Download Finalize Fraction Operations

2015-2016 Curriculum Blueprint
Grade: 5
Course: Mathematics
4th Quarter – Remediation, Enrichment, and STEP UP Lessons
Flexible Time
Line
30 days
Topic Overview
Time is reserved during the 4th quarter to remediate and enrich standards based on assessment data. Opportunities should be provided for students through
the use of real world tasks and projects. Please review Table 1: Common Addition and Subtraction Situations (Page 88) and Table 2: Common Multiplication
and Division Situations (Page 89) to ensure students opportunities with all types of addition, subtraction, multiplication, and division problems, specifically
within the context of fractions. **PLCS may use their discretion in determining which 5th grade skills need to be remediated during this unit.
Vertical Progression
th
4 Grade: Students add and subtract fractions with like denominators. Students multiply fractions by a whole number.
6th Grade: Students will develop fluency with division of whole numbers, fractions, and decimals.
Learning Goal
Essential Question
The students will be able to add, subtract, multiply, and divide fractions fluently.
What are the standard procedures for adding, subtracting, and
multiplying, fractions?
What strategies can you use to divide a whole number by a fraction and
a fraction by a whole number?
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
Topic 7 Review
Step 1: Problem-Based Learning “Solve and Share”
Review vocabulary as
Lesson 7-11: Add and Subtract Mixed Numbers
Problem-Based Learning Lesson Flow Map
necessary based on
Conceptual understanding is developed when mathematics is
student needs
Topic 8 Review
introduced in the context of solving a real problem in which
Lesson 8-7: Multiply Mixed Numbers
ideas related to the new content are embedded. Conceptual
understanding results because the process of solving a problem
Topic 9 Review
requires students to connect their prior knowledge with the new
Lesson 9-7: Solve Problems Using Division
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
*Step Up Lessons (use at your discretion)
Note: FLDOE Units of Study provide a variety of resources for
digging deep into fractions, multiplication, and division. The
MFAS & Illustrative Mathematics Tasks in Additional
Resources below can help with remediation and enrichment
of specific standards.
Each lesson in the book begins with a Solve and Share. See the
links below for additional tasks to be used as needed:
Math Formative Assessment System (MFAS) Tasks by Standard
Illustrative Mathematics Tasks by Standard
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
lesson through the use of the worked-out problem in the
textbook.
Deconstructed Standards
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.
 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.
MAFS.5.NF.2.4 (DOK 2) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a) Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For
example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In
general, (a/b) × (c/d) = ac/bd.)
b) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is
the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as
rectangular areas.
 Multiply fractions by whole numbers.
 Multiply fractions by fractions.
 Interpret the product of fractions times a whole number as total number of parts of the whole.
 Determine the sequence of operations that results in the total number of parts of the whole.
 Interpret the product of a fractions times a fractions as the total number of parts of the whole.
 Represent fraction products as rectangular areas.
 Justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side
lengths.
 Find area of a rectangle with fractional side lengths using different strategies.
 Model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles.
MAFS.5.NF.2.7 (DOK 2) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a
visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 =
1/3.
b) Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using
visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
 Know the relationship between multiplication and division.
 Interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, by creating
story problems, using visual models, and relationship to multiplication, etc.
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Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by
representing the quotient with a visual fraction model.
Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using
strategies such as visual fractions models and equations.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.6.1 Attend to precision.
Additional Resources & Links
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
Georgia Units
*Higher order questions should be utilized to foster a deep, conceptual
Unit 4 : Adding, Subtracting, Multiplying, and Dividing Fractions
understanding of the topic. Encouraging students to express their
*NOTE: all of Unit 4 pertains to this Topic.
mathematical thinking in writing helps them solidify their learning.
EngageNY - Module 3
EngageNY - Module 4
FLDOE Units of Instruction
Grade 5 Fractions
Grade 5 Multiplication & Division
www.pearsonrealize.com
Home-School Connection Page
Reteaching Pages
Marzano Proficiency Scales Bank
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks and rubrics that the teacher can implement with
their students.
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks, videos, lesson plans,
and curriculum modules.
Common Core Flip Books: Provides additional information and sample problems
for every standard
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How can you apply what you learned in 5th grade to this 6th grade
skill ______?
Can you explain and justify your model?
How can benchmark fractions help you estimate?
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?
How can decomposing fractions help us multiply fractions?
Why should we use models to solve problems with fractions?
How can we model an area with fractional pieces?
How else can you model this problem?
How would you model this equation?
Interpret the product of a fraction.
Compare the size of a product to the size of a factor.
Examine how numbers change when we multiply by fractions.
What are some various strategies to solve word problems involving
the multiplication of a fraction by a mixed number?
How can comparing factor size to one help us predict what will
happen to the product?
Why should we use models to solve problems with fractions?
How would you model this equation?
 Explain the relationship between multiplication and division.
 What is the most efficient strategy for solving this problem?
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
Fluency Practice
FSA Test Item Specifications