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When you have a student who isn’t “clicking” with the idea of subtraction with regrouping it can be tempting to go out and find more activities and experiences to help them on their way.
In reality, it might not be that your student needs more— there’s a reason this skill isn’t sticking in the first place. Instead, we need to take the approach of taking an inventory of what our students know and determining exactly where their understanding stops– this is where focusing your time and energy will give you the most bang for your buck!
Subtraction With Regrouping Checklist
Rather than troubleshooting by determining what your students do not know, it can be helpful to look at the progression of subtraction with regrouping teaching and find out exactly what they do know so you can support your students with the very next step.
Regardless of the numbers you are using in daily instruction, explore this checklist first with 2-digit numbers before moving on to 3 or 4 digit numbers.
- Can your students demonstrate subtraction with regrouping using a groupable model (ex: linking cubes) on a place value mat?
- Can your students demonstrate subtraction with regrouping using a pre-grouped model (ex: base ten blocks) on a place value mat?
- Can your students demonstrate subtraction with regrouping with a representative model (ex: drawing on a place value chart) alongside a hands-on model.
- Can your students demonstrate subtraction with regrouping with a written method (ex: the algorithm) alongside a hands-on model.
- Can your students demonstrate subtraction with regrouping with a representative model alone?
- Can your students demonstrate subtraction with regrouping using a written method alongside a representative model?
- Can your students demonstrate subtraction with regrouping using a written method?
Within this progression, it will be much easier to see any individual misconceptions your student may hold and you will be able to determine whether those misconceptions are a matter of a math concept that they haven’t yet developed a full understanding of or whether their errors are aligned with a procedural misunderstanding when it comes to notation using the standard algorithm.
Try this Subtraction with Regrouping Activity!
Use this activity (download free here) to strengthen your students’ connection between hands-on, pictorial and written subtraction methods.
- Choose a popcorn container. This tells the number of kernels you are starting with.
- Choose a kernel card. This tells the number of kernels that fell out of the container.
- Subtract using hands-on tools, pictures and/or numbers to find the number of kernels left in the container.
When using this activity with a student, start with hands-on materials (like linking cubes or base ten blocks) alone. When a student demonstrates that they understand the concept, add in another method such as a place value drawing or the written algorithm alongside the hands-on tool.
If your student makes an error, check to see where the error occurred. Does your student lack an understanding at the concrete level? Do they understand correctly at the concrete level but lack an understanding of the conventions of recording their thinking using pictures or numbers? Identifying exactly where the first error occurs will influence your next steps!
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