Download Topic 7 - Lake County Schools

2016-2017 Curriculum Blueprint
Grade: 5
Course: Mathematics
Topic 7 – Use Equivalent Fractions to Add and Subtract Fractions
Flexible Time
Line
13 days
Unit Overview
Topic 7 focuses on deep understanding of using equivalent fractions to add and subtract fractions and mixed numbers. The use of fraction tiles and fraction
kits will help students develop a concrete understanding for operations with fractions.
Vertical Progression
4th Grade: The students find factors and multiplies of given numbers and find equivalent fractions. The students add and subtract fractions and mixed
numbers with like denominators.
6th Grade: The students will be able to evaluate expressions and solve equations that involve fractions and mixed numbers.
Learning Goal
Essential Question
The students will be able to estimate fraction sums and differences along with
How can sums and differences of fractions and mixed numbers be
adding and subtracting fractions and mixed numbers.
estimated?
What are standard procedures for adding and subtracting fractions and
Topic 7 Scale
mixed numbers?
Deconstructed Standards
MAFS.5.NF.1.1 (DOK 2) 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.) [conceptual understanding; application]
• Generate equivalent fractions to find the like denominator.
• Solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction
strategy.
MAFS.5.NF.1.2 (DOK 2) 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.
[conceptual understanding; application]
• Generate equivalent fractions to find like denominators.
• Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction.
• Solve word problems, involving addition and subtraction of fractions with unlike denominators referring to the same whole.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.4.1 Model with mathematics.
Suggested Learning Progression
The following learning progression provides students with an opportunity to
construct meaning and create connections through the CRA Method: Concrete
– Representational – Abstract.
*Collaborative teams should be selective in choosing standards-aligned tasks
for instruction and assessment. Teams may adjust the sequence and use
additional resources based on the needs of their students.
Topic 7: Use Equivalent Fractions to Add and Subtract Fraction
Sample Thinking Map of Strategies to Add & Subtract Fractions with Unlike
Denominators:
Teachers may use this map for professional development or as a teaching tool.
Teachers may build this map with their students as they learn the strategies
throughout the topic. Teachers should be selective in choosing strategies that
they feel will benefit their students’ understanding of the standard.
Topic Resource: Teaching Tools Number Lines pg. 12 & Fraction strips pg. 13
Students should have access to fraction strips throughout the topic.
Lesson 7-1: Estimate Sums and Differences of Fractiions (NF.1.1 and NF.1.2)• Additional Resources:
o
Georgia Units Unit 4 – Equal to One Whole, More, or Less?
o i-Ready Lesson (Number & Operations): Add and Subtract
Fractions
Lesson 7-2: Find Common Denominators (NF.1.1 and NF.1.2)
Recommended Instructional Sequence
This instructional sequence is intended to provide a framework for student
learning. Various options are listed below each step in the sequence.
Collaborative teams may adjust the sequence as necessary to meet the
needs of their students.
Step 1: 5-Minute Spiral Review
• Pearson Daily Review
• Common Misunderstandings or Errors
Step 2: Problem-Based Learning
• Solve and Share
•
Math Formative Assessment System (MFAS) Tasks by Standard
• Illustrative Mathematics Tasks by Standard
Step 3: Focus Lesson & Opportunities for Practice
• Visual Learning Bridge
• Guided Practice
• Thinking Map/Graphic Organizer
• Collaborative work
• Interactive Notebook
• Independent Practice
• Whole Group i-Ready Lesson
• Task Oriented Instruction
(additional opportunities for PBL)
Step 4: Differentiated Instruction
• Small group instruction
• Guided Practice
• Centers/stations (including i• Intervention/Enrichment
Ready)
Step 5: Student Debrief
• Thinking Map/Graphic Organizer
• Reflection
o So what? What did you
• Exit Ticket
learn?
• Interactive Notebook
o So why? Why is it
important?
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
*Higher order questions should be utilized to foster a deep, conceptual
understanding of the topic. Encouraging students to express their
mathematical thinking in writing helps them solidify their learning.
Lesson 7-3: Add Fractions with Unlike Denominators* (NF.1.1 and NF.1.2)
• Additional Resources:
o EngageNY - Module 3 Lesson 3 and 5
o i-Ready Lesson (Number & Operations): Adding and
Subtracting Unlike Fractions
Lesson 7-4: Subtract Fractions with Unlike Denominators* (NF.1.1 and NF.1.2)
Lesson 7-5: Add and Subtract Fractions (NF.1.1 and NF.1.2)
• Additional Resources:
o EngageNY - Module 3 Lesson 3 and 5
•
•
•
•
Lesson 7-6: Estimate Sums and Differences of Mixed Numbers (NF.1.2 and
NF.1.1)
•
•
How was that strategy similar/different than…?
How are equivalent fractions helpful when solving problems?
Why is it important to know how close a fraction is to one whole?
How can addition/subtraction of fractions be represented by objects,
pictures, words, numbers, and models?
Explain and justify your model.
How can benchmark fractions help you estimate?
Lesson 7-7: Use Models to Add Mixed Numbers* (NF.1.1 and NF.1.2)
Lesson 7-8: Add Mixed Numbers* (NF.1.1 and NF.1.2)
• Additional Resources:
o Georgia Units Unit 4 – Flip It Over & Create Three
o EngageNY - Module 3 Lessons 9 and 10
Lesson 7-9: Use Models to Subtract Mixed Numbers* (NF.1.1 and NF.1.2)
• Additional Resource: i-Ready Lesson (Number & Operations):
Rewriting Mixed Numbers and Fractions Greater Than 1
Lesson 7-10: Subtract Mixed Numbers* (NF.1.1 and NF.1.2)
• Additional Resource: Georgia Units Unit 4 – Flip It Over & Create Three
Lesson 7-11: Add and Subtract Mixed Numbers (NF.1.1 and NF.1.2)
• Additional Resources:
o Georgia Units Unit 4 – Flip It Over & Create Three
o EngageNY - Module 3 Lessons 10 and 12
Lesson 7-12: Math Practices and Problem Solving: Model with Math (NF.1.2)
• Additional Resource: i-Ready Lesson (Number & Operations): Add and
Subtract Fractions in Word Problems
*May combine to save time:
Lessons 7-3 and 7-4 , Lessons 7-7 and 7-8, Lessons 7-9 and 7-10
Professional Development
Resources
EngageNY Math Studio Talk: Common Core Instruction for Pearson enVisionMath2.0
5.NF
Home-School Connection Page
Reteaching Pages
This video segment focuses on strategies for performing
Daily Review
operations with fractions. (Beginning of video – 7:50)
* YouTube must already be opened on your browser
Florida Interim Assessment Item Bank and Test Platform
before clicking the link.
Math Formative Assessment System (MFAS) Tasks by Standard
Marzano Proficiency Scales Bank
CPALMS - MFAS includes tasks and rubrics that the teacher can
Common Core Flip Books: Provides additional information implement with their students.
and sample problems for every standard
Illustrative Mathematics Tasks by Standard
FSA Test Item Specifications
The site illustrates standards with impeccably crafted tasks, videos,
lesson plans, and curriculum modules.
Essential Vocabulary
benchmark fraction
common
denominator
• equivalent fractions
• mixed numbers
•
•