Primary Standards:
MAFS.4.NBT.2.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Content Knowledge:
Students in prior grades have used foundational place value based strategies to add and subtract multi-digit numbers, including number lines, concrete and pictorial models and working with numbers in expanded form. In 4th grade students will now explore the standard algorithms by applying their conceptual understanding of addition and subtraction.
When introducing students to the standard algorithms, the goal is to help them make sense of the process and connect it to their prior experiences with place value strategies. Rather than telling students a series of steps to be memorized, we introduce standard algorithms through comparisons to place value strategies and involve students in making the connections.
The standard algorithms have been taught in classrooms for many years. They can be efficient and accurate for most problems, but often hold little meaning for students because they focus on digits rather than numbers. Students often do not even notice when computational errors occur, because they are not thinking of the value of the numbers themselves. Included in the goals of this standard is the ability of students to use place value and estimation skills to determine if a sum or difference is reasonable. Also, students should recognize there are other strategies which at times may be more efficient, for example 1000 – 997.
GCG 1 – Learning Goal: As a mathematician, I can Connect place value strategies for addition to the standard algorithm
- Step 1: Use estimation to determine a reasonable sum prior to computation
- Step 2: Explain connections between place value strategies and the standard addition algorithm (w/o regrouping)
- Step 3: Students can explain connections between place value strategies and the standard addition algorithm (w/regrouping)
- Step 4: Fluently add using the standard algorithm and justify with estimation
GCG 2 – Learning Goal: As a mathematician, I can Connect place value strategies for subtraction to the standard algorithm
- Step 1: Use estimation to determine a reasonable difference prior to computation
- Step 2: Explain connections between place value strategies and the standard subtraction algorithm (w/o regrouping)
- Step 3: Explain connections between place value strategies and the standard subtraction algorithm (w/regrouping)
- Step 4: Fluently subtract using the standard algorithm and justify with estimation