Transcript What`s That Portion? Investigations Unit 4

What’s That Portion?
Investigations Unit 4
5th Grade Math Alliance Meeting
Beverly Woods Elementary
What is the Math in this Unit?
What do the students need to know
before teaching this unit?
What understanding should they
develop while studying this unit?
Think about how this unit addresses
the Common Core standards……..
Investigation 1: Using
Percents and Fractions
1.1 Everyday uses of Fractions, Decimals and
Percents
1.2 Relating Percents and Fractions
1.3 Finding percents of an area
1.4 Percent equivalents for thirds and sixths
1.5 Assessment: Solving problems with
fractions and percents
Everyday Uses of Fractions,
Decimals and Percents
Make a list of the everyday uses of
fractions, decimals, and percents
Keep a chart of Conjectures about Fractions…
p.48 Unit Guide
Relating Percents and
Fractions
Play “Guess My Rule”
Finding Percents of an Area
Percent Equivalents for
Thirds and Sixths
1.How does an understanding of what 5/6
means, help you figure out the percent
equivalent????
2.Which is greater 5/6 or 3/4?
How do you know?
Assessment:
Solving Problems with Fractions
and Percents
• How many twentieths is one fourth? 1/4 = ?/20
• Eleven of what is one fourth? 1/4 = 11/?
• What if the denominator were 200? 1/4 = ?/200
• What if the numerator were 5? 1/4 = 5/?
Investigation 2:
Comparing and Ordering
Fractions
2.1 Percent equivalent strips
2.2 Comparing fractions
2.3 Ordering fractions
2.4 Solving problems with fractions and
percents
2.5 Solving problems with fractions and
percents (continued)
2.6 Assessment: Using fractions and
percents
Percent Equivalent Strips
Fill in halves, thirds, fourths, fifths,
sixths and eighths
Look at Math Note on p.59- fractions
in simplest form or lowest terms- not
reduced fractions
Comparing Fractions
Which fractions could you compare on
the 4 x 6 rectangles?
Suppose you wanted to compare 3/5
and 7/12. Which rectangle would you
use? Why?
How about 3/8 and 1/3?
Ordering Fractions
Play the game “In Between”……….
http://illustrativemathematics.org/
Solving Problems with
Fractions and Percents
Can 1/4 be greater than 1/2?
Fractional Parts of a
Whole
• If the yellow hexagon represents one
whole, how might you partition the
whole into equal parts? Name the
fractional parts with unit fractions
Fractional Parts of a Whole
• One blue rhombus = 1 whole
What is the value of the red trapezoid,
the green triangle and the yellow
hexagon?
•
Show and explain your answer
Identifying Fractional
Parts of a Whole
• What part is red?
16
Create the whole if you
know a part…
• If the blue rhombus is ¼, build the
whole.
• If the red trapezoid is 3/8,
build the whole.
Investigation 3:
Adding and Subtracting Fractions
3.1 Fractions on clocks
3.2 Using a clock to add fractions
3.3 Assessment: Adding fractions
3.4 Fraction Tracks
3.5 Fraction Tracks (continued)
3.6 The Fraction Track Game
3.7 Addition and Subtraction Problems and games
part 1
3.8 Addition and Subtraction Problems and games
part 2
3.9 Addition and Subtraction Problems and games
part 3
3.10 End-of-Unit Assessment
Fractions on the Clock
Use the clock to add
and subtract fractions
Play “Roll Around the Clock”
The Fraction Track Game
Play the game to “1” first,
and then use the whole
board
Homework…..
Please bring some samples of student
work that demonstrate mastery,
partial mastery, and non-mastery of
any of the following pages:
SAB pp. 21, 24, 26, 33, 40, 48 or M20
What’s Next????
•
•
•
•
What worked well/what didn’t??
I still need…..
A look at student work samples
Multiplication and division of fractions
[email protected]
980-343-2792
What’s That Portion?
Investigations Unit 4
5th Grade Math Alliance Meeting
Beverly Woods Elementary
Session 2
Warm Up Problem
How many different fraction models
can be used to show
5/4?
Draw your models!
Was this one of your model types?
Understand a fraction a/b as a multiple
of 1/b
5
is the product of
4
5
4
1
=5x 4
5
1
x( )
4
A Look at Student Work
What is
1/5 + 2/3?
Show your
work……
Common Misconceptions when
Multiplying and Dividing Fractions
»Multiplication does not always make
things bigger
»Multiplication is not “just” repeated
addition
»The meaning of “times” 3 x 4 = 4 x 3.
Are they the same? (think about
groups)
Common Misconceptions continued
• Translating multiplication expressions like
5 x 6 could be 5 groups of 6 or
5 taken 6 times
• We need pictorial representations when it
comes to fractions!!- the idea of
• 1/2 taken 1/4 times makes no sense.
1/2 a group of 1/4 makes more sense.
• If students can connect multiplication
equations to real things, it will help
them make sense of problems
More Misconceptions…
•
Students shouldn’t be focused on
just the numbers, but make sense
of the magnitude of the fractions.
Example: 3 1/2 x 3 1/2
The answer can’t be more
than 4 x 4 or less than 3 x 3.
There is a real connection
between multiplication and
division of fractions (they
are not just opposites)
Example:
10 x 1/2 is the same thing as 10 ÷ 2
Critical Area:
Fraction Operations
• The meaning of each operation on fractions is
the same as the meaning for the operations
on whole numbers
―
X
+
÷
• For division of fractions, it is useful to think
of the operation as partitioning
Investigation 4A:
Multiplying and Dividing
Fractions
4A.1: Multiplying a whole number by a fraction
4A.2: Multiplying whole numbers by fractions and mixed
numbers
4A.3: Multiplying fractions or mixed numbers
4A.4: Multiplying fractions by fractions
4A.5: A rule for multiplying fractions
4A.6: Using arrays for multiplying fractions
4A.7: Assessment: Multiplying fractions and multiplying mixed
numbers
4A.8: Dividing a whole number by a fraction
4A.9: Dividing a fraction by a whole number
4A.10: Assessment: Dividing with fractions
Multiplying a Whole Number
by a Fraction
The Big Bicycle Race
Use of Fraction Bars
And Writing Equations
Multiplying Whole Numbers by
Fractions and Mixed Numbers
Mitch is riding his bike 90 miles. He’s
gone 2/3 of the way. How many miles
has he gone?
Multiplying Fractions or
Mixed Numbers
The bike path is 15 miles long. Hannah
bikes 2 ½ times the length of the
path. How many miles does she bike?
Why is this still considered
multiplication? (CC p.42) it is still
“groups of”
Multiplying Fractions by Fractions
Shading fraction bars
½ of ½
Fill in the table…….
A Rule for Multiplying Fractions
The rule is easy….Why don’t we just
teach them the rule?
Using Arrays for Multiplying Fractions
(paper folding)
1/4
1/2
1/8
1/4
1/8
1/4
1/8
Notice the labeling!!!!
From Paper Folding to
the Open Array
Assessment: Multiplying Fractions and
Multiplying Mixed Numbers
Do students need to use a
representation???
Turn and Talk……….(notice Teacher
Note on page CC p67)
Another way of looking at multiplying a
whole number times a fraction
•Understand a multiple of a/b as a multiple of 1/b,
and use this understanding to multiply a fraction by a
whole number
2
1
3 sets of 5 is the same as 6 sets of
5
Dividing a Whole Number
by a Fraction
What does 6 ÷ ½ mean?
Notice the STUDENT REASONING!!!!!
Dividing a Fraction
by
a Whole Number
Use of the Array again….
½÷3
?
Assessment:
Dividing with Fractions
Is multiplication or division of fractions
harder? Why do you think so?
Turn and talk!
(Note the student dialogue on p.CC81)
Check out the Teacher Note CC p82
Homework…..
Please bring some student work:
An example of mastery, partial
mastery and non-mastery of either
the multiplication or division
assessment.
What’s Next????
•
•
•
•
What worked well/what didn’t??
I still need…..
A look at student work samples
More multiplication and division of
fractions (and also decimals)
[email protected]
980-343-2792