Math Framework Standard for Mathematical Practice #8
Kindergarten
Look for and express
regularity in repeated
reasoning.
Grade 1
Look for and express
regularity in repeated
reasoning.
Grade 2
Look for and express
regularity in repeated
reasoning.
In the early grades, students notice repetitive actions in counting,
computations, and mathematical tasks. For example, the next number
in a counting sequence is one more when counting by ones and ten
more when counting by tens (or one more group of ten). Students
should be encouraged to answer questions such as “What would
happen if…? In the task “There are 8 crayons in the box. Some are red
and some are blue. How many of each could there be?” Kindergarten
students realize 8 crayons could include 4 of each color (8 = 4 + 4), 5
of one color and 3 of another (8 = 5 + 3), etc. For each solution,
students repeatedly engage in the process of finding two numbers to
join together to equal 8.
In the early grades, students notice repetitive actions in counting and
computation. When children have multiple opportunities to add and
subtract “ten” and multiples of “ten” they notice the pattern and gain a
better understanding of place value. Students continually check their
work by asking themselves, “Does this make sense?” Grade one
students begin to look for regularity in problem structures when solving
mathematical tasks. For example, students add three one-digit
numbers by using strategies such as “make a ten” or doubles.
Students recognize when and how to use strategies to solve similar
problems. For example, when evaluating 8 + 7 + 2, a student may say,
“I know that 8 and 2 equals 10, then I add 7 to get to 17. It helps if I
can make a 10 out of two numbers when I start.” Students use
repeated reasoning while solving a task with multiple correct answers.
For example, solve the problem, “There are 12 crayons in the box.
Some are red and some are blue. How many of each could there be?”
Students use repeated reasoning to find pairs of numbers that add up
to 12 (e.g., the 12 crayons could include 6 of each color (6 + 6 = 12), 7
of one color and 5 of another (7 + 5 = 12), etc.) Students should be
encouraged to answer questions, such as “What is happening in this
situation?” or “What predictions or generalizations can this pattern
support?
Second grade students notice repetitive actions in counting and
computation (e.g., number patterns to count by tens or hundreds).
Students continually check for the reasonableness of their solutions
during and after completing a task by asking themselves, “Does this
make sense?” Students should be encouraged to answer questions,
such as “What is happening in this situation?” or “What predictions or
generalizations can this pattern support?”
Mathematics Framework Chapters – MP.8
The State Board of Education adopted the Mathematics Framework on November 6, 2013.
Grade 3
Look for and express
regularity in repeated
reasoning.
Grade 4
Look for and express
regularity in repeated
reasoning.
Grade 5
Look for and express
regularity in repeated
reasoning.
Grade 6
Look for and express
regularity in repeated
reasoning.
Students notice repetitive actions in computations and they look for
“shortcut” methods. For instance, students may use the distributive
property as a strategy to work with products of numbers they do know
to solve products they do not know. For example, to find the product of
7 × 8, students might decompose 7 into 5 and 2 and then multiply 5 ×
8 and 2 × 8 to arrive at 40 + 16 or 56. Third grade students continually
evaluate their work by asking themselves, “Does this make sense?”
Students should be encouraged to answer questions, such as “What is
happening in this situation?” or “What predictions or generalizations
can this pattern support?”
Students notice repetitive actions in computations and they look for
“shortcut” methods. For instance, students may use the distributive
property as a strategy to work with products of numbers they do know
to solve products they do not know. For example, to find the product of
7 × 8, students might decompose 7 into 5 and 2 and then multiply 5 ×
8 and 2 × 8 to arrive at 40 + 16 or 56. Third grade students continually
evaluate their work by asking themselves, “Does this make sense?”
Students should be encouraged to answer questions, such as “What is
happening in this situation?” or “What predictions or generalizations
can this pattern support?”
Fifth graders use repeated reasoning to understand algorithms and
make generalizations about patterns. Students connect place value
and their prior work with operations to understand and use algorithms
to extend multi-digit division from one-digit to two-digit divisors and to
fluently multiply multi-digit whole numbers. They use various strategies
to perform all operations with decimals to hundredths and they explore
operations with fractions with visual models and begin to formulate
generalizations. Teachers might ask, “Can you explain how this
strategy works in other situations?” or “Is this always true, sometimes
true or never true?”
In grade six, students use repeated reasoning to understand
algorithms and make generalizations about patterns. During
opportunities to solve and model problems designed to support
𝑎
𝑐
𝑎𝑑
generalizing, they notice that ÷ = and construct other examples
𝑏
𝑑
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and models that confirm their generalization. Students connect place
value and their prior work with operations to understand algorithms to
fluently divide multi-digit numbers and perform all operations with
multi-digit decimals. Students informally begin to make connections
between covariance, rates, and representations showing the
relationships between quantities. Students should be encouraged to
answer questions, such as “How would we prove that…?” or “How is
this situation like and different from other situations?”
Mathematics Framework Chapters – MP.8
The State Board of Education adopted the Mathematics Framework on November 6, 2013.
Grade 7
Look for and express
regularity in repeated
reasoning.
In grade seven, students use repeated reasoning to understand
algorithms and make generalizations about patterns. After multiple
opportunities to solve and model problems, they may notice that ��
= �� if and only if �� = �� and construct other examples and
models that confirm their generalization. Students should be
encouraged to answer questions, such as “How would we prove
that…?” or “How is this situation like and different from other situations
using this operations?”
Grade 8
Look for and express
regularity in repeated
reasoning.
In grade eight, students use repeated reasoning to understand the
slope formula and to make sense of rational and irrational numbers.
Through multiple opportunities to model linear relationships, they
notice that the slope of the graph of the linear relationship and the rate
of change of the associated function are the same. As students
repeatedly check whether points are on the line of slope 3 through the
point (1, 2), they might abstract the equation of the line in the form (�
− 2)/(� − 1) = 3. Students divide to find decimal equivalents of rational
numbers (e.g. ⅔ = 0.6) and generalize their observations. They use
iterative processes to determine more precise rational approximations
for irrational numbers. Students should be encouraged to answer
questions, such as “How would we prove that…?” or “How is this
situation like and different from other situations using this operations?”
Mathematics Framework Chapters – MP.8
The State Board of Education adopted the Mathematics Framework on November 6, 2013.