One of the most common problems I see in intervention with elementary math students is a lack of understanding of multi digit subtraction with regrouping. Traditionally students were taught the standard algorithm by memorizing steps, which they would often forget. When children learn to perform an algorithm without understanding it, they will often develop errors that they will make consistently. Probably the most common one I see is trying to subtract the smaller number from the larger instead of regrouping .
Teachers would try to counteract this with rhymes such as “more on the top, no need to stop; more on the floor go next door” but many kids had no understanding of what they were doing or why.
Now we teach students to use other strategies for subtraction based on place value, properties of operations, and the relationship between addition and subtraction. All of these come before teaching the standard algorithm.
Teachers and students spend a lot of time discussing a variety of strategies, exploring different models, and practicing mental math.While it has led to a lot of backlash from people saying the standard algorithm is more efficient, and the other strategies unnecessary, the goal of course is for students to understand WHAT they are doing when they subtract. Eventually they should be able to explain why the standard algorithm works and why it is an efficient strategy. They should also have the skills to perform a lot of subtraction mentally.
Understanding the Strategies for Teachers and Parents
If you are unfamiliar with the strategies used in the Common Core, Owl Teacher has a great explanation on Understanding Addition and Subtraction Strategies. She also has a follow up post on Teaching Addition and Subtraction Strategies using a workshop model.
If you prefer video explanations see 5 Strategies For Teaching Subtraction With Regrouping by Lucky Little Learners. She also has a free printable place value mat to use with manipulatives.
If you would like a free resource explaining the strategies written specifically for parents the South Windsor (Connecticut) Public Schools have made their parent guide for K-2 available as a free PDF. It’s 31 pages of explanations and examples!
For a more concise free/editable parent letter see Addition and Subtraction Strategies Freebie by Mandy’s Tips for Teachers.
For 3 digit numbers here is one from Teaching Has a Pizza My Heart you can buy from TPT.
As the Owl Teacher wrote, all of the strategies can be put in one of three groups. These are: breaking apart numbers based on place value, using a number line, or using friendly numbers. Here are some resources for each.
Breaking Apart Numbers Based On Place Value
Expanded Form
Here’s a free lesson plan from Better Lesson for teaching subtraction using expanded form.
Strategy based lesson from C Palms using expanded form and place value for 3 digit subtraction (includes free pdf copies of task cards, worksheets, exit slips, and assessment)
Here is a YouTube explanation video of this strategy.
Scaffolding into standard algorithm using manipulatives
While traditionally teachers use base ten blocks for this, I find it more effective to use manipulatives that students can break apart and put together to model regrouping. Unifix cubes work well.
Here are a couple of other options:
Popsicle Stick Regrouping Fun.
Double Digit Addition and Subtraction Using Lego Bricks
Another strategy is to use money to introduce subtraction with regrouping as explained by Math Geek Mama here
Subtracting On the Number Line
If you have taught Subtraction As Difference using smaller numbers, this is an easy strategy for students to use with larger numbers.
Using Friendly Numbers
Of course if your students understand place value and that subtraction is difference, they can adjust any subtraction problem to be able to solve it without having to regroup! Friendly numbers can be used with open number lines as explained above.
For using without a number line, check out Math Geek Mama’s article Simple Trick to End the Frustration With Subtraction Regrouping. As she writes, “I’m really not a fan of teaching math “tricks.” Often, they are short cuts that only work under particular circumstances (which are not always made clear to students), and thus cause students confusion later…. So just to be clear, this is not really a “trick,” per se, just an observation and mathematical truth that students can use to potentially make subtraction easier.”
Also see Howie Hua demonstrate this method on TikTok:
Resources for Standard Algorithm
When you are ready to teach standard algorithm, or need to review with struggling or intervention students, here are some free resources.
CPalm 4th grade lesson plan Subtraction Attraction
Khan Academy has a 4th grade video to relate place value to standard algorithm
Math Antics Video- Multi Digit Subtraction
Number Rock Subtraction With Regrouping song
Better Lesson 2 partner games for 4th graders to practice multi digit subtraction and developing number sense
Free printable Subtraction With Regrouping with standard algorithm checklist for students
Online Games For Students
Mr. Nussbaum Math Regrouping Games
Intervention Resources
Subtraction intervention resources available for free download at Elementary Math Interventions and Progress Monitoring