Transcript 5 NF Unit Plan grade 5

Fractions
5.NF
Essential Questions:
Essential Understanding:
How do we add or subtract with unlike denominators?
How can we use visual models to solve problems using fractions?
How can we use an estimation to check our answer?
How are fractions related to division?
How are multiplying whole numbers and multiplying fractions
related?
Does size of fractions matter? How does the thinking about resizing a
number help to interpret possible products for a multiplication
problem?
How can you write a number sentence for a word problem and how
can you determine the reasonable answers involving fractions?
How does the context of a problem relate to the models or
equations?
Students will apply their understanding of fractions and fraction
models to represent the addition and subtraction of fractions with
unlike denominators as equivalent calculations with like
denominators. They develop fluency in calculating sums and
differences of fractions, and make reasonable estimates of them.
Students also use the meaning of fractions, of multiplication and
division, and relationship between them to understand and explain
why the procedures for multiplying and dividing fractions make
sense.(Limited to the case of dividing unit fractions by whole numbers
and whole numbers by unit fractions.
Vocabulary:
Assessment
fraction, equivalent, addition, sum, subtract, difference, unlike denominator,
numerator, benchmark fraction, estimate, reasonableness, mixed numbers,
denominator, common denominator, multiple, factor, fraction models-area, tape,
number line, etc., partition, product, quotient, array, square unit, unit fraction,
resizing, scaling, improper and proper fractions, length and width
Summative: Assessment for each of the four operations with fractions
(x,/,+,-) will consist of procedural problems along with real world
problems that will require students to use their knowledge of
fractional relationships to be solved. Answers will require justification
using representations and explanations.
Guiding questions:
How do you find quick common denominators?
What strategies do you use to find the common denominator and/or simplest
form?
Why is it important to have more than one method for finding equivalent fractions?
How is adding with unlike denominators different from adding with like
denominators?
Why do we use number models to represent problems?
Which representation of fraction multiplication helps you most? Why?
How could it help you to know different methods for solving the same problems?
How do visual models help you in math?
Formative:
We will be using a skills checklist as we progress through the lessons
of this unit.
Lesson
Math
Concept
Standard
Skills
Problems to
Pose
Anticipated
Errors
1
Part to whole
and decomposing
fractions
Benchmark fractions
5.NF.A2
Represent a fraction
Decompose a fraction,
add/subtract with like
denominators, use
benchmark fractions
Closer to 0, ½, or whole
Break down 4/6 into
sixths
1/3+2/3=?
4 2/3- 3/3
Vocabulary difficulties
Benchmark fractions
used incorrectly
Numerator vs.
denominator roles
2
Equivalent fractions
5.NF.A1
Identify and create
equivalent fractions
Use several strategies
and justify answers
½ is equivalent to ?
Show why 2/3 is
equivalent to ? Using
a model
Not multiplying the
numerator and
denominator by the
same amount
Calculation errors
3
Comparing fractions
with like and unlike
denominators
5.NF.A1
5.NF.A2
Use benchmark fractions
correctly
Find common multiples
and create equivalent
fractions
Greater than less than
with fractions,
sequenced from like to
unlike denominators
Order fractions
Incorrect multiples, not
4
Adding fractions with
unlike denominators
5.NF.A.1
Finding common
denominators
Adding fractions
2/3+1/2 with
numbers getting
more difficult
Adding the
denominator
Incorrect common
denominators
5
Subtracting fractions
with unlike
denominators
5.NF.A.1
Finding common
denominators
Subtracting fractions
2/3-1/2 with
numbers getting
more difficult
Subtracting the
denominator
Incorrect common
denominators
6
Add/subtract
fractions with mixed
numbers and whole
numbers
5.NF.A.1
Converting mixed
numbers and adding
and subtracting
fractions
6-2/3
3 ½ +3/4
Converting mixed
numbers improperly
Calculation errors
Forgetting the whole
numbers
7
Solve word problems
add/subtract
fractions with unlike
denominators
5.NF.A.2
Interpret problem, find
correct number
sentence, justify
reasonableness of
answer
Incorrect equations
to be fixed
Word problems
Not understanding
what the fractions
refer to, incorrect
number sentences
ordering correctly
because of trouble
finding common
denominators
Lesson
Math
Concept
Standard
Skills
Problems to
Pose
Anticipated
Errors
8
Multiplying fractions
5.NF.B.4
5.NF.B.5
Multiplying fractions
including whole numbers
and mixed numbers
Using area arrays and
models
Scaling to check
reasonableness
6x¾
61/2 x ¾
Converting mixed
numbers
May try to use common
denominators
Representations
2 ½ x 3 1/4
9
Word problems requiring
multiplication of
fractions and mixed
numbers
5.NF.B.6
5.NF.5
Interpret the problem to
determine the correct
number sentence
Using models to justify
reasonableness of
answer
Real world problems
Interpreting the problem
correctly
Calculation errors
May try to use common
denominators
10
Interpret a fraction as
division
5.NF.B.3
a/b=a divided by b
See NCSS standards
Interpreting the
relationship between
terms correctly. What
happens with
remainders?
Interpreting this
relationship correctly
using story problems
11
Dividing fractions
5.NF.B.7-7A-7B
Relationship between
multiplication and
division, dividing
fractions
Creating models
6 divided by ½
Or
½ divided by 6
Mixing up divisors and
dividends
Incorrect models
Not understanding
relationship
12
Word problems with
division of fractions
5.NF.B.7C
Interpreting the
relationship between
terms, justifying
reasonableness of
answers using models
Story problems
Interpreting the terms
correctly (do not divide
up the cats)