Ke n t u c k y Co n t i n u o u s In s t r u c t i o n a l Improvement Te c h n o l o g y System
Ma t e r i a l s Ba n k
Unit 4: Multiplying and Dividing Fractions and Mixed Numbers
Unit: Mathematics , Grade(s) 05
Multiplying and Dividing Fractions and Mixed Numbers
Duration: 11 Days
Unit
Pacing Guide
Day 1: Chapter Opener and Pre­Assessment
Day 2: Lesson 4.1: Multiplying Proper Fractions
Day 3: Lesson 4.2: Real World Problems: Multiplying Proper Fractions
Day 4: Lesson 4.3: Multiplying Improper Fractions
Day 5: Lesson 4.4: Multiplying Mixed Numbers and Whole Numbers
Day 6: Lesson 4.5: Real World Problems: Multiplying with mixed numbers
Day 7: Lesson 4.6: Dividing a fraction by a whole number
Day 8­9: Lesson 4.7: Real­World Problems: Multiplying and Dividing with fractions
Day 10: Review and Chapter Wrap up
Day 11: Unit 4 Post Test
Due to training, common assessments, students activities, Thanksgiving break will not be a continuious 11 days. It will be broken up to accomodate the
schedule aboave.
Curriculum Map
I can...
Multiply proper fractions.
Solve real­world problems involving multiplication of proper fractions.
Multiply improper fractions by proper or improper fractions.
Multiply a mixed number by a whole number.
Solve real­world problems invovling multiplication of whole numbers and mixed numbers.
Divide a fraction by a whole number.
Solve real­world problems involving multiplication and divison in fractions. Standards-Based Unit of Study
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Ma t e r i a l s Ba n k
Vocabulary: product, common factor, proper fraction, improper fraction, mixed number, reciprocal
Day 1: Take the Pre­Assessment from the Assessment Book
Day 2: Lesson 4.1: Students will...
use model to multiply fractions
multiply fractions without models (GP 1­4)
Hands­on activity 1­6
Let's Explore
Let's Practice 1­6
Workbook Pages 131­132
Day 3:Lesson 4.2: Students will...
Multiply fractions to solve real­world problems (GP 1)
Give the answer as a fractional remainder (GP 2)
Let's Practice 1­7
Workbook pages 133­138
Day 4:Lesson 4.3: Students will...
Multiply improper fractions by proper fractions (GP 1­8)
Let's Practice 1­8
Workbook pages 139­142
Day 5: Lesson 4.4 Students will:
multiply mixed numbers by whole numbers (GP 1)
Hands on activity
Let's Explore (1­2)
Let's Practice: 1­5
Workbook pages 143­146
Day 6: Lesson 5.5: Students will...
Multiply mixed numbers by whole numbers to solve real world propblems (GP­1)
Express the product of a mixed number and a whole number as a decimal (GP 2)
Solve two­step problems involving multiplication with mixed numbers (GP 3)
Let's Practice 1­6
Workbook pages 147­148
Day 7: Lesson 4.6 Students will....
Divide a fraction by a whole number (GP 1)
Divide a fraction by a whole number (GP 2)
Hands­on activity (GP 1­2)
Let's Practice 1­10
Workbook pages 149­152
Day 8­9: Lesson 4.7 Students will...
Find parts of a whole to solve real­world problems (GP 1)
find a fractional parts of a whole and the remainder
Find fractional parts and whole given one fractional part (GP 2)
Find fractional parts of a remainder when given wholes (GP 3­4)
Let's Practice (1­6)
Workbook pages 153­158
Day 10: Chapter Wrap­Up and Review
Day 11: Assessment
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Ke n t u c k y Co n t i n u o u s In s t r u c t i o n a l Improvement Te c h n o l o g y System
Ma t e r i a l s Ba n k
Standards Covered
5.3NF: Number and Operations-Fractions
5.3NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.4: A p p l y a n d e x t e n d p r e v i o u s u n d e r s t a n d i n g s o f m u l t i p l i c a t i o n t o m u l t i p l y a f r a c t i o n o r w h o l e n u m b e r b y a f r a c t i o n .
a: I n t e r p r e t t h e p r o d u c t ( a / b ) × q a s a p a r t s o f a p a r t i t i o n o f q i n t o b e q u a l p a r t s ; e q u i v a l e n t l y , a s t h e r e s u l t o f a s e q u e n c e o f
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: F i n d t h e a r e a o f a r e c t a n g l e w i t h f r a c t i o n a l s i d e l e n g t h s b y t i l i n g i t w i t h u n i t s q u a r e s o f t h e a p p r o p r i a t e u n i t f r a c t i o n s i d e l e n g t h s ,
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.
5.NF.5: I n t e r p r e t m u l t i p l i c a t i o n a s s c a l i n g ( r e s i z i n g ) , b y :
a: C o m p a r i n g t h e s i z e o f a p r o d u c t t o t h e s i z e o f o n e f a c t o r o n t h e b a s i s o f t h e s i z e o f t h e o t h e r f a c t o r , w i t h o u t p e r f o r m i n g t h e
indicated multiplication.
b: E x p l a i n i n g w h y m u l t i p l y i n g a g i v e n n u m b e r b y a f r a c t i o n g r e a t e r t h a n 1 r e s u l t s i n a p r o d u c t g r e a t e r t h a n t h e g i v e n n u m b e r
(recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a
fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b =
(n×a)/(n×b) to the effect of multiplying a/b by 1.
5.NF.6: S o l v e r e a l w o r l d p r o b l e m s i n v o l v i n g m u l t i p l i c a t i o n o f f r a c t i o n s a n d m i x e d n u m b e r s , e . g . , b y u s i n g v i s u a l f r a c t i o n m o d e l s o r e q u a t i o n s
to represent the problem.
5.NF.7: A p p l y a n d e x t e n d p r e v i o u s u n d e r s t a n d i n g s o f d i v i s i o n t o d i v i d e u n i t f r a c t i o n s b y w h o l e n u m b e r s a n d w h o l e n u m b e r s b y u n i t f r a c t i o n s .
(Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the
relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)
a: I n t e r p r e t d i v i s i o n o f a u n i t f r a c t i o n b y a n o n - z e r o w h o l e n u m b e r , a n d c o m p u t e s u c h q u o t i e n t s . F o r e x a m p l e , c r e a t e a s t o r y c o n t e x t
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.
c: S o l v e r e a l w o r l d p r o b l e m s i n v o l v i n g d i v i s i o n o f u n i t f r a c t i o n s b y n o n - z e r o w h o l e n u m b e r s a n d d i v i s i o n o f w h o l e n u m b e r s b y u n i t
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?
_ M P . 1 : Make sense of problems and persevere in solving them.
_ M P . 2 : Reason abstractly and quantitatively.
_ M P . 3 : Construct viable arguments and critique the reasoning of others.
_ M P . 4 : Model with mathematics.
_ M P . 5 : Use appropriate tools strategically.
_ M P . 6 : Attend to precision.
_ M P . 7 : Look for and make use of structure.
_ M P . 8 : Look for and express regularity in repeated reasoning.
Materials
For a closer look at the materials list below, log onto https://ciits.kyschools.us/ButlerCounty
Resources:
1. Chapter 4
Organizers
Characteristics of Highly Effective Teaching & Learning - LEARNING CLIMATE
1. Teacher Characteristics: A.
6. Teacher Characteristics: G.
11. Student Characteristics: C.
creates learning environments
effectively allocates time for
collaborates/teams with other
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Ma t e r i a l s Ba n k
where students are active
participants as individuals and as
members of collaborative groups
students to engage in hands-on
students
experiences, discuss and process
content and make meaningful
connections
2. Teacher Characteristics: B.
7. Teacher Characteristics: H.
12. Student Characteristics: D.
motivates students and nurtures
designs lessons that allow students exhibits a sense of accomplishment
their desire to learn in a safe,
to participate in empowering
and confidence
healthy and supportive environment activities in which they understand
which develops compassion and
that learning is a process and
mutual respect
mistakes are a natural part of
learning
3. Teacher Characteristics: C.
8. Teacher Characteristics: I. creates 13. Student Characteristics: E. takes
cultivates cross cultural
an environment where student work educational risks in class
understandings and the value of
is valued, appreciated and used as
diversity
a learning tool
4. Teacher Characteristics: E.
9. Student Characteristics: A.
14. Student Characteristics: F.
displays effective and efficient
accepts responsibility for his/her
Practices and engages in safe,
classroom management that
own learning
responsible and ethical use of
includes classroom routines that
technology
promote comfort, order and
appropriate student behaviors
5. Teacher Characteristics: F.
10. Student Characteristics: B.
provides students equitable access actively participates and is
to technology, space, tools and time authentically engaged
Characteristics of Highly Effective Teaching & Learning - CLASSROOM ASSESSMENT & REFLECTION
1. Teacher characteristics: A. Uses 5. Teacher characteristics: G.
9. Student characteristics: B.
multiple methods to systematically Provides regular and timely
Monitors progress toward reaching
gather data about student
feedback to students and parents learning targets
understanding and ability
that moves learners forward
2. Teacher characteristics: B. Uses 6. Teacher characteristics: H. Allows 10. Student characteristics: D. Uses
student work/data, observations of students to use feedback to
teacher and peer feedback to
instruction, assignments and
improve their work before a grade is improve his/her work
interactions with colleagues to
assigned
reflect on and improve teaching
practice
3. Teacher characteristics: C.
7. Teacher characteristics: I.
11. Student characteristics: E.
Revises instructional strategies
Facilitates students in self- and
Reflects on work and makes
based upon student achievement peer-assessment
adjustments as learning occurs
data
4. Teacher characteristics: D.
8. Teacher Characteristics: J.
Uncovers students’ prior
Reflects on instruction and makes
understanding of the concepts to be adjustments as student learning
addressed and addresses students’ occurs
misconceptions/incomplete
conceptions
Characteristics of Highly Effective Teaching & Learning - INSTRUCTIONAL RIGOR & STUDENT ENGAGEMENT
1. Teacher characteristics: A 4. Teacher characteristics: D 6. Teacher characteristics: I -Teacher
Teacher instructs the complex
Teacher provides meaningful
clarifies and shares with students
processes, concepts and principles learning opportunities for students. learning intentions/targets and
contained in state and national
criteria for success.
standards using differentiated
strategies that make instruction
accessible to all students.
2. Teacher characteristics: B –
5. Teacher characteristics: E 7. Student characteristics: A Teacher scaffolds instruction to help Teacher challenges students to
Student articulates and understands
students reason and develop
think deeply about problems and learning intentions/targets and
problem-solving strategies.
encourages/models a variety of
criteria for success.
approaches to a solution.
3. Teacher characteristics: C -
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Teacher orchestrates effective
classroom discussions, questioning,
and learning tasks that promote
higher-order thinking skills.
Characteristics of Highly Effective Teaching & Learning - INSTRUCTIONAL RELEVANCE
1. Teacher characteristics: A4. Teacher characteristics: D7. Teacher characteristics: GTeacher designs learning
Teacher selects and utilizes a
Teacher makes lesson connections
opportunities that allow students to variety of technology that support to community, society, and current
participate in empowering activities student learning.
events.
in which they understand that
learning is a process and mistakes
are a natural part of the learning.
2. Teacher characteristics: B5. Teacher characteristics: E8. Student characteristics: A-Student
Teacher links concepts and key
Teacher effectively incorporates
poses and responds to meaningful
ideas to students’ prior experiences 21st Century Learning Skills that
questions.
and understandings, uses multiple prepare students to meet future
representations, examples and
challenges.
explanations.
3. Teacher characteristics: C6. Teacher characteristics: FTeacher incorporates student
Teacher works with other teachers
experiences, interests and real-life to make connections between and
situations in instruction.
among disciplines.
Characteristics of Highly Effective Teaching & Learning - KNOWLEDGE OF CONTENT
1. Teacher characteristics: A4. Teacher characteristics: E7. Student characteristics: C-Student
Teacher demonstrates an
Teacher provides essential supports connects ideas across content
understanding and in-depth
for students who are struggling with areas.
knowledge of content and
the content.
maintains an ability to convey this
content to students.
2. Teacher characteristics: B5. Student Characteristics: A8. Student characteristics: DTeacher maintains on-going
Student demonstrates growth in
Student uses ideas in realistic
knowledge and awareness of
content knowledge.
problem solving situations.
current content developments.
3. Teacher characteristics: C6. Student characteristics: B-Student
Teacher designs and implements uses and seeks to expand
standards-based
appropriate content vocabulary.
courses/lessons/units using state
and national standards.
NCTM Process Standards
1. Problem Solving
3. Communication
5. Representation
2. Reasoning & Proof
4. Connections
Additional Properties
Author: McKinney, Alicia
Publisher: Kentucky Continuous Instructional Improvement Technology System
Cost/Fee: no
Restricted Use: no
Rights:
Keywords:
Created by: McKinney, Alicia (10/29/2012 3:47:00 PM)
Last modified by: McKinney, Alicia (11/13/2012 5:24:00 PM)
Other revisions of this resource:
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