Transcript Operating with Fractions*Oh Boy!

Making Fraction Strips
NO LABELING OF FRACTION STRIPS!
• Pink:
whole
• Green:
halves, fourths, eighths
• Yellow:
thirds, sixths, ninths
• Blue:
fifths, tenths
Apply and Extending
Previous Understanding to
Operate with Fractions
Academic Coaches – Math Meeting
February 15, 2013
Beth Schefelker
Bridget Schock
Connie Laughlin
Hank Kepner
Kevin McLeod
2
Closest to Half
Turn and Talk:
Use the task “Closest to Half” from February
1st professional practice.
What understandings or misconceptions
surfaced in your student work?
3
3
Nearest Answer
Find the nearest answer and explain why you
selected the answer you did.
A
B
C
D
⅟₁₁ + ⁸⁄₉
1
2
9
18
⅓ + ⁷⁄₈
¾
⁸⁄₁₁
⁸⁄₂₄
⁵⁄₄
5 ⁹⁄₁₁ – 2 ⁷⁄₈
2
3
3⅔
³²⁄₃
Learning Intentions & Success Criteria
Learning Intention
We are learning to understand addition as
combining and subtraction as the inverse.
Success Criteria
We will be successful when we can explain why
the operations of addition and subtract are the
same for fractions as they are for whole
numbers.
…APPLY AND EXTEND PREVIOUS
UNDERSTANDING
Bridget’s Week 1 Run
Bridget is training to run a marathon by fall. She
starts by running 4 miles on Monday and 5 miles
on Friday. How many miles did she run?
Bridget’s Week 2 Run
Because of the snow, she was only able to run
4
5
of a mile on Monday and 3 of a mile on
3
Friday. How many miles did she run?
Use visual fraction models to help explain your
reasoning.
4.NF.3a & b
Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
3. Understand a fraction a/b with a>1 as a sum of
fractions 1/b.
a. Understand addition and subtraction of fractions as
joining and separating parts referring to the same
wholes.
b. Decompose a fraction into a sum of fractions with the
same denominator in more than one way, recording each
decomposition by an equation. Justify decomposition by
using a visual fraction model.
Extending Thinking to 4.NF.3b
How many different ways
can you decompose the
number:
9
Think-Pair-Share
How many different ways
can you decompose the
number:
9
8
Think-Pair-Share
4.NF.3c & d
Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
3. Understand a fraction a/b with a>1 as a sum of
fractions 1/b.
c. Add and subtract mixed numbers with like denominators,
e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the
relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of
fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and
equations to represent the problem.
Which Operation?
• Work in pairs.
• Take turns flipping a card and reading the
problem.
•Use your white boards to write an expression
that represents the problem.
•Keep track of problems that raised interesting
discussions.
•Discuss these problems as a table group.
Progressions Document
• Read p. 6-7 “Adding and Subtracting
Fractions” (stop on p.7 at “repeated
reasoning…”).
• Highlight connections to today’s session.
Discuss your understanding
1. “The meaning of addition is the same for both
fractions and whole numbers, even though
algorithms for calculating their sums can be
different.”
2. “It is not necessary to know how much 2/3 + 8/5
is exactly in order to know what the sum
means.”
3. “Converting a mixed number to a fraction
should not be viewed as a separate technique to
be learned by rote, but simply as a case of
fraction addition.”
Learning Intentions & Success Criteria
Learning Intention
We are learning to understand addition as
combining and subtraction as the inverse.
Success Criteria
We will be successful when we can explain why
the operations of addition and subtract are the
same for fractions as they are for whole
numbers.
Reflection
As we’ve progressed in our study of Fractions, in
what way did today’s session build on our
knowledge of unit fractions and exemplify MP7.
Look for and make use of structure?