Domain:
Operations and Algebraic Thinking
Cluster:
Understand and apply properties of operations and the relationship
between addition and subtraction.
1.OA.B.3
Apply properties of operations as strategies to add and subtract.* Examples: If 8+3 = 11 is known, then 3+8 = 11 is also
known. (Commutative property of addition.) To add 2+6+4, the second two numbers can be added to make a ten, so
2+6+4 = 10+2 = 12. (Associative property of addition.)
*Students need not use formal terms for these properties.
Notes to Teacher:
Adding more than two numbers (1.OA.A.2) is the ideal context for developing students’ understanding of number
properties—specifically the commutative and associative properties. As students work with three addends teachers
should encourage them to explore different ways to combine the numbers to make them easier to add. Ask students
to try changing the order of the addends to see if there is a particular order that works best. Ask them to check the
solutions each time to verify that the sum doesn’t change (commutative property). Ask students to group the
numbers in different ways to see if there is a particular grouping that works best. Ask them to check the solutions
each time to verify that the sum doesn’t change (associative property). Provide students with numerous
opportunities to share their thinking with each other. Facilitate conversations about various strategies that children
used to solve these problems. Through these discussions, guide students to discover that order and grouping do not
affect the sum.
Task
Explanation/Comments
Sample Student Work
There are 4 boys and 5 girls on Laticia’s
Example of Commutative Property of
soccer team. There are 5 boys and 4 girls on Addition
her brother’s team.
Laticia says that she knows that there is the
same number of players on both teams
because she knows that 4+5 and 5+4 are
the same amount.
Do you agree with Laticia? Explain. You
may use objects or drawings to help you
solve this problem.
On Monday, 3 girls and 2 boys sat at the
round table. 4 boys sat at the square table.
Use objects or drawings to represent this
situation.
On Tuesday, only the 3 girls sat at the round
table. Two boys sat with the other 4 boys at
the square table.
Use objects or drawings to represent this
situation.
Regina says that there were more children
seated at the tables on Monday than on
Tuesday. Do you agree? Explain.
Example of Associative Property of
Addition