Teaching subtraction relies heavily on a student’s conceptual understanding of the number system. When students lack an understanding of how numbers are built and how our number system works, it is common for them to make mistakes. These mistakes reveal the lack of conceptual understanding that FIRST must be addressed before students will successfully understand subtraction strategies. Be on the lookout for these 3 common subtraction errors and how to fix them.
Common Subtraction Error #1: Not aligning place values correctly
When given a subtraction problem, these students misalign the place values. They lack the conceptual understanding of how numbers are built. They see a three digit number and a two digit number and align them according to the positionality of the digit. The first digits are aligned with one another. The second digits with one another. This is a common subtraction error of students who need more support in understanding the place value system.
To fix this, return to two digit numbers. Students should use manipulatives and a place value chart to build them. Using base ten blocks, students count out by ones. When they have reached the target number, ask them if there is an easier way to group these blocks. Grouping them into ten makes it easier to count. After the student has made groups of ten, reintroduce the tens block. Have them line up enough ones cubes to create a tens block. Then, they should trade in their groups of ten for tens blocks.
Once they become confident, give them subtraction problems in horizontal form so they must ALIGN the place values themselves. Begin also with numbers that do not require regrouping. As struggling students master these skills, move onto subtraction problems with regrouping.
Don’t stop at two digit numbers:
Once proficient, students move onto three digit numbers. This time skip count by tens instead of ones. Students group tens into bundles of ten to make hundreds. The should stack the tens on top of a hundreds block so they can see how many tens make 100. Repeat the process of introducing horizontal subtraction problems. This gives them practice aligning the place values.
Students are then ready to be introduced to mixed subtraction problems, those with two and three digit numbers. This reinforces place value skills as students must THINK about a number’s value and line up the place values accordingly. Support this development using a place value chart and eventually removing it.
Fourth and fifth grade teachers will find using place value disks more effective for larger numbers. This is a common subtraction error that can be fixed with hands on practice.
Common Subtraction Error #2: Subtracting Up
The minuend, or the number being subtracted from, of one place value has a smaller value than the number being subtracted from it. These students focus on only the one place value within the whole number. In order to fix this, they need practice in understanding the ENITRE number is greater than the number being taken from it.
So, practice building the minuend with these students. Modeling with base ten blocks or place value disks, have students build the number being subtracted from. When they do not have enough of a place value to subtract, have them practice regrouping to get more of the place value they need.
As students become more confident, integrate the standard algorithm to help students record these steps.
Common Subtraction Error #3: Making 10 instead of regrouping 10
Students that make this common error only MAKE 10, rather that regrouping an entire 10.
What do I mean?
They know they NEED more tens, hundreds, or another place value. They also know that if they trade in a hundred, or a ten, they either get 10 of the smaller place value.
The trouble is, if they already have a set amount, say 3 ones, they count those 3 ones as a part of the 10 when they regroup, so they only take 7 more ones.
How can you remedy this? Students line up 10 ones alongside a tens rode before they trade it. Be sure they set aside the ONES they already have. Also, if regrouping a hundred into tens, they should stack the tens on top of the hundred they are trading. This is a great visual reminder for these students who need further conceptual understanding.
Before subtracting, have students COUNT the ones they now have. Be sure they have the TEN ones they regrouped and the ones they started with.
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