Welcome to the
Common Core
Summer Institute
for
Fourth Grade!
June 26th- June 28th
Click
Welcome
Sign
-Lexi and Shanna
• Be engaged! You deserve
the opportunity to learn
and collaborate with
colleagues.
• Use our parking lot for
questions, comments, and
concerns.
This could happen to you if your not
prepared for the CORE!
Numbers and
Operations /Fractions
Today we will look at the content standards
from Numbers and Operations /Fractions.
Our work today focuses on:
*Highlighting the BIG IDEAS in the 4th
grade content standards
*Linking these BIG IDEAS with the Math
Practice Standards
*Examining how Investigations lessons fully
support the Common Core State Standards
for 4th grade
Task
2/3 of an apple is used to make an
apple pie. We need to make 9
apple pies. How many apples do
we need?
Be sure to include an equation and visual
representation to match your solution!
Task
2/3 of an apple is used to make an
apple pie. We need to make 9
apple pies. How many apples do
we need?
Be sure to include an equation and visual
representation to match your solution!
• Fact: Fraction concepts are
difficult
• Fact: Our students (and many
adults) struggle with fraction
concepts.
• Fact: What we have been doing
isn’t working
• Fact: The Common Core is
grounded in research about
how students come to
understand fraction concepts.
We would like two
volunteers to show how
they solved this problem
2/3 of an apple is used to make an
apple pie. We need to make 9 apple
pies. How many apples do we need?
• Fractions are a part of our
everyday lives.
• Fraction work begins in 1st
grade
• The foundation for a child’s
conceptual understanding of
fractions begins with
partitioning and sharing.
• Students need practice
partitioning unmarked regions
Pre-partitioned regions lead
to a common misconception
In K-2 Common Core
fraction work….
Students are…
Students used to but
are NOT……
•Partitioning (splitting)
a region (circle,
rectangle, square) into
2, 3 or 4 equal regions
•Communication about
processes, content,
vocabulary words.
•Sharing sets equally
•Working with sets or
multiple objects
•Writing fractions and
fraction bars
•Learning “numerator”
and “denominator”
Partitioning
• K-2: Regions
• 3: Regions and Number lines
• 4:Strengthen Number lines,
regions beginning to phase out
• 5: Number lines
Directions for math tasks:
•
Task
Please take 20 minutes to rotate around the room with your group
to work on the following tasks. Please have a meaningful discussion
of how each task connects with the Common Core and how you
could implement these tasks in your classrooms.
Lexi ate ¾ of
her yogurt
container.
Shanna ate
3/8 of her
yogurt
container.
They both ate
the same
amount of
yogurt.
Explain…
How can ½ be
represented by
5 in one
instance and 7
in another? In
other words,
½ = 5 and ½ = 7
Why?
List
combinations of
fractions that
equal 1 whole
Ex: ¾ + 1/8 + 1/8 =1
Task
Lexi ate ¾ of
her yogurt
container.
Shanna ate
3/8 of her
yogurt
container.
They both ate
the same
amount of
yogurt.
Explain…
How can ½ be
represented by
5 in one
instance and 7
in another? In
other words,
½ = 5 and ½ = 7
Why?
List
combinations of
fractions that
equal 1 whole
Ex: ¾ + 1/8 + 1/8 =1
15 Minute Break
http://www.youtube.com/watch?v=6i5_EopdUGc
Please come back in a timely fashion!
As a group, look through your Common Core
State Standards: 4.NF.1 - 4.NF.7 (pages 2032 in Unpacking document)
Locate the BIG IDEAS (main concepts, most
important) and list them on your poster.
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 1?
Standard - CC.4.NF.1 Explain why a fraction
a/b is equivalent to a fraction (n × a)/(n ×b) by
using visual fraction models, with attention to
how the number and size of the parts differ
even though the two fractions themselves are
the same size.
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 2?
Standard - CC.4.NF.2 Compare two fractions
with different numerators and different
denominators, e.g., by creating common
denominators or numerators, or by comparing to
a benchmark fraction such as 1/2. Recognize
that comparisons are valid only when the two
fractions refer to the same whole. Record the
results of comparisons with symbols >, =, or <,
and justify the conclusions, e.g., by using a visual
fraction model. (Grade 4 expectations in this
domain are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the big ideas of standard 3?
Standard - CC.4.NF.3 Understand a fraction a/b with a > 1 as a sum of
fractions 1/b. (Grade 4 expectations in this domain are limited to
fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
a. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
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 decompositions, e.g., by using a visual fraction
model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 +
1 + 1/8 = 8/8 + 8/8 + 1/8.
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.
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 4?
a.
b.
c.
Understand a fraction a/b as a multiple of 1/b. For example, use a
visual fraction model to represent 5/4 as the product 5 × (1/4),
recording the conclusion by the equation 5/4 = 5 × (1/4).
Understand a multiple of a/b as a multiple of 1/b, and use this
understanding to multiply a fraction by a whole number. For
example, use a visual fraction model to express 3 × (2/5) as 6 ×
(1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n ×
a)/b.)
Solve word problems involving multiplication of a fraction by a
whole number, e.g., by using visual fraction models and equations to
represent the problem. For example, if each person at a party will
eat 3/8 of a pound of roast beef, and there will be 5 people at the
party, how many pounds of roast beef will be needed? Between
what two whole numbers does your answer lie?
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 5?
Standard - CC.4.NF.5 Express a fraction with
denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two
fractions with respective denominators 10 and 100. For
example, express 3/10 as 30/100 and add 3/10 + 4/100 =
34/100. (Students who can generate equivalent fractions
can develop strategies for adding fractions with unlike
denominators in general. But addition and subtraction
with unlike denominators in general is not a requirement
at this grade.)
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 6?
Standard - CC.4.NF.6 Use decimal notation
for fractions with denominators 10 or 100. For
example, rewrite 0.62 as 62/100 ; describe a
length as 0.62 meters; locate 0.62 on a number
line diagram. (Grade 4 expectations in this
domain are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Let’s review some of the big ideas per by
each standard.
During our discussion did we cover the
big ideas of standard 7?
Standard - CC.4.NF.7 Compare two decimals
to hundredths by reasoning about their size.
Recognize that comparisons care valid only when
two decimals refer to the same whole. Record
the results of comparisons with the symbols >, =,
or <, and justify the conclusions, e.g., by using a
visual model. (Grade 4 expectations in this
domain are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Game Time!
Tossing Fraction Tiles
Concept addressed: 4.NF.3
A.
B.
Understand addition and subtraction fractions as
joining and separating parts referring to the
same whole.
Decompose a fraction into a sum of fractions
with the same denominator in more than one way,
recording each decomposition by an equation.
Let’s refer to BOB
(aka: The Back of the Book)
• D
Pages 151-156
HOW IS YOUR MATH
REASONING?
MATH REASONING!
Please solve the following
problem
MATH REASONING!
Roles:
1 teacher
1 student
Please solve the following
problem
MATH REASONING!
Roles:
1 teacher
1 student
Please solve the
following problem
MATH REASONING!
Roles:
1 teacher
1 student
MATH REASONING!
Now, let’s take a look at
our CMS students and
how they reason
mathematically!
Time for Lunch
http://www.youtube.com/watch
?v=CoxNc-atJ14
Beyond Pizzas & Pies
Chapter 2
Silently read and then turn and talk to a neighbor
New Common Core Lesson
3A.1 and 3A.2
• Multiplying a whole number
by a fraction
• Use visual models to solve
word problems involving
multiplication of a fraction
and a whole number
Counting Around the Class: Let's count
around the class by 1/4s. Say each
number as a fraction, not a mixed
number. Keep track of the fractions on
the number line.
Pizza Pizza
• Jake bought three kinds of pizza
for a party. Each pizza was the
same size. People were not very
hungry, and at the end of the
party there was ¾ of each pizza
left. How much pizza was left in
all?
Write an equation and solve using a picture
and a number line
Group work
Please work on numbers 2-4 on page 44D.
Be sure to include:
•
•
•
•
Equation
Number line representation
Picture representation
Story problem context for numbers 3
and 4
Egg Carton Time!
(1) Eggs come in cartons of 12. Richard was making
cakes for a party and used 2 cartons of eggs.
How many eggs did he use?
(2) Sabrina was making a cake for herself. She used
¼ of a carton of eggs. There are 12 eggs in each
carton. How many eggs did she use?
Number of
Cartons
(1)
(2)
Number of
Eggs in a
Carton
Number of
Eggs
Equation
Directions for math tasks:
•
Please take 20 minutes to rotate around the room with your
group to work on the following tasks. Please have a meaningful
discussion of how each task connects with the Common Core and
how you could implement these tasks in your classrooms.
The water
balloon both
has ¾ of a
gallon left.
They need to
fill 5 balloons.
How much
water should
they use for
each balloon?
Amy is serving
strawberry ice
cream. Each
scoop contains
¼ of a cup. By
the end of her
first shift, she
has scooped
out 4 servings.
How much ice
cream has she
served?
Glow sticks are
a popular
carnival prize.
A box of glow
sticks weighs ¼
of a pound. If
I am carrying 7
pounds, how
many boxes am
I carrying?
Task
Solve the school carnival tasks at your table.
Represent your solutions on a number line
and model each with an equation.
The water
balloon both
has ¾ of a
gallon left.
They need to
fill 5 balloons.
How much
water should
they use for
each balloon?
Amy is serving
strawberry ice
cream. Each
scoop contains
¼ of a cup. By
the end of her
first shift, she
has scooped
out 4 servings.
How much ice
cream has she
served?
Glow sticks are
a popular
carnival prize.
A box of glow
sticks weighs ¼
of a pound. If
I am carrying 7
pounds, how
many boxes am
I carrying?
15 Minute Break
Please come back in a timely fashion!
http://www.youtube.com/watch?v=D7QsgSpaoH8
Making Fraction Cards
Use the list of “Fractions for Fraction Cards”
from SAB page 27 (Page 72 in your Teacher’s
Manual – Unit 6) to create fraction cards at your
table.
Work with 2 or 3 partners to create ALL fraction
cards. You may use the square template at
your table or create your own representations.
After, play Capture Fractions with your group.
(Directions are on the yellow sheet.)
Making Fraction Cards
What did you learn as you made these?
What learning would be taken away if these
were handed to you already finished?
What are some benefits of making mistakes?
How does playing these games
connect back to the standards?
How can we enrich and or adjust
this game to meet the needs of
all learners, without jeopardizing
their understanding of the
standard(s) and MPs?
1:1:1Exit
Write down and share
• 1 thing you learned
• 1 idea you will use in your classroom
• 1 question you still have
• Tomorrow you will Report to Room __
alexis.picciano@cms.k12.nc.us
shanna.rae@cms.k12.nc.us