Math 5th Grade Unit - Santa Ana Unified School District

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Getting
?to
?the
?Core
?
Grade
?5
?Unit
?of
?Study
?
?Multiplication
?and
?Division
?of
?Fractions
?
1
?
Table
?of
?Contents
?5th
?Grade
?Math
?
?
?Multiplication
?&
?Division
?of
?Fractions
?
?
Pages
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?Lessons
?and
?Activities
?
3¨C8
?
Unit
?Overview
?
9¨C11
? Prerequisite
?Skills
?Test
?
12¨C16
? Preparing
?the
?Learner
?Lesson
?A:
?
?Preparing
?a
?Fraction
?Bar
?Toolkit
?
17¨C21
? Preparing
?the
?Learner
?Lesson
?B:
?
?Launching
?Mathematical
?Discourse
?
22¨C26
? Preparing
?the
?Learner
?Lesson
?C:
?Learning
?the
?Language
?of
?Contrast
?
27¨C31
? Lesson
?1:
?
?Quotients
?of
?Whole
?Numbers
?
32¨C41
? Lesson
?2:
?
?Multiplying
?Whole
?Numbers
?and
?Fractions
?
42¨C49
? Lesson
?3:
?
?Multiplying
?Fractions
?with
?Whole
?Numbers
?
50¨C58
? Lesson
?4:
?
?Multiplying
?Fractions
?with
?Fractions
?
59¨C65
? Lesson
?5:
?
?Multiplying
?Fractions
?by
?Fractions
?
66¨C76
? Lesson
?6:
?
?Comparing
?Size
?of
?Products
?
77¨C86
? Lesson
?7:
?
?Multiplying
?Fractions
?with
?Whole
?Numbers
?and
?Fractions
?
87¨C93
? Lesson
?8:
?
?Division
?of
?Fractions
?
94¨C101
? Lesson
?9:
?
?Dividing
?Unit
?Fractions
?by
?Whole
?Numbers
?
102¨C108
? Lesson
?10:
?
?Dividing
?Unit
?Fractions
?by
?Whole
?Numbers
?and
?Whole
?
Numbers
?by
?Unit
?Fractions
?
109¨C114
? Lesson
?11:
?
?Dividing
?Unit
?Fractions
?by
?Whole
?Numbers
?
115¨C124
? Lesson
?12:
?Culminating
?Task
?and
?Unit
?Assessment
?
118¨C122
? Multiple
?Choice
?Test
?with
?Answer
?Key
?
123¨C124
? Performance-?©\Based
?Task
?with
?Rubric
?
125¨C129
? Additional
?Menu
?Activities
?and
?Check
?Off
?Sheets
?
?
?
?
?
2
?
Information, Media and Technology:
Critical Thinking & Problem Solving
?
Tier III:
Multiply
Divide
Simplest form
Mixed number
Denominator
Numerator
Unit fraction
Improper fraction
Mixed number
Equivalent fraction
Reciprocal
Hardware
Creativity & Innovation
3
?
How will pre-assessment guide instruction?
Students missing two or more in any section will need intervention
through the Preparing the Learner lessons.
Software
Communication & Collaboration
How are fractions related to division?
How can the area of a rectangle with fractional sides be represented?
How can a visual model help to show multiplication of a fraction by a whole number?
How does multiplying by a fraction or by a mixed number affect the size of the product?
How can multiplication of fractions and mixed numbers be used in real life situations?
How can division of fractions be used in real life situations?
Learning and Innovation:
?
?
?
?
?
?
Multiplying and Dividing Fractions
5th Grade
Time Frame: 3 weeks
The properties of multiplication and division of whole numbers apply also to the multiplication and division of
fractions.
Online Tools
?
Essential
Tier II:
Academic
Contrast
Language:
However
Although
Nevertheless
Moreover
In addition
Similarly
What pre-assessment will be given?
Prerequisite Skills Test
21st Century
Skills:
Unit Title:
Grade Level:
Big Idea
(Enduring
Understandings):
Essential
Questions:
Santa Ana Unified School District Common Core Unit Planner-Mathematics
?
?
?
Instructional Activities:
(What
?learning
?experiences
?will
?students
?engage
?in?
?How
?will
?you
?use
?these
?learning
?experiences
?to
?drive
?responsive
?teaching?)
?
?
Preparing
?the
?Learner
?Lesson
?A
?
Preparing
?the
?Learner
?Lesson
?B
?
Preparing
?the
?Learner
?Lesson
?C
?
Preparing
?a
?Fraction
?Bar
?Toolkit
?
Launching
?Mathematical
?Discourse
?
Learning
?the
?Language
?of
?Contrast
?
?
?
?
?
?
?
CCS
?5.4.b
?Multiply
?fractions
?by
?whole
?numbers
?and
?
CCS
?
? 5.3
?Interpret
?Fractions
?as
?
CCS
?5.4.a
?Multiply
?fractions
?by
?whole
?
by
?other
?fractions:
?
Division:
?
numbers
?and
?by
?other
?fractions:
?
Find
?the
?area
?of
?a
?rectangle
?with
?fractional
?side
?
?
Fractions
?are
?defined
?as
?
Apply
?and
?extend
?previous
?
lengths
?by
?tiling
?it
?with
?unit
?squares
?of
?the
?
?
division
?of
?the
?numerator
?by
?
understandings
?of
?multiplication
?to
?
appropriate
?unit
?fraction
?side
?lengths,
?and
?show
?that
?
?
the
?denominator.
?
multiply
?a
?fraction
?or
?whole
?number
?by
?a
?
the
?area
?is
?the
?same
?as
?would
?be
?found
?by
?
fraction.
?
?
multiplying
?the
?side
?lengths.
?Multiply
?fractional
?side
?
?
When
?multiplying
?a
?fraction
?times
?a
?
?
lengths
?to
?find
?areas
?of
?rectangles,
?and
?represent
?
whole,
?the
?parts
?of
?the
?fraction
?are
?
fraction
?products
?as
?rectangular
?areas.
?
?
?
partitioned
?among
?the
?whole
?number.
?
?
?
The
?area
?of
?a
?rectangle
?with
?fractional
?lengths
?can
?
?
be
?found
?by
?multiplying
?the
?length
?times
?the
?width,
?
?
just
?as
?with
?whole
?numbers.
?
?
?
?
?
?
CCS5
?.7.a,b,c
?Real
?world
?problems
?with
?division
?
CCS
?5.
?6
?
?Real
?world
?problems
?
? CCS
?5.5.a,b
?Scaling:
?
of
?fractions
?and
?
?whole
?numbers:
?
with
?multiplication
?of
?fractions
?
? Comparing
?the
?size
?of
?a
?product
?to
?the
?
Apply
?and
?extend
?previous
?understandings
?of
?
and
?
?mixed
?numbers:
?
? size
?of
?one
?factor
?on
?the
?basis
?of
?the
?size
?
division
?to
?divide
?unit
?fractions
?by
?whole
?
of
?the
?other
?factor,
?without
?performing
?
Visual
?and
?numeric
?models
?of
?
? the
?indicated
?multiplication.
?
numbers
?and
?whole
?numbers
?by
?unit
?fractions:
?
multiplication
?of
?fractions
?and
?
? Multiplying
?by
?a
?fraction
?reduces
?the
?
Interpret
?division
?of
?a
?unit
?fraction
?by
?a
?non-?©\
mixed
?numbers
?are
?used
?to
?
zero
?whole
?number,
?and
?compute
?such
?
? size
?of
?the
?product,
?while
?multiplying
?
quotients.
?
solve
?
p
roblems
?
i
n
?
d
aily
?
l
ife.
?
?
?
?
by
?
a
?
m
ixed
?
n
umber
?
i
ncreases
?
t
he
?
s
ize
?
o
f
?
?
?Interpret
?division
?of
?a
?whole
?number
?by
?a
?unit
?
the
?product.
?
?
?
fraction,
?and
?compute
?such
?quotients.
?
?
?
?
Division
?of
?fractions
?is
?used
?to
?solve
?problems
?in
?
daily
?life.
?
?
?
?
?
?
?
?
Assessment
?or
?
?
Performance
?Task
?
4
?
Performance
?Task
?
?
Other Evidence:
Teacher observations
?
S: Performance Task: Culminating Task
S: End of Unit Assessment
S: Benchmark Tests
?
5
?
Student
comprehension of
unit concepts and the
big idea:
The properties of
multiplication and
division of whole
numbers apply also
to the multiplication
and division of
fractions.
?
Ongoing evidence of
students¡¯
understanding of the
concepts presented
Diagnostic
information for
intervention or
acceleration
F: Problem solving journal
F: Visual representation of thinking
F: Performance Task : Lesson 1-4 Review Tasks
F: Lesson 7 Performance Task
Common Core Mathematics Content Standards:
Number and Operations¨CFractions
Apply and extend previous understandings of multiplication and
division to multiply and divide fractions.
3. Interpret a fraction as division of the numerator by the denominator (a/b =
a ¡Â b). Solve word problems involving division of whole numbers leading to
answers in the form of fractions, mixed numbers, e.g., by using visual
fraction models or equations to represent the problem.
4. Apply and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction.
a. Interpret the product (a/b) ¡Á q as a parts of a partition of q into b equal
parts; equivalently, as the result of a sequence of operations a ¡Á q ¡Â b. For
example, use a visual fraction model to show (2/3) ¡Á 4 = 8/3, and create a
story context for this equation. Do the same with (2/3) ¡Á (4/5) = 8/15.(In
general, (a/b) ¡Á (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.
5. Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of
the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1
results in a product greater than the given number (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 ¡Á a)/(n b) to the effect of multiplying a/b by 1.
6. Solve real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent the
problem.
7. 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) ¡Â 4,
and use a visual fraction model to show the quotient. Use the relationship
Assessment of Standards
What assessments will be utilized for this
What does the
unit? (F = formative, S = summative)
?
assessment tell us?
?
Standards
Common Core Learning Standards Taught and Assessed
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