Elementary Common Core
Team Training
Math Lesson
Summer 2013
Learning Goals


Increase knowledge of the Standards for
Mathematical Practices
Unpack the Common Core Standards using
Unpacking Standards Graphic Organizer
Success Criteria


Identify the Eight Mathematical Practices in a
lesson
Unpack Common Core Standards using the
Unpacking Document
Parking Lot Questions
“Good Math Students”
Think about a few students who
are “really good” in math.



How do they approach problems?
How do they solve problems?
How do they discuss their strategies?
“Common Core will have kids thinking out loud, discussing
solutions with each other, and explaining their answers.”
-Stateimpact.npr.org/florida/2013
Standards for
Mathematical Practice

What are they?

What do they look
like in a K-5
classroom?
Do You Know
The Mathematical Practices?
INDIVIDUALLY:
Take a moment and jot down the
Mathematical Practices on the
sticky note provided.
Do You Know
The Mathematical Practices?
WITH A PARTNER:
Pair-Share:
Share with your partner the list you
wrote down. Compare your lists.
Do You know
The Mathematical Practices?
Rate Yourself
What is your knowledge of the
Mathematical Practices today?
Place your sticky on the scale.
Do You Know
The Mathematical Practices?
Progression Scale
Level 4I can state all 8 Mathematical Practices and I use them daily
in my classroom.
Level 3I can state all 8 Mathematical Practices and I may use them
in my classroom.
Level 2I can state half of the Mathematical Practices.
Level 1I can state 2 of the Mathematical Practices.
Level 0What is a Mathematical Practice?
Standards for
Mathematical Practice
Mathematical Practices
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning
of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Standards for
Mathematical Practice
The Standards for
Mathematical
Practices describe
the behaviors of
mathematically
proficient
students.
Structure of Standards

Standards for Mathematical Practice
A set of 8 standards that describe the ways in
which the mathematical content standards should
be approached.

Standards for Mathematical Content
These standards define what students should
understand and be able to do in their study of
mathematics.
12
MP 1 - Make Sense of Problems and
Persevere in Solving Them
•
•
•
•
•
•
2b,
3c
Make sense of the meaning of the task
Find an entry point or a way to start the
task
Focus on concrete manipulatives before
moving to pictorial representations
Develop a foundation for problem-solving
strategies
Reexamine the task when they are stuck
Ask, “Does my answer make sense?”
What does MP 1 look like in a
classroom?
“Old” problem (little or no rigor)
Tina had ten balloons. She gave seven of
them away. How many balloons did Tina
have then?
“New” problem (with rigor)
Burger Barn has one small table that can
seat four people. They also have one large
table that can seat double that amount.
Fifteen (15) people came in at lunch time.
How many people did not get a seat?
14
MP 2 - Reason Abstractly and
Quantitatively
•
•
•
•
15
Make sense of quantities and their
relationships
Decontextualize
Contextualize
Represent symbolically (ie. Equations,
expressions)
3c
What does MP 2 look like in a
classroom?
I had two pencils. My mom gave me
some more. Now I have five pencils.
How many pencils did my mom give
me?
Decontextualize the problem:
2+□=5
16
What does MP 2 look like in a
classroom?
2+□=5
Contextualize the problem:
I had two pencils. My mom gave me
some more. Now I have five pencils.
How many pencils did my mom give
me?
17
What does MP 2 look like in a
classroom?
How many buses are needed for 99 children to
go on a field trip if each bus seats 44 students?
99÷44
Is the answer: 2r11 or 2¼ or 2.25?
Recontextualize to get the answer: 3 buses
18
MP 3 - Construct Viable Arguments and
Critique the Reasoning of Others
2a, 3b, 3c
•
•
•
•
•
19
Use mathematical terms to construct
arguments
Use definitions and previously established
solutions in their arguments
Engage in discussions about problemsolving strategies
Recognize and discuss reasonableness of
strategies
Recognize and discuss similarities and
differences between strategies
What does MP3 look like in a
classroom?

I can make a plan, called a strategy, to
solve the problems and discuss other
students’ strategies too.
http://insidemathematics.org/index.php/classroom-videovisits/public-lessons-proportions-a-ratios/205-proportions-aratios-problem-3-part-d?
MP 4 - Model with Mathematics.
2e, 3c
•
•
•
•
•
•
21
Model with manipulatives and much more
Model with a number sentence or equation
Check to make sure the number sentence
matches the context of their problem
Model with concrete manipulative
representations
Model with pictorial representations
Have matching equations for their
representations
What does MP 4 look like in a
classroom?
Model with
Symbols
Model with
Tools
Model with
Pictures
22
I have three
cars. My friend
gives me some
more cars. Now I
have seven cars.
How many toy
cars did my
friend give me?
3+□=7
Model with
Words
I have three cars.
I get four more.
Now I have seven
cars.
Break
MP 5 - Use Appropriate Tools Strategically
2c, 2e
The purpose is to move students toward a
deeper understanding of these tools.
• Have access to a variety of tools
•
24
(counters, place value blocks, hundred
boards, number lines, geometric shapes,
paper/pencil, etc…)
Need to express in their own words the
“what, why, and how” to help them clarify,
perfect, and organize their thinking.
What does MP 5 look like in a
classroom?
•
•
Students have easy access to
math tools.
Students select their own tools.
25
MP 6 – Attend to Precision
2b
•
•
•
•
26
Communicate precisely with teachers and
peers (written and verbal)
Clearly define terms
Identify the meanings of mathematical
symbols and use them appropriately
Specify units of measure
What does MP 6 look like in a
classroom?
How might a student explain their solution
to the subtraction problem shown below?
413
-168
27
MP 7 - Look for and Make Use of
3c
Structure
•
•
•
•
28
Look for patterns
Recognize mathematical structures
Generalize to other problem situations
Simplify complex problems
What does MP7
look like in a
classroom?
53 + 23 = ?76
82 - 14 = ?
82 - 14 = 68
29
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9 10
19 20
29 30
39 40
49 50
59 60
69 70
79 80
89 90
99 100
MP 8 - Look for and Express Regularity
3b
in Repeated Reasoning
•
•
•
30
Look for regularity in problem structures
when solving mathematical tasks
Maintain oversight
Check for reasonableness during and
after task
What does MP 8 look like in a
classroom?
Doubles Plus One
Decompose 7
Add the double
Add one more
6 + 7 =13
6
1
12 + 1 = 13
31
Identify Mathematical
Practices
Try to identify as many examples of the
mathematical practices in action as
possible as you view this video of a
kindergarten class.
32
“If the Standards for Mathematical
Practice are not in place, well then,
you’re not really using the
Common Core.”
– Phil Daro, Common Core author Mathematics
Let’s take a Break…
Do You Know
The Mathematical Practices?
Rate Yourself
Take a moment and jot down the
Mathematical Practices on the sticky
note provided.
Place your sticky on the scale.
Handouts
Observing Mathematical Practices in a
Classroom
 Questions to Develop Mathematical
Thinking correlated to the SMP
 SMP in Student Friendly Language
 SMP Unpacked by Grade Level
 Depth of Knowledge Chart
 3rd Grade Quarter 1 Placemat
 Unpacking Documents

Question to Ponder


What does it mean
to “really
understand”?
What are indicators
of knowledge
without
understanding?

What are concrete
indicators of really
understanding
something?

What can the
person with
understanding do
that the person
with only
knowledge cannot
do?
Be able to KNOW and
UNDERSTAND
What we want students to
know






Vocabulary
Definitions
Concepts
Key facts
Critical details
Laws, formulas
What we want students to
understand





Decoding
Computation
Communication skills
– listening, speaking,
writing
Thinking skills –
compare, confer,
analyze
Research – inquiry,
investigate
Unpacking Standards
1c
 Why
unpack?
•
Standards require a close read and analyze
for meaning
•
Standards are rarely taught in isolation
•
Not all standards are equal in rigor
Standard
MACC.5.NBT.2.6
Find wholenumber
quotients of
whole numbers
with up to fourdigit dividends
and two-digit
divisors, using
strategies based
on place value,
the properties of
operations,
and/or the
relationship
between
multiplication
and division,
illustrate and
explain the
calculation by
using equations,
rectangular
arrays, and/or
area models.
What Students Students Will
What Students
Need to
Be able To
Need to Know
Understand
Student
Friendly
Language
Standard
MACC.5.NBT.2.6
Find wholenumber
quotients of
whole numbers
with up to fourdigit dividends
and two-digit
divisors, using
strategies based
on place value,
the properties of
operations,
and/or the
relationship
between
multiplication
and division,
illustrate and
explain the
calculation by
using equations,
rectangular
arrays, and/or
area models.
What Students Students Will
What Students
Need to
Be able To
Need to Know
Understand
Whole-number
quotients
Four-digit
dividends
Two-digit
divisors
Strategies
Place value
Properties of
operations
Multiplication
Division
Equations
Rectangular
Arrays
Area Models
Student
Friendly
Language
Standard
MACC.5.NBT.2.6
Find wholenumber
quotients of
whole numbers
with up to fourdigit dividends
and two-digit
divisors, using
strategies based
on place value,
the properties of
operations,
and/or the
relationship
between
multiplication
and division,
illustrate and
explain the
calculation by
using equations,
rectangular
arrays, and/or
area models.
What Students Students Will
What Students
Need to
Be able To
Need to Know
Understand
Whole-number
quotients
Find
Four-digit
dividends
Use
Two-digit
divisors
Illustrate
Strategies
Place value
Properties of
operations
Multiplication
Division
Equations
Rectangular
Arrays
Area Models
Explain
Student
Friendly
Language
Standard
MACC.5.NBT.2.6
Find wholenumber
quotients of
whole numbers
with up to fourdigit dividends
and two-digit
divisors, using
strategies based
on place value,
the properties of
operations,
and/or the
relationship
between
multiplication
and division,
illustrate and
explain the
calculation by
using equations,
rectangular
arrays, and/or
area models.
What Students Students Will
What Students
Need to
Be able To
Need to Know
Understand
Whole-number
quotients
Find
Four-digit
dividends
Use
Two-digit
divisors
Illustrate
Strategies
Place value
Properties of
operations
Multiplication
Division
Equations
Rectangular
Arrays
Area Models
Explain
Use various
strategies to
divide
Interpret
remainders
Explain the
strategy used
Student
Friendly
Language
Standard
MACC.5.NBT.2.6
Find wholenumber
quotients of
whole numbers
with up to fourdigit dividends
and two-digit
divisors, using
strategies based
on place value,
the properties of
operations,
and/or the
relationship
between
multiplication
and division,
illustrate and
explain the
calculation by
using equations,
rectangular
arrays, and/or
area models.
What Students Students Will
What Students
Need to
Be able To
Need to Know
Understand
Whole-number
quotients
Find
Four-digit
dividends
Use
Two-digit
divisors
Illustrate
Strategies
Place value
Properties of
operations
Multiplication
Division
Equations
Rectangular
Arrays
Area Models
Explain
Use various
strategies to
divide
Interpret
remainders
Explain the
strategy used
Student
Friendly
Language
I can solve
division
problems
using
different
strategies.
I can explain
my strategy.
Your turn!



Form groups with 35 participants in
each group.
Each group will be
given five 3rd grade
standards from
chapter1.
Each group member
should unpack at
least one standard.



Share your unpacked
standards with your
group members.
Look for similarities
and/or differences in
these standards.
Groups should share
their discoveries.
Break
If you find it difficult to distinguish between
the “KNOW” and the “UNDERSTAND” it is
likely because, as written, the learning
sequence focuses only on facts and skills.
-Catherine Brighton
Model for Instructional
Planning
Course
Descriptions
Learning
Goals
Lesson
Plans
48
• “Chunk” the standards to identify 10 to 12 critical areas
of focus or big ideas.
• Integrate standards across content areas as appropriate.
•Define 10 to 12 major learning goals based upon the “chunks” of
integrated standards from the course description.
•Develop learning progression scales to describe the steps students
will take to attain each learning goal as well as what success looks
like at each step.
•Use the learning progressions to guide lesson development;
include formative assessment tasks as part of the instructional
plan, identify resources in advance, and incorporate the use of
technology as a tool for learning when applicable.
•Use the formative assessment data to revise and/or differentiate
instruction as appropriate to meet the needs of ALL students.
Content Standards
MACC.4.NBT.1.1: Recognize that in a multi-digit whole
number, a digit in one place represents ten times what it
represents in the place to its right.
For example, recognize that 700 ÷ 70 = 10 by applying
concepts of place value and division.
MACC.4.NBT.1.2 : Read and write multi-digit whole numbers
using base-ten numerals, number names, and expanded form.
Compare two multi-digit numbers based on meanings of the
digits in each place, using >, =, and < symbols to record the
results of comparisons.
MAACC.4.NBT.1:3 Use place value understanding to round
multi-digit whole numbers to any place.
Learning Goal:
1c
Students will be able to solve problems using
place value understanding to read, compare, and
round multi-digit numbers by:
• Recognizing a digit in one place represents ten
times what it represents in the place to its right.
• Reading and writing whole numbers using baseten numerals, number names, and expanded
form.
• Comparing two numbers based on the meaning
of the digits in each place.
• Using symbols to record comparisons.
• Rounding whole numbers to any place using
place value understanding.
Wrap – Up
 Exit
Pass: How
are you going to
share with your
school the MP,
Unpacking the
Standards, and
Learning Goals?