2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and
strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy to a
written method. Understand that in adding or subtracting three-digit
numbers, one adds or subtracts hundreds and hundreds, tens and tens,
ones and ones; and sometimes it is necessary to compose or decompose
tens or hundreds.
Unpacked
Students extend the work from 2.NBT.5 to 3-digit numbers. Students should
have ample experiences using concrete materials and pictorial
representations to support their work. Decompose is the process of
separating numbers into their components (to divide a number into smaller
parts). This standard also references composing and decomposing a ten. This
work should include strategies such as making a 10, making a 100, breaking
apart a 10, or creating an easier problem. The standard algorithm of
carrying or borrowing is not an expectation in Second Grade. Students
are not expected to add and subtract whole numbers using a standard
algorithm until the end of Fourth Grade.
One example of this standard is as follows:
Example: 354 + 287 = __
See strategies below:
Invented Strategies:
* noting the observation above in regard to teaching algorithms, student invented
strategies are an important and strategic progression into the direct
instruction/introduction of algorithms.
Invented strategies are developed out of a strong understanding of numbers. The standard
development of place value often leaves students ill prepared for the challenges of
inventing computational strategies. For example, some third and fourth-grade students
have difficulty naming a number that is ten more or ten less than a given two-digit
number. Therefore, students need a classroom environment were they can act like
mathematicians and explore ideas without trepidation. Here are some factors to keep in
mind:
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Expect and encourage student to student interactions, discussions, and conjectures
Celebrate when students clarify previous knowledge
Encourage curiosity and an open mind when trying new things
Talk about both right and wrong ways in a non-evaluative or threatening way
Move unsophisticated ideas to more sophisticated thinking through coaxing,
coaching, and guided questioning
 Use contexts and story problems to capture student interest
 Consider carefully whether you should step in or step back when students are
formulating new ideas (when in doubt-step back)
(Van de Walle, 2010)
The Launch Explore Summarize lesson is a good structure for an invented strategies
lesson, because students are encouraged to explore and share their thinking with their
peers.
Invented Addition Strategies
Problems involving the sum of 2 or more digits will provoke a wide variety of strategies.
One way may be a strategy that involve starting with one or the other number and
working from that point, either by adding on to get the next ten or by adding tens,
hundreds, thousands etc. from one number to the other. Other approaches involve
decomposing or splitting the numbers in parts and adding the easier parts separately.
Example:
46 + 35
A student may add four more to 46 to get fifty, and then add 31 to fifty.
A student might first add 30 to 46 and then add 4 more to get 80 and 1 more.
A student might first decompose the numbers into tens and ones, and then add. 40 + 6 +
30 + 5, and then rearrange the order to 40 + 30 = 70 and 6 + 5 = 11, therefore 70 + 11 =
81
One example of an invented strategy:
Invented Subtraction Strategies
Subtracting by Counting Up:
This strategy is very powerful for many expressions, but not appropriate for all. An
example would be for 38-19 the idea is to think, “How much do I add to 19 to get 38?”
The following problem and those like it lend themselves to be solved using “counting
up.” Simply asking for the difference between two numbers may also prompt this strategy
(Van de Walle).
Jennifer counted all of her markers. Some of them worked and some did not. She had 68
markers in all. 36 of the markers did work. How many do not work?
The following examples illustrate this problem.
Add Tens to Get Close, Then Ones
68-36
36+30 (40 is too much)
Then add two more is 68. That’s 30 and 2 or 32.
Add Ones to Make a Ten, Then Tens and Ones
68-36
36 and 4 is 40.
40 and 20 is 60.
8 more is 68.
4+20=24 24+8=32
Take-Away Subtraction:
When the subtracted number is a multiple of ten or close to a multiple of ten or close to a
multiple of ten, take-away can be an easy method to use (Van de Walle, 2010).
Example:
There were 63 students in the cafeteria. The 48 students who finished their lunch went
out to recess. How many children are still in the cafeteria?
The following examples illustrate this problem:
Take Tens from the Tens, then subtract Ones
63-48
60-40 is 20
Then take away 8 more is 12
Now add back 3 ones is 15
Take Away Tens, Then Ones
63-48
63- 40= 23
Then take away 8 more.
23-8=15