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1.OA.3.Apply properties of operations as strategies to add and subtract.2 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 = 2 + 10 = 12. (Associative property of addition.).
What is the purpose of the word subtract in this standard? Subtraction is neither commutative nor associative. One application is that the identity property applies to subtraction: 9-0 = 9. Is it talking about situations like 9 + 5 – 4 = 9 – 4 + 5 = 5 + 5 = 10?
[Edited to remove duplicate and correct one equation, Bill McCallum, 3/21]
Here’s one example from the OA progression (p. 15):
For example, a student can change 8 + 6 to the easier 10 + 4 by decomposing 6 as 2 + 4 and composing the 2 with the 8 to make 10: 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14.
This method can also be used to subtract by finding an unknown addend:
14 – 8 = box, so 8 + box = 14,
so 14 = 8 + 2 + 4 = 8 + 6,
that is 14 – 8 = 6.
Related: A strategy for word problems (so connected with 1.OA.1) that draws on the commutative property:
Students re-represent Add To/Start Unknown box + 6 = 14 situations as 6 + box = 14 by using the commutative property (formally or informally).
This is from the Appendix of the Progression under Level 3: Convert to an Easier Equivalent Problem. Start Unknown problems are described in Table 2 of the OA Progression. Students work with such problems in Grade 1 but need not master them until Grade 2.
I’m writing “box” for the symbol that looks like a little square.
Seems to me that falls under 1.OA.6 not 1.OA.3 seeing as these are generic strategies and not strategies based on properties of operations:
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).
It falls under both. Cathy’s point is that because of 1.OA.4, Understand subtraction as an unknown-addend problem, properties of operations do potentially apply to subtraction problems because those subtraction problems might be recast as unknown-addend problems. Although it is true that subtraction does not satisfy the same properties as addition, that does not mean that those properties cannot be used to solve a subtraction problem, as Cathy’s examples illustrate.
Some comments on the issue that I think Jim has moved on to: differences between what’s in 1.OA.3 and 1.OA.6.
1.OA.3 comes under the cluster heading “Understand and apply properties of operations and the relationship between addition and subtraction.”
1.OA.6 comes under the cluster heading “Add and subtract within 20.” As noted in 1.OA.6, a student might do this by counting on rather than using strategies that involve properties of operations.
Within the examples of strategies shown for 1.OA.6 are uses of the properties of operations as described in 1.OA.3.
Making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14): Going from 8 + 2 + 4 to 10 + 4 is a use of the associative property. It seems to me that making a ten in calculating sums within 20 always involves use of the associative property unless one of the numbers is already 10. It seems to me that “use the associative property to add” is more generic than make-a-ten. Also, make-a-ten is a strategy that a student might identify, but “use the associative property to add” might not be so readily identified.
Creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13): Going from 6 + 6 + 1 to 12 + 1 is also a use of the associative property.
Using the following example story situation:
Tim had 12 pennies. He gave 4 pennies to Sam. How many pennies does Tim have now?
If a student thinks of adding up to answer the question and writes 4+8=12, should the student be required to write an equation to match the story, 12-4=8? In 1st grade, students are expected to write an equation with a symbol for the unknown number to represent the problem. If they think of adding up, can write an equation to show their thinking, and be able to tell you what each number represents, is there a need for them to write the subtraction equation that matches the story situation?
From the Progressions, it’s my understanding that we want students to move away from writing situational equations to writing solution equations. That would make sense because the standards set the expectation of using the relationship between addition and subtraction in problem solving. Also, 1-OA-4 states “understand subtraction as an unknown-addend problem.
Thanks in advance for your help.
Jana, I don’t see that the OA Progression says “move away from writing situation equations to writing solution equations,” but rather writing a situation equation, then a solution equation.
The OA Progression says:
Learning where the total is in addition equations . . . students move from a situation equation to a related solution equation. (pp. 13–14)
Grade 6 students continue the K–5 focus on representing a problem situation using an equation (a situation equation) and then . . . writing an equivalent equation that is easier to solve (a solution equation). (pp. 34–35)
See also, pp. 16, 18.
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