A Look at Standards for
Mathematical Practice, Grades K-2
Learning Intentions
We Are Learning To:
 Recognize how Mathematical Practices
1, 2 and 5—sense making, reasoning,
and tools—are connected to a selected
standards’ content progression for
learning basic facts.
 Identify how students will develop and
demonstrate Practices 1, 2 and 5 in their
work and discussions.
Success Criteria

We will know we are successful when
we can articulate how Mathematical
Practice Standards 1, 2 and 5—sense
making, reasoning, and tools—are
infused in mathematical tasks or lessons
for a standards’ content progression.
Wisconsin
Common
Core
Standards
Getting started…

Mentally compute the answer to the
following…
No pencil
1005 – 998
54 + 48
or paper
please!
Turn and share your strategy.
 Why
does your strategy work?
 What
do you understand about
number relationships that allow you
to mentally compute answers?
 How
does this understanding grow
in young children?
Wisconsin CCSS
 Standards
for Mathematical Practice
8
Practices
 Describe ways in which students ought
to engage with mathematics.
 Mathematical
 21-26
Content Standards
Content Standards per grade, K-2
 Describe what students should
understand and be able to do
Guidance from CCSS
 Review
the Key Standards for
Mathematical Practices for our
work today.
 What
sounds familiar as you glance
through these practices?
Mathematical Practices
The Mathematical Practices rest on
“important ‘processes and proficiencies’ with
longstanding importance in mathematics
education” (CCSS, 2010, p. 6).

National Council of Teachers of Mathematics
(NCTM, 2000) Process Standards

National Research Council (NRC, 2001)
Strands of Mathematical Proficiency (Adding It Up)
Domain
Content strand across grades:
Operations & Algebraic Thinking
Cluster
“Big Idea” that groups together
a set of related standards.
Standards
Statements that define what
students should understand and
be able to do at a grade level.
A Content Standards Progression
Domain: Operations and Algebraic Thinking (OA)
Clusters:
K:
Understand addition as putting together and
adding to, and understand subtraction as taking
apart and taking from.
1:
Understand and apply properties of operations
and the relationship between addition and
subtraction.
1&2: Add and subtract within 20.
Standards: K.OA.3; K.OA.4; 1.OA.4; 1.OA.6; 2.OA.2
Let’s start with the end in mind…

Standard 2.OA.2:
Fluently add and subtract within 20 using mental
strategies. By end of Grade 2, know from
memory all sums of two one-digit numbers.
“Acquiring proficiency in single-digit arithmetic
involves much more than memorizing.”
(Adding It Up, NRC,

2001, p. 6)
What is that “more” and how do we help
students get there?
Laying the Foundation in PK-K
K.OA.3
Decompose numbers less than or equal to 10 into
pairs in more than one way, e.g., by using objects
or drawings and record each decomposition by a
drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.4
For any number from 1 to 9, find the number that
makes 10 when added to the given number, e.g.,
by using objects or drawings, and record the
answer with a drawing or equation.
Prompting quantitative reasoning
a.k.a “number relationships”
 Dot
Patterns & Ten Frames
 Play
“Flash”
 How many dots did you see?
 How did you see it?
 What’s
the math?
Dot Pattern
How many dots?
How did you see it?
How many dots?
How did you see it?
How many dots?
How did you see it?
Ten Frames
Ten frames show relationships of small
numbers to five and ten.
How many dots?
How did you see it?
How many dots?
How did you see it?
How many dots?
How did you see it?
Laying a foundation for understanding
Morgan, Dot Plates, & Ten Frames
Enjoy!
Through the lens of the Math Content
K.OA.3: Decompose numbers less than or equal to
10 into pairs in more than one way, e.g., by using
objects or drawings…
K.OA.4: For any number from 1 to 9, find the number
that makes 10 when added to the given number,
e.g., by using objects or drawings...
What is Morgan understanding
and what is she able to do?
Through the lens of the Math Practices

Make sense of problems and persevere
in solving them.

Reason abstractly and quantitatively.

Use appropriate tools strategically.
How is Morgan engaged in these
practices while working with the
content of decomposing numbers?
Guidance from CCSS
 Review
the Grade 1 and Grade 2
Key Standards for Mathematical
Content in regards to our work today.
 Small
Group Discussion:
 What’s
familiar? What’s new?
 How much emphasis is given to
“mental strategies” in your curricula
and classroom?
Grade 1: Content Standard 1.OA.6
Add and subtract within 20, demonstrating fluency
for addition and subtraction within 10.
Use strategies such as counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
decomposing a number leading to a ten (e.g., 13 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship
between addition and subtraction (e.g., knowing
that 8 + 4 = 12, one knows 12 - 8 = 4); and
creating equivalent but easier or known sums
(e.g., adding 6 + 7 by creating the known
equivalent 6 + 6 + 1 = 12 + 1 = 13).
Strategies for Single Digit Addition
 Make
 Use
a ten.
an easier “equivalent” problem.
Use doubles
Use fives
Use a helping fact
8+6
Put 8 counters on your
first frame & 6 counters
on your second frame.
Strategies:
 Make a ten.
 Use a double.
 Use fives.
 Use some other
equivalent problem.
Make a ten: 8 + 6
How could you
make a ten?
Make a ten: 8 + 6
How could you
make a ten?
Move 2 counters
to the top frame.
Then you have 10
and 4 more counters.
Write an equation.
8 + 6 = 8 + 2 + 4 = 10 + 4 = 14
Use a double: 8 + 6
What doubles
might you use?
Reason 6 + 6 = 1
12.
Then add 2 more.
Write an equation.
8+6=6+6+2=
12 + 2 = 14
Use fives: 8 + 6
Can you see some
fives? Where?
Reason: 5 + 5 is 10;
need to add 3 more
and 1 more.
Write an equation.
8+6=5+5+3+1
= 10 + 4 = 14
7+9
6+7
Select a problem.
 Draw a strategy card for the group.
 Everyone uses ten frames and counters to
reason through the strategy and writes an
equation(s) that shows the reasoning.
 Share, compare, and discuss as a group.
 Repeat with another strategy card.

Reflect: Which strategies seem
to work best for each problem?
Decompose to ten: 15 – 6

Place 15 counters on
the double ten frame.

Completely fill one
frame, place 5 on the
other frame.
Decompose to ten: 15 – 6

How can you remove
6 counters in parts by
decomposing it in a
way that gets you to
or “leads to a ten”?
Remove 5 counters
to get to ten.
 Remove 1 more.


Write an equation.
15 – 5 – 1 = 9
or 15 – 5 = 10; 10 – 1 = 9
Try it:
13 – 5
16 – 7
 Use
ten frames and counters to reason
through the “Decompose to Ten” strategy.
 Write an equation(s) to show the reasoning.
 Share and discuss in your small group.
--------------------------- Brainstorm:
What other subtraction facts
would lend themselves well to this strategy?
Make a list of facts and try them out.
Reflect
 How
do these tasks engage you in the
content learning infused with practices?
(Mathematical Practices Standards 1, 2, 5)
 How
do these tasks help you to better
understand the mathematics?
(Content Standards K.OA.4, K.OA.5, 1.OA.6)
Checking in…

Standard 2.OA.2:
Fluently add and subtract within 20 using mental
strategies. By end of Grade 2, know from
memory all sums of two one-digit numbers.
“Acquiring proficiency in single-digit arithmetic
involves much more than memorizing.”
(Adding It Up, NRC,

2001, p. 6)
What is that “more” and how do we
help students get there?
What other
practices
were
infused
in the
content
learning?
Provide
specific
examples.
Summary
We were learning to recognize three of the
Standards for Mathematical Practices—sense
making, reasoning, and tools— within a chosen
Content Standards progression.
We will know we are successful when we
can articulate how both a Content Standard
and a Standard for Mathematical Practice are
infused in a math lesson in the classroom.