4.NBT.B.4
*This standard is part of a major cluster
Standard:
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Unpacked Standard:
Students build on their understanding of addition and subtraction, their use of place value
and their flexibility with multiple strategies to make sense of the standard algorithm.
They continue to use place value in describing and justifying the processes they use to
add and subtract. This standard refers to fluency, which means accuracy and efficiency
(using a reasonable amount of steps and time), and flexibility (using a variety of
strategies such as the distributive property, decomposing and recomposing numbers, etc.).
Understanding how the standard algorithm works and why it is a good choice (over other
strategies) is central to the development of procedural fluency. The main focus in
teaching the standard algorithm is not as a memorized series of steps but as making sense
of the procedure as a process. Apply the same rule to standard algorithm as to all
strategies: If you use it, you must understand why it works and be able to explain it (Van
de Walle, 2012).
*This is the first grade level in which students are expected to be proficient at using the
standard algorithm to add and subtract. However, other previously learned strategies are
still appropriate for students to use, and will have built a robust foundation for
understanding of why the standard algorithm works. In order to support the idea that just
like other strategies, it may be more useful in some instances than others, pose problems
in which a mental strategy is much more useful such as 504-498. Discuss which method
seems best. Point out that for a problem such as 4,568 + 12,813, the standard algorithm
has advantages (Van de Walle, 2012). Referencing the aligned standards for grade 3 in
the vertical alignment document is a helpful resource in understanding other strategies
that students can build on for supporting the development of the standard algorithm.
In their NCSM article, Fuson and Beckman, describe how standard algorithms are
developed in mathematics.
Computation algorithm. A set of predefined steps applicable to a class of problems that
gives the correct result in every case when the steps are carried out correctly.
Computation strategy. Purposeful manipulations that may be chosen for specific
problems, may not have a fixed order, and may be aimed at converting one problem into
another.
When students begin using the standard algorithm their explanation may be quite lengthy.
After much practice with using place value to justify their steps, they will develop
fluency with the algorithm. Students should be able to explain why the algorithm works.
3892 +1567
Student explanation for this problem:
1. Two ones plus seven ones is nine ones.
2. Nine tens plus six tens is 15 tens.
3. I am going to write down five tens and think of the 10 tens as one more
hundred.
(notates with a 1 above the hundreds column)
4. Eight hundreds plus five hundreds plus the extra hundred from adding the tens
is 14 hundreds.
5. I am going to write the four hundreds and think of the 10 hundreds as one more
1000
(notates with a 1 above the thousands column)
6.Three thousands plus one thousand plus the extra thousand from the hundreds is
five thousand
3546 – 928
Student explanation for this problem:
There are not enough ones to take 8 ones from 6 ones so I have to use one ten as
10 ones. Now I have 3 tens and 16 ones. (Marks through the 4 and notates with a
3 above the 4 and writes a 1 above the ones column to be represented as 16 ones.)
Questions to check for understanding and increase rigor:
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What two addends could equal a sum of 146? (e.g. 67, 298, 1,130, etc.) Model
and explain your reasoning.
What two numbers could you subtract to make a difference of 94? What could the
two numbers be when regrouping is required? What could the two numbers be if
no regrouping is required? Model and explain your reasoning.
How many different ways can you solve 39+84? 73-25? What is similar/different
between these strategies and the standard algorithm?
Do you think the standard algorithm is more efficient than other strategies? Why
or why not?
What is the relationship between the standard algorithm and place value?
Using two 3-digit numbers, create two different addition equations with a sum
between 300 and 400. Model and explain your reasoning.
Using the digits 3, 5, 1, 8, 2 and 6, create a subtraction equation with the largest
possible difference. Model and explain your reasoning.