Make sense of problems and persevere in
solving them.
When given a problem, I can make
a plan to solve it and check my
answer.
Mathematical Practice 1
5
4
3
2
1
0
180°
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
BEFORE...
Think about the
problem.
THINK!
Make a plan to
solve the
problem.
DURING...
Don't give up!
AFTER...
CHECK my work.
Does this
make sense?
Is there another
way to solve
the problem?
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Jordan School District 2012, Grades K-1 Reason abstractly and quantitatively.
I can use numbers and words to
help me make sense of problems.
Mathematical Practice 2
Numbers to Words
2+3=5
Words to Numbers
I have 2 yellow flowers and 3 red flowers.
How many flowers altogether?
I have 2 yellow flowers and 3 red flowers.
How many flowers altogether?
2+3=5
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Jordan School District 2012, Grades K-1
Construct viable arguments and critique the
reasoning of others.
I can explain my thinking and
consider the mathematical thinking
of others.
Mathematical Practice 3 I can explain my strategy
using…
I can compare my strategy
with others by…
• objects
• listening
• drawings
• asking questions
• actions
• making connections
between my own
thinking and others
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Jordan School District 2012, Grades K-1
Represent
Math
Model with mathematics.
I can recognize math in everyday
life and use math I know to solve
problems.
Mathematical Practice 4
I can use…
(Objects)
(Pictures)
(Symbols)
4-2=2
4 birds are in a tree.
2 birds flew away.
How many are left?
I have 4.
I take 2 away.
Now I have 2.
(Words)
…to solve everyday problems.
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Jordan School District 2012, Grades K-1
K-1 images
Use appropriate tools strategically.
Mathematical Practice 5
I can use math tools to help me
explore and understand math in my
world.
I have a math toolbox.
12
11
x
Toolbo
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1
2
10
3
9
4
8
7
0
6
1
5
2
3
4
5
6
7
8
9
10
Jordan School District 2012, Grades K-1
Attend to precision.
Mathematical practice 6
I can be careful when I use math
and clear when I share my ideas.
Careful and clear mathematicians use…
PLUS:
join
EQUAL:
the same as
2 cats + 3 dogs = 5 pets
label units
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• math vocabulary
• symbols
• labels
• addition and subtraction
strategies
Jordan School District 2012, Grades K-1
Look for and make use of structure.
Mathematical Practice 7
I can see and understand how
numbers and shapes are put
together as parts and wholes.
Numbers
Shapes
April 03, 2012
April 03, 2012
= 11
10 + 1 = 11
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=
2 + 1 = 1 + 2
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Jordan School District 2012, Grades K-1
Look for and express regularity in
repeated reasoning.
Mathematical Practice 8
April 02, 2012
I can notice when calculations are
repeated.
May 27, 2012
11 = 10 + 1
12 = 10 + 2
13 = 10 + 3
14 = 10 + 4
15 = 10 + 5
I see number patterns!
1
2
3
4
5
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I a
by
see
I see a
pattern!
Jordan School District 2012, Grades K-1 Make sense of problems and persevere in
solving them.
When given a problem, I can make
a plan, carry out my plan, and
check my answer.
Mathematical Practice 1
BEFORE...
Think about the
problem.
Ask myself, "Which
strategy will I use?"
Make a plan to
solve the
problem.
DURING...
Stick to it!
AFTER...
CHECK my work.
Ask myself, "Does
this make sense?"
Change my plan if it
isn't working out.
Ask myself,
"Is there another
way to solve
the problem?"
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Jordan School District 2012, Grades 2-3 Reason abstractly and quantitatively.
I can use numbers and words to
help me make sense of problems.
Mathematical Practice 2 March 29, 2012
Numbers to Words
26 + 27 = 53
Words to Numbers
There are 26 boys and 27 girls on the playground.
How many children are on the playground?
+26
There are 26 boys and 27 girls on the playground.
How many children are on the playground?
+26
0
+20
26
0
+20
26
+4 +3
46 50 53
26 + 20 = 46
46 + 4 = 50
50 + 3 = 53
+4 +3
46 50 53
26 + 20 = 46
46 + 4 = 50
50 + 3 = 53
26 + 27 = 53
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Jordan School District 2012, Grades 2-3
Construct viable arguments and critique the
reasoning of others.
I can explain my thinking and
respond to the mathematical
thinking of others.
Mathematical Practice 3
I can explain my strategy
using…
I can compare strategies with
others by…
• objects, drawings, and
actions
• listening
• examples and non-examples
• understanding mathematical
connections between strategies
• contexts
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• asking useful questions
Jordan School District 2012, Grades 2-3
Model with mathematics.
I can recognize math in everyday
life and use math I know to solve
problems.
Mathematical Practice 4
I can use….
I can use take-away to find the difference between
the number of crayons Jill and Rob have.
(Words)
46
- 23
23
(Symbols)
Rob has 23 crayons. Jill has 46
crayons. How many more
crayons does Jill have than Rob?
(Objects)
(Pictures)
Difference of 23 crayons
Rob's Crayons
Jill's Crayons
0
10
20
23
30
40
46
50
…to solve everyday problems.
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Jordan School District 2012, Grades 2-3
Use appropriate tools strategically.
Mathematical Practice 5
x
Toolbo
I can use certain tools to help me
explore and deepen my math
understanding.
I have a math toolbox.
11
12
1
10
2
8
4
3
9
7
6
5
• I know HOW and WHEN to use
math tools.
• I can reason: “Did the tool I used
give me an answer that makes
sense?”
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-1
0
1
2
3
4
5
6
7
8
9
Jordan School District 2012, Grades 2-3 Attend to precision.
Mathematical practice 6
I can be precise when solving
problems and clear when I share
my ideas.
Careful and clear mathematicians use…
symbols
PLUS:
join
EQUAL:
the same as
23¢ + 52¢ = 75¢
units of measure:
CENTS
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• math vocabulary
• symbols that have meaning
• context labels
• units of measure
• calculations that are accurate
and efficient
Jordan School District 2012, Grades 2-3
Look for and make use of structure.
Mathematical Practice 7
I can see and understand how
numbers and shapes are organized
and put together as parts and
wholes.
Numbers
Shapes
April 04, 2012
April 04, 201
For example:
For example:
These shapes
have three sides
These are the same!
123
1 hundred, 2 tens, and 3 ones
Base Ten System
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These shapes have
four right angles
These are the same!
Orientation
Attributes
Jordan School District 2012, Grades 2-3
Look for and express regularity in
repeated reasoning.
I can notice when calculations are
repeated.
Mathematical Practice 8
March 29, 2012
5 x 2 = 10
2 + 2 + 2 + 2 + 2 = 10 I am adding 2 five times. 0 1
2
3 4
5
6 7
I am counting rows with 2 in each row five times. 8
9 10
I am making 5 hops of 2 on the number line. Clip art licensed from the Clip Art Gallery on DiscoverySchool.com
Jordan School District 2012, Grades 2-3
0 1
2
3 4
5
6 7
8
9 10
Make sense of problems and persevere in
solving them.
When presented with a problem, I
can make a plan, carry out my plan,
and check its success.
Mathematical Practice 1
BEFORE…
EXPLAIN the problem to
myself.
MAKE A PLAN to
solve the problem
— What is the question?
— What do I know?
— What do I need to find out?
— What tools/strategies will I use?
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DURING…
PERSEVERE
(Stick to it!)
AFTER…
CHECK
MONITOR my work
— Is my answer correct?
— How do my representations connect to
my solution?
ASK myself, “Does this
EVALUATE
make sense?”
CHANGE my plan if
— What worked/didn’t work?
— How was my solution similar or
different from my classmates’? it isn’t working out
Jordan School District 2012, Grades 4-5 Reason abstractly and quantitatively.
I can use numbers, words, and
reasoning habits to help me make
sense of problems.
Mathematical Practice 2 Ap
April 02, 2012
Contextualize (Numbers to Words)
𝟏
𝟐
Decontextualize (Words to Numbers)
𝟏
0
𝟏
x 6 = 3 or 6 x = 3 𝟐
1
2
Mary practices the piano hour a day for 6 days.
𝟐
How many total hours does she practice?
0
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
𝟏
Mary practices the piano hour a day for 6 days.
𝟐
How many total hours does she practice?
Day 1
Hours
0
Day 2
1
2
Day 3
Day 4
1
2
1
Day 5
0
1
2
1
1
2
1
2
2
3
Day 6
1
2
2
Hours
𝟏
3
𝟐
Reasoning Habits
𝟏
x 6 = 3 or 6 x = 3
𝟐
1
1 1 1 1 1 1
62
+ + + + =
2+2 2 2 2 2
2
1) Make an understandable representation of the problem. 3) Pay attention to the meaning of the numbers.
2) Think about the units involved.
1
1
1
1
1
1
1
62
+ + + + + =
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2 2 2 2 2
2
1
2
4) Use the properties of operations or objects.
Jordan School District 2012, Grades 4-5
Construct viable arguments and critique the
reasoning of others.
I can make logical arguments and
respond to the mathematical
thinking of others.
Mathematical Practice 3
I can make and present
arguments by…
I can analyze the reasoning
of others by…
• using objects, drawings, diagrams
and actions
• listening
• using examples and non-examples
• relating to contexts
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• asking and answering questions
• comparing strategies and
arguments
Jordan School District 2012, Grades 4-5
Apri
Model with mathematics.
Mathematical Practice 4
I can recognize math in everyday
life and use math I know to solve
problems.
I can…
My box turtle is getting a new tank. He is 5
1/2" long and 3" tall. One side length of the
tank needs to be 5 times his length. How long
will the length of the tank need to be?
Consider my answer -Does it make sense?
I thought about the
problem again and a 30"
side length on the tank
makes sense!
Use estimates to
make the problem
simpler.
Find important
numbers.
Turtle: About 6" long
Tank: 5 times the length
of the turtle
I will round 5 1/2" to 6".
Think about the relationship
to find an answer.
The tank (30") is 5 times
bigger than the turtle
length (6").
Turtle
Tank Use tools to show
Length Length
relationships.
(inches) (inches)
4
5
6
7
8
20
25
30
35
40
…to solve everyday problems.
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Jordan School District 2012, Grades 4-5 Use appropriate tools strategically.
Mathematical Practice 5
I can use certain tools to help me
explore and deepen my math
understanding.
Cº
• I know HOW and WHEN to use
math tools.
Aº
axb=bxa
• I can reason: “Did the tool I used
give me an answer that makes
sense?”
-1
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0
1
2
3
4
5
6
7
8
9
Jordan School District 2012, Grades 4-5 Attend to precision.
Mathematical practice 6
I can be precise when solving
problems and clear when
communicating my ideas.
Mathematicians communicate with others using… symbol:
equal
(the same as)
48 inches = 4 feet
units of
measure
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• math vocabulary with clear
definitions
• symbols that have meaning
• context labels
• units of measure
• calculations that are accurate
and efficient
Jordan School District 2012, Grades 4-5
Look for and make use of structure.
Mathematical Practice 7
I can see and understand how
numbers and spaces are organized
and put together as parts and
wholes.
Numbers
Spaces
April 04, 201
April 08, 2012
For Example:
For Example:
I know that
3
30
is equal to
.
10
100
Lines and Angles
So,
3
10
4
+ 100 =
34
.
100
A
0 1 2 3 4 5 6 7 8 9
Symmetry
9
8
7
6
5
4
3
2
1
Location
Equivalent Fractions Clip art licensed from the Clip Art Gallery on DiscoverySchool.com
Jordan School District 2012, Grades 4-5
Look for and express regularity in
repeated reasoning.
I can notice when calculations are
repeated. Then, I can find more
general methods and short cuts.
Mathematical Practice 8
As I work…
…I think about
what I’m trying to
figure out while I
pay attention to
the details
𝟑
𝟏
𝟖
𝟖
There are many ways to decompose because it is composed of repeated
I CAN…..
….draw a whole and shade
!
in three s parts.
…I evaluate if my
results are
reasonable.
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!
April 02, 2012
….add eighths.
𝟑
𝟖
….count by eighths.
(one-eighth, two eighths, three eighths)
𝟏
𝟏
𝟏
𝟑
𝟖
𝟖
𝟖
𝟖
0
8
1
8
2
8
= + +
s.
=
𝟏
𝟖
,
𝟏
𝟖
, 𝟏
𝟖
!
….jump three size jumps
!
on a number line.
0
3
8
4
8
5
8
6
8
7
8
8
8
1
Jordan School District 2012, Grades 4-5
Make sense of problems and persevere in
solving them
When presented with a problem, I
can make a plan, carry out my plan,
and evaluate its success.
BEFORE…
EXPLAIN the problem to
myself.
 Have I solved a problem like this before?
ORGANIZE information…
 What is the question I need to answer?
 What is given?
 What is not given?
 What are the relationships between known
and unknown quantities?
 What tools will I use?
 What prior knowledge do I have to help me?
DURING…
PERSEVERE
AFTER…
CHECK
MONITOR my work
 Is my answer correct?
 How do my representations connect to
my algorithms?
CHANGE my plan if
EVALUATE
it isn’t working out
ASK myself, “Does this
make sense?”
 What worked?
 What didn’t work?
 What other strategies were used?
 How was my solution similar to or
different from my classmates’?
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Jordan School District 2011, Grade 6
Reason abstractly and quantitatively
I can use reasoning habits to help
me contextualize and
decontexualize problems.
CONTEXTUALIZE
DECONTEXTUALIZE
I can take numbers and put them
in a real-world context.
I can take numbers out of context and
work mathematically with them.
For example, if given
3 x 2.5 = 7.5
I can create a context:
For example, if given
‘I walked 2.5 miles per day for 3 days.
How far did I walk?’,
I can write and solve
I walked 2.5 miles per day for 3 days. I walked a
total of 7.5 miles.
3 x 2.5 = 7.5
Reasoning Habits include 1) creating an understandable representation of the problem
solved, 2) considering the units involved, 3) attending to the meaning of quantities,
and 4) using properties to help solve problems.
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Jordan School District 2011, Grade 6
Construct viable arguments and critique the
reasoning of others
I can make conjectures and critique
the mathematical thinking of
others.
I can construct, justify, and
communicate arguments by…
I can critique the reasoning
of others by…
◆ considering context
◆ listening
◆ using examples and non-examples
◆ comparing arguments
◆ using objects, drawings, diagrams
and actions
◆ identifying flawed logic
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◆ asking questions to clarify or
improve arguments
Jordan School District 2011, Grade 6
Model with mathematics
I can recognize math in everyday
life and use math I know to solve
everyday problems.
I can…
◆ make assumptions and
estimate to make complex
problems easier
◆ identify important quantities
and use tools to show their
relationships
◆ evaluate my answer and
make changes if needed
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concrete
models
symbols
pictures
Represent
Math
oral
language
real-world
situations
Jordan School District 2011, Grade 6
Use appropriate tools strategically
I know when to use certain tools to
help me explore and deepen my
math understanding.
I have a math toolbox.
x
Toolbo
◆ I know HOW to use math tools.
0
◆ I know WHEN to use math tools.
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4
6
8 10
axb=bxa
11
◆ I can reason: “Did the tool I used
give me an answer that makes
sense?”
2
12
1
2
10
9
3
4
8
7
6
5
V=bxh
Jordan School District 2011, Grade 6
Attend to precision
I can use precision when solving
problems and communicating my
ideas.
Communicating
Problem Solving
◆ I can calculate accurately.
◆ I can calculate efficiently.
◆ My answer matches what the
problem asked me to do –
estimate or find an exact
answer.
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◆ I can SPEAK, READ, WRITE, and
LISTEN mathematically.
◆ I can correctly use...
● math symbols
● math vocabulary
● units of measure
Jordan School District 2011, Grade 6
Look for and make use of structure
I can see and understand how
numbers and spaces are organized
and put together as parts and
wholes.
Numbers
Spaces
For Example:
◆ Base 10 structure
◆ operations and properties
◆ terms, coefficients, exponents
10
10
100
50
◆ attributes
◆ transformation
+ 3
30
+
5
For Example:
◆ dimension
◆ location
15
13 x 15
(10 + 3) x (10 + 5)
100 + 30 + 50 +15
195
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Jordan School District 2011, Grade 6
Look for and express regularity in repeated
reasoning
I can notice when calculations are
repeated. Then, I can find more
efficient methods and short cuts.
For example:
25 ÷ 11
2.2727
11 25.0000
22
I am repeating
30
this calculation.
22
quotient is a
80 The
repeating decimal.
77
30
22
80
77
30
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Jordan School District 2011, Grade 6