SOME STANDARDS ARE MORE
DIFFICULT TO INTERPRET AND
UNDERSTAND IN
MATHEMATICS
Summer 2014
College and Career-Readiness Conference
Based on RIGOR:
Reduce Side Chatter
Involve Yourself in the Process
Give Your Thoughts and Ideas
Open Your Mind to How You Can Change Instruction
Remember to Silence Electronic Devices
Cluster A. Apply and extend previous
understandings of multiplication and
division to divide fractions by fractions.
Standard 1. Interpret and compute quotients
of fractions, and solve word problems
involving division of fractions by fractions,
e.g., by using visual fractions models and
equations to represent the problem.
TODAY’S OUTCOMES
Participants will:
1. Briefly review the instructional shift, COHERENCE,
and make connections between division of fractions
by fractions and other content from elementary
school and middle school standards.
2. Explore a variety of models that each show what
happens mathematically when values are divided
by a fraction.
3. Compute quotients of fractions divided by fractions,
and interpret the quotients.
OUTCOME #1
Participants will:
1. Review the instructional shift of
COHERENCE, and make connections
between division of fractions by
fractions and other content from
elementary school and middle
school standards.
A purposeful placement of standards to create
logical sequences of content topics that bridge
across the grades, as well as across standards
within each grade.
https://www.turnonccmath.net
1.OA.4: Understand subtraction as the
unknown-addend problem. For example, find
10 – 8 by finding the number that makes 10
when added to 8.
inverse operations
10 – 8 = x
8 + x = 10
3.OA.6: Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by
finding the number that makes 32 when
multiplied by 8.
inverse operations
32 ÷ 8 = a
8 x a = 32
4.NF.3b: Decompose a fraction into a sum of
fractions with the same denominator… for example:
4.NF.4a: Understand a fraction a/b as a multiple of
1/b… for example:
5.NF.3b: Interpret a fraction as division of
the numerator by the denominator.
Students use
models for “equal
sharing” to explain
their understanding.
Grade 5 and Grade 6
OUTCOME #2
Participants will:
2. Explore a variety of models that
each show what happens
mathematically when values are
divided by a fraction.
• Area Model
• Number line model
• Tape diagram model
• Common denominator model
5.NF.B.7b:
Interpret division of a whole
number by a unit fraction, and
compute such quotients
8
How many parts can be partitioned from 2 “wholes”?
How many times does a part fit into 2 “wholes”?
2
?
eight
8
How many
parts can be partitioned from 2 “wholes”?
2
?
eight
8
How many
one
parts can be partitioned from 2 “wholes”?
two
three
four
five
?
eight
six
seven
eight
1
?
remainder
remainder
1
??
remainder
The remainder equals of one part.
So the answer is 1 .
remainder
1
remainder
remainder
remainder
5.NF.B.7a:
Interpret division of a unit
fraction by a non-zero whole
number, and compute such
quotients.
1
The quotient must be a fraction!
1
1
1
1
15
1
1
1
2
3
1
4
5
6
7
8
1
9
10
11
12
13
14
15
OUTCOME #3
Participants will:
3. Compute quotients of
fractions divided by fractions,
and interpret the quotients.
6.NS.A.1:
Interpret and compute quotients of
fractions, and solve word problems
involving division of fractions by
fractions, e.g., by using visual
fractions models and equations to
represent the problem.
When the dividend is greater than
the divisor…
2
Two
parts
one
two
2
one
two
2
one
two
When the dividend is greater than
the divisor, with a remainder…
one
two
three
one
two
three
four
one
one
remainder
When the dividend is less than the
divisor…
Inverse Operations and Reciprocal Pairs
Illustrative Math https://www.illustrativemathematics.org/
• Bill McCullum, CCSS lead writer
• Sample Lessons that illustrate specific standards
Achieve The Core
https://achievethecore.org
• Jason Zimba, CCSS lead writer
• Multiple Resources – e.g. Lesson Plans, Assessments, Professional
Development courses, Grade-at-a-Glance
PARCC http://parcconline.org
• Information about PARCC Assessments
• Sample Lessons
• Practice Tests