Transcript Lessons for Multiplying and Dividing Fractions

Welcome Back!
5th Grade Planning
*Please make a fraction kit while we wait for everyone to arrive.*
December 2, 2014
8:00 – 10:45 am
Survey Results: Focus for Today
Focus on Instruction: A few
math experiences together, 1 indepth lesson, plan to co-teach
Integrate PUSD Units and
Math Expressions
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1st Choice
2nd Choice
3rd Choice
4th Choice
1st Choice
Navigate Math Expressions:
"Flip" the instruction
2nd Choice
3rd Choice
4th Choice
Build Math Content Knowledge
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2nd Choice
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Survey Results: Current Curriculum
What math content will you be
teaching?
What ME unit will you be
teaching?
5
4.5
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3.5
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2.5
2
1.5
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Unit 3
Unit 4 & 5
Review Unit 4/Begin
Fractions
Begin Fractions
Mutiply & Divide
Fractions
What math content do you want to
focus on?
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
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Mutiply and Divide
Fractions
Fractions
Divide Decimals
Divide Fractions
Fractions
Multiply and Divide
Decimals
Guiding Questions for Today
What are the 5th grade CC content standards for multiplying
and dividing fractions?
How does the SBAC assess understanding of these standards?
What experiences does Math Expressions offer?
How might we integrate Math Expressions and the PUSD
Units to enhance student understanding?
Is there a lesson we would like to co-teach?
Let’s use the Canvas Page!
• What do we want to put on the page?
• How might we make it a tool for collaboration?
How will students be held accountable
on the SBAC?
SBAC Practice Item
How many squares with a side length of 1/4 m are needed to tile
this rectangle?
¼m
¼m
5NF.4b 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. Lessons 4, 6
SBACish Practice Item
If you covered this
rectangle completely
with stickers with a
side length of
1/100, how many
stickers will cover
the whole shape?
12/100 m
5/100 m
5NF.4b 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. Lessons 4, 6
SBACish Practice Item
What is the area of this rectangle?
1/3 in
1/4 in
5NF.4b 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. Lessons 4, 6
SBACish Practice Item
Lucy is making a bracelets. She has 3 feet of string. Each bracelet
requires 1/4 feet of string.
Write an equation to find the number of bracelets she can make.
Calculate how many bracelets she can make.
5.NF.7c Solve real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit 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? Lessons 10-14
Models Offered in Math Expressions
TE pages 187BB – 187HH
How do these models compare to those detailed in
the CC Progressions and on the SBAC practice items?
Are there any gaps we need to fill?
Give yourself a brief tour of chapter 3.
• What do you notice?
• What is the overall instructional style offered in the
book: teacher shows – students practice; students
explore – teacher asks questions…?
A Perspective on Textbooks: An argument for
professional decision making (Phil Daro)
• Each lesson is written for 5 different teacher “types” or
perspectives.
• A lesson was never intended to be taught in its entirety.
• Publishers anticipate you will use what fits into your perspective.
You know more than the publisher. Trust yourself to make
informed curriculum decisions.
PUSD Unit of Study
ME Chapter 3, Multiply and Divide Fractions
Pathway:
• My Connect
• Math Central
• Units of Study
• 5th Grade
• Unit 3
Give yourself a brief tour of the unit.
How can we connect our understanding
of multiplying whole numbers to
multiplying fractions?
Jobs
• Standards Tracker
– What standard/s is/are addressed in each lesson?
• Note-Taker on GoogleDocs
– What ideas and adjustments did we discuss?
• Time Keeper
• Task Master
Other areas of focus/expertise:
• Homework
– What would be appropriate homework for each lesson?
• Differentiation
– How might we differentiate the lesson?
ME Unit 3:
Multiplication and Division with Fractions
Big Idea 1: Multiplication with Fractions
Lesson 1: Basic Multiplication Concepts
Lesson 2: Multiplication with Non-Unit Fractions
Lesson 3: Multiplication with Fractional Solutions
Lesson 4: Multiply a Fraction by a Fraction
Lesson 5: Multiplication Strategies
Lesson 6: Multiply Mixed Numbers
The District Instructional Leaders
replaced Lesson 1 with an
investigation.
(This might be a good lesson to co-teach.)
Statements to Explore
1. Multiplication is the same as
repeated addition.
2. Times means “groups of.”
3. A multiplication problem
can be shown as a rectangle.
4. You can reverse the order of
the factors and the product
stays the same.
5.You can break numbers apart
to make multiplying easier.
6. When you multiply two
numbers, the product is larger
than the factors.
Whole Numbers
(Always true, Never
True, Sometimes True)
Fractions
(Always true, Never
True, Sometimes True)
Lesson 2
• Since the DILs left it as is in ME . . .
– As a critical connoisseur of curriculum, what are
your thoughts?
Lesson 3
Let’s discuss . . .
Will the students be ready to work with a new model (area model) at this point?
If so . . .
• How might we make the rectangle area model more understandable?
• How might we modify Farm Fractions to make it more of a problem solving
experience?
If not . . .
• What additional modeling experiences will they need with the number line?
• How might the commutative property support students when looking at the
number line experience on TE 205 (student book 74)
• How might working with fraction strips enhance student access to multiplying
a fraction by a whole number?
• What additional number talks might help students find patterns and
relationships?
Lesson 4
• How might the use of fraction strips enhance the
experience in Activity 1?
• How might the “Reflect and Generalize” problems be
usable as a number talk?
• How might we use fraction strips to solve problems
similar to those in Activity 2 and guide students toward
a generalization about multiplying a fraction by a
fraction?
Additional
Experience
Recommended by
the District
Instructional
Leaders
Might be a good
lesson to co-teach.
Lesson 5
What is the focus standard in this lesson?
Which parts of this lesson can we weave together into a cohesive opportunity for
thinking deeply about mathematics?
What parts can we leave out?
Activity 1: Think about Simplification
How might we turn this into an experience where students “uncover” these
methods before we label them?
– Unit Fraction Method
– Multiply and then Simplify Method
– Simplify and then Multiply Method
Activity 2: Solve Multiplication Problems
–
How might we turn this into an opportunity for students to make
decisions about how they are multiplying and simplifying the problems?
Lesson 6: Multiply and Divide Mixed Numbers
• What is the key standard in this lesson?
• What makes sense to use from the book and from the PUSD
unit to give students a powerful mathematical experience?
• How else might we engage students in the mathematics so they
can construct understanding?
ME Unit 3:
Multiplication and Division with Fractions
Big Idea 2: Multiplication Links
Lesson 7: Relate Fraction Operations
Lesson 8: Solve Real World Problems
Lesson 9: Make Generalizations
Lesson 7: Relate Fraction Operations
The DILs recommend skipping this lesson.
Differentiation Intervention (Activity Card 3-7, TE p. 241): Predict
and Verify . . . Quite an interesting investigation. Might be worth
exploring.
The Challenge activity is also fairly interesting and definitely
challenging.
Lesson 8: Fraction Word Problems
• What is the key standard in this lesson?
• How might having students write word problems support their
thinking?
• How might a problem sort (greater than ___, less than ___)
support their thinking?
• How might using a visualization, representation, and sensemaking protocol support their thinking?
• How might the Trail Mix problem provide a rich context for
thinking about operations with fractions in-context?
• Look at the Differentiation Challenge Level (TE 253)
The Trail Mix Problem
How much of each ingredient will you need to feed the exact number of
students in your class?
Trail Mix
Trail mix is a healthy snack food. It got its name from
hikers and backpackers who ate it on their journeys.
You will need:
½ cup raisins
¾ cup peanuts
2/3 cup granola
½ cup dried fruit
2 tablespoons sunflower seeds
¼ cup M&Ms
Combine ingredients in bowl. Mix well. Scoop into
baggies for a snack on the go.
Serves 6
Lesson 9: Make Generalizations
• What is the key standard in this lesson?
• How might we turn this into a rich math
experience? (Could we design a game?)
• What number talk would lay a foundation for
thinking about scale factors?
ME Unit 3:
Multiplication and Division with Fractions
Big Idea 3: Division with Fractions
Lesson 10: When Dividing is also Multiplying
Lesson 11: Solve Division Problems
Lesson 12: Distinguish Multiplication from Division
Lesson 10: When Dividing Is Also
Multiplying
• What if we paralleled our introduction to
multiplication by doing the same investigation
with division . . .
– In Lessons for Multiplying and Dividing Fractions
by Marilyn Burns: Chapter 8, Introducing Division
of Fractions, p. 75
Division Statement
1. You can solve a division
problem by subtracting.
2. To divide two numbers, a ÷ b,
you can think, “How many bs
are in a?”
3. You can check a division
problem by multiplying.
4. The division sign (÷) means
“into groups of.”
5. The quotient tells “how many
groups” there are.
6. You can break the dividend
apart to making dividing easier.
Whole Numbers
(Always true, Never
True, Sometimes
True)
Fractions
(Always true, Never
True, Sometimes True)
Division Statement
7. Remainders can be
represented as whole numbers or
fractions.
8. If you divide a number by
itself, the answer is one.
9. If you divide a number by
one, the answer is the number
itself.
10. You can reverse the order of
the dividend and the divisor, and
the quotient stays the same.
Whole Numbers
(Always true, Never
True, Sometimes
True)
Fractions
(Always true, Never
True, Sometimes True)
Back to Lesson 10
• What is the key standard?
• What parts of the lesson support that standard?
• How can we modify the lesson so it is engaging and
allows students to construct conceptual understanding?
• How might fraction strips help?
How might Division Patterns (p. 84) and The Quotient Stays the
Same (p. 97) support the key ideas in this lesson?
(Multiplying and Dividing Fractions by Marilyn Burns)
Lesson 11: Solve Division Problems
• Activity 1: The “describe a situation” problems are
interesting. How might we make them even more
interactive? (Perhaps have a student write a situation and
another student has to figure out the problem that goes with it . . .
Kind of like a riddle.)
• Activity 2: How might we make this page of problems
more interesting? (Use the “less is more” principle)
Lessons 12 - 14
• What are the important elements of each lesson
according to the content standards?
• What is important to teach and what can be cut?
• How might we make the lessons more
interactive and meaningful?