2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Unpacked
The word fluent is used in the Standards to mean “fast and accurate.”
Fluency in each grade involves a mixture of just knowing
some answers, knowing some answers from patterns (e.g., “adding
0 yields the same number”), and knowing some answers from the
use of strategies. It is important to push sensitively and encouragingly
toward fluency of the designated numbers at each grade level,
recognizing that fluency will be a mixture of these kinds of thinking
which may differ across students. The extensive work relating addition
and subtraction means that subtraction can frequently be solved
by thinking of the related addition, especially for smaller numbers.
It is also important that these patterns, strategies and decompositions still be available in Grade 3 for use in multiplying and dividingand in distinguishing adding and subtracting from multiplying anddividing. So the important press toward fluency should also allowstudents to fall back on earlier strategies when needed.
Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected. (PARCC MCF, v3.0, p. 12)
There are various strategies that students understand and use when adding and subtracting within 100 (such as those listed in the standard). The standard algorithm of carrying or borrowing is neither an expectation nor a focus in Second Grade. Students use multiple strategies for addition and subtraction in Grades K-3. By the end of Third Grade students use a range of algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 1000.
The emphasis of this cluster of standards is not as much on the tasks that are required of the student as on the strategies and thought processes that the student uses to arrive at a solution. Although the tasks will often resemble the traditional ones from the textbook and worksheets, the work produced by the student should look very different. Students will work with concrete objects adding ones with ones, groups of ten with groups of ten, and hundreds with hundreds. Through questioning, such as “Is there a way you could arrange these ones to make them easier to count?” teachers can lead students to make groups of ten. As they work with concrete objects, children will naturally discover the need to form groups of ten when adding and to break up tens when subtracting. Teachers should ask questions to encourage students to express and clarify their thinking while they work, such as “How will it help with this subtraction if you know how many you need to add to 5 to get 9?
Students will be asked to draw, demonstrate, and/or explain their thinking. Through sharing and listening to each other’s thinking, children will develop strategies for making tens and looking for doubles and other well-known combinations to help them make sense of problems. Teachers should not be surprised if students tend to add or subtract the hundreds or the tens before attending to the ones. It is not necessary to impose restrictions on students as they are developing their own sense-making, other than to correct inaccurate or false assumptions. Students will develop more efficient practices through numerous experiences with concrete objects and drawings and listening to the reasoning of other students. It is imperative that frequent discussions and think-alouds take place in a mathematics classroom in order for real conceptual development to occur.
Since the expectation of this standard is for students to develop fluency in adding and subtracting within 100, there will need to be a gradual transition from concrete models, to representational drawings, and then finally to symbols alone.
Teachers should resist the urge to teach children a process of lining up digits and adding in columns before they have fully grasped the concept of composing and decomposing tens. The use of the standard algorithm for multi-digit addition and subtraction is not mentioned in the standards until 4th grade.
Questions to Focus Instruction:
Can students add and subtract multiples of ten fast and accurately, and explain the strategy used?
Can students add and subtract within 100 without only counting, but using strategies based on place value, properties of operations and the relationship between addition and subtraction?
Can students explain the reasoning behind the strategy used?
Can students add and subtract numbers within 100 quickly and accurately?