Students, ELL, GATE)
13 - 16
Puedo sumar y
restar fracciones
incluyendo
números mixtos…
•
•
•
17 - 18
Puedo resolver
problemas de la
vida real…
19 - 21
Puedo resolver
los problemas de
fracciones
representados en
palabras…
•
•
•
•
•
•
•
FAL, Long Jump (Intranet Assessments)
•
Long Jump - FAL, Differentiated
Activities
•
Lesson 6.10: Problem Solving
– Practice Addition and
Subtraction
Lesson 6.11: Algebra – Use
Properties of Addition
•
•
Good Questions, p. 28 (#4)
Carnival Day Performance Task
•
Making sense of fractional quantities.
Reading to understand, plan, solve,
and check.
Estimating answers mentally to see if
they make sense.
Using Properties of Addition to make
finding the sum more efficient.
Communicating reasoning.
Instructional Tools – Elementary – 5th Grade)
Lesson 6.7: Add and Subtract
Mixed Numbers
Lesson 6.8: Subtraction with
Renaming
Lesson 6.9: Patterns with
Fractions
•
FORMATIVE ASSESSMENT LESSON
Classroom Challenge: Long Jump
• Using my understanding of addition
and subtraction of fractions.
• Communicating my reasoning.
• Checking to see if my answers make
sense.
•
22
23
•
Using manipulatives and visual
models to find common
denominators.
Multiplying the numerator and the
denominator by the same non-zero
whole number to find common
denominators.
Solving word problems and
communicating reasoning.
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math Intranet -
•
•
•
Good Questions, p. 28 (#5)
Mixed Numbers with Unlike
Denominators Task
Cady’s Cats Performance Task
Addition and Subtraction of
Fractions with Mixed Numbers
Quiz
Unit Assessment
Ch. 6 Performance Task – “Sugar and Spice” (Assessment Guide, pp. AG135 – AG139D)
We would appreciate feedback on the following:
Unit Guide bit.ly/Grade5UnitGuide
Assessment and FAL bit.ly/Grade5Assessment
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
7
Posted 6/10/16