Investigating the Standards for
Mathematical Practice, K-8
Team Take Away #1
For Grade Level Teams and Vertical Teams
Standards for 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.
Task:
 Read the problem provided. Determine the important mathematics necessary for the
problem.
 List the key grade level content standard(s) for the sample problem.
 Choose two mathematical practices (listed above).
 When completing the sample problem for yoru grade level, consider how students
might demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
 Describe characteristics in students’ thinking and actions that you might observe for
each practice in the chart provided.
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (K)
Task (Kindergarten):





Sample Kindergarten Mathematics Problem
Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key Kindergarten content standard(s) for the sample
problem:
Choose two mathematical practices: 1)Sense-making and
Persevering, 2)Abstract & Quantitative Reasoning, 3)Constructing
Arguments & Critiquing, 4)Modeling, 5)Using Tools Strategically,
6)Attending to Precision, 7)Recognizing & Using Structure, and
8)Looking for and Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students
might demonstrate the chosen Mathematical Practices at
Rudimentary and Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Trace the drawing:


Cross out 3 lines to leave 2 triangles
How many different way can this be
done?
Kindergarten Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (1)
Task (1st grade):





Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 1st grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and
Persevering, 2)Abstract & Quantitative Reasoning, 3)Constructing
Arguments & Critiquing, 4)Modeling, 5)Using Tools Strategically,
6)Attending to Precision, 7)Recognizing & Using Structure, and
8)Looking for and Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students
might demonstrate the chosen Mathematical Practices at
Rudimentary and Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Sample 1st Grade Mathematics Problem
Use the clues to figure out the distance
 Glovers Cove to Cruz Beach to Nelsons
Cliff is 70km
 Cruz Beach to Nelsons Cliff is 30km
 Glovers Cove to Cruz Beach to Nelsons
Cliff to Glovers Cove is 170km
Glovers Cove
Cruz Beach
Nelsons Cliff
Key 1st Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (2)
Task (2rd grade):





Sample 2nd grade Mathematics Problem
Read the problem at right. Determine the important mathematics
Daniel spent $24 on 5 sandwiches. The
necessary for this problem.
Chicken sandwich cost $5 and the tuna
List the key 3rd grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and Persevering,
sandwich cost $4.
2)Abstract & Quantitative Reasoning, 3)Constructing Arguments &
Critiquing, 4)Modeling, 5)Using Tools Strategically, 6)Attending to
How many of each sandwich did he buy?
Precision, 7)Recognizing & Using Structure, and 8)Looking for and
Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students might
demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Key 2rd Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (3)
Task (3rd grade):





Sample 3rd grade Mathematics Problem
Read the problem at right. Determine the important mathematics
necessary for this problem.
Using any combination of +, -, x or ÷ in
List the key 3rd grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and Persevering,
each  to make the sentence true.
2)Abstract & Quantitative Reasoning, 3)Constructing Arguments &
Critiquing, 4)Modeling, 5)Using Tools Strategically, 6)Attending to
18  9  3  6  4 = 4
Precision, 7)Recognizing & Using Structure, and 8)Looking for and
Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students might
demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you might observe for each practice in the chart
below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Key 3rd Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (4)
Task (4th grade):





Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 4th grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and Persevering,
2)Abstract & Quantitative Reasoning, 3)Constructing Arguments &
Critiquing, 4)Modeling, 5)Using Tools Strategically, 6)Attending to
Precision, 7)Recognizing & Using Structure, and 8)Looking for and
Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students might
demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Sample 4th grade Mathematics Problem:
Support your answer to the following
questions with a sketch:
 How many fifths are there in a whole?
 How many thirds are there in 2 1/3?
 How many 2/5 are there in 4?
How could the problems above be
represented as multiplication and addition
problems (number sentences)?
Key 4th Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (5)
Task (5th grade):





Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 5th grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and Persevering,
2)Abstract & Quantitative Reasoning, 3)Constructing Arguments &
Critiquing, 4)Modeling, 5)Using Tools Strategically, 6)Attending to
Precision, 7)Recognizing & Using Structure, and 8)Looking for and
Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students might
demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and
doing?)
Sample 5th grade Mathematics Problem:
Nick conducted a survey to find out how
students get to school every morning.
 1/3 of the students walk to school.
 1/4 of the students are driven to school.
 1/6 of the students ride their bikes.
 24 students take the bus to school.
How many students participated in the survey
and what mathematics did you write to figure
it out?
Key 5th Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (6)
Task (6th Grade):





Sample 6th grade Mathematics Problem:
Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 6th grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and
Persevering, 2)Abstract & Quantitative Reasoning, 3)Constructing
Arguments & Critiquing, 4)Modeling, 5)Using Tools Strategically,
6)Attending to Precision, 7)Recognizing & Using Structure, and
8)Looking for and Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students
might demonstrate the chosen Mathematical Practices at
Rudimentary and Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and doing?)
Approximately 7.5 gal. of water is
needed to fill 1 cubic ft. of volume.
Approximately how many times will a
person have to fill a quart-size
container to fill an aquarium that
measures 2 ft.×1 ft.×6 ft.?
Key 6th Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (7)
Task (7th grade):





Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 7th grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and Persevering,
2)Abstract & Quantitative Reasoning, 3)Constructing Arguments &
Critiquing, 4)Modeling, 5)Using Tools Strategically, 6)Attending to
Precision, 7)Recognizing & Using Structure, and 8)Looking for and
Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students might
demonstrate the chosen Mathematical Practices at Rudimentary and
Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and doing?)
Sample 7th grade Mathematics
Problem:
In a neighborhood café there are
10 seats in a row at the counter.
In the morning, customers enter the café for
their morning coffee. They don’t really want
to have a conversation, so they prefer not to
sit next to one another at the counter. Two
people enter the café when it opens. How
many different ways can these two
customers sit at the counter so that they are
not next to each other?
Key 7th Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Investigating the Standards for Mathematical Practice (8)
Task (8th Grade):





Sample 8th grade Mathematics Problem:
Read the problem at right. Determine the important mathematics
necessary for this problem.
List the key 8th grade content standard(s) for the sample problem:
Choose two mathematical practices: 1)Sense-making and
Persevering, 2)Abstract & Quantitative Reasoning, 3)Constructing
Arguments & Critiquing, 4)Modeling, 5)Using Tools Strategically,
6)Attending to Precision, 7)Recognizing & Using Structure, and
8)Looking for and Expressing Regularity in Repeated Reasoning.
When completing the sample problem, consider how students
might demonstrate the chosen Mathematical Practices at
Rudimentary and Sophisticated stages of development.
Describe characteristics in students’ thinking and actions that you
might observe for each practice in the chart below.
Important Mathematics Necessary for this Problem
Standard for
Mathematical
Practice
Characteristics of Rudimentary Practice
Mathematical Practices
(What might students be thinking and doing?)
Alex made several cylinders. For each cylinder,
he made clay spheres so that the sphere fit
exactly inside the cylinder. He squished the
clay down to see how much of the cylinder it
filled. Every time it filled the cylinder up to 2/3
of its height. How could this help him to find
the volume of the sphere?
Key 8th Grade Content Standard(s) for this Problem
Characteristics of Sophisticated Practice
Mathematical Practices
(What might students be thinking and doing?)
Practice #1:
Practice #2:
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.
Activities taken from the 2010 CESA SIS Investigations Guides, Compiled by CESA #4.