Did you know that students learn better when they are given a variety of strategies to use in math? This way they can find the strategy that works best for them. Finding a strategy that works is extremely important when teaching math. As teachers, we always have to remember that not all students learn the same way.
Subtracting large numbers is always a difficult skill for students to learn, especially when regrouping is involved. Many of my students struggle with how to do this. There are actually 4 easy strategies for subtracting large numbers that I will share below!
1. Subtract using Base 10 blocks
Teaching students to subtract using base 10 blocks shows them really important math skills:
It is hands-on and engaging.
They learn to draw diagrams.
They learn to use objects.
Teaching them to subtract with base ten blocks shows students the "why" of both addition and subtraction. It shows how the numbers are put together and taken apart to get their final answer. This is extremely important for students to learn how things work in order for them to understand the algorithm. This is also especially important when students have to regroup. If your school does not supply them, I have found them affordable here on Amazon!
Students should understand what regrouping actually means and that it is more than just carrying the 1 and dropping a number. I liked to make sure my students had a really solid foundation of regrouping before moving on to the next concept. When I teach subtraction using base 10 blocks, I like to use Base 10 Student Anchor Charts with my class.
2. Subtract using Expanded Form
Next, try teaching students to subtract using expanded form. They can simply break larger numbers into expanded form and then subtract each place value before putting them back together.
Here is an example of using expanded form to subtract:
EX: 456 -235 = (400+50+6) - (200+30+5) = 200+20+1 = 221.
Students can get additional practice writing numbers in expanded form if needed by using this Understanding Place Value Activity.
3. Subtract using the Algorithm
The algorithm is for more advanced learners who understand the "why" of how the numbers work together. This is also known as "old math" (like we were taught!) This is simply following the steps. The algorithm is harder for students to memorize and understand if they do not have a strong foundation for what the numbers mean or the true meaning of regrouping. Subtracting using the algorithm is also harder for students to compute mentally when regrouping is involved.
4. Subtract Using the The Townhouse Regrouping Method
A hard concept with subtracting is dealing with regrouping multiple place values. For example the problem, 1,008 - 569.
Students struggle with going all the way to the thousands place but having to make the hundreds and tens into 9. My favorite strategy for teaching this is using the townhouse method.
Here’s how to use the Townhouse Method for Subtraction:
The ones place (house) wants to bake cookies for grandparents day. They need to use 9 cups of sugar but they only have 8 so they go next door. That neighbor says they have 0 cups of sugar, but because she stopped there, they now want to make cookies and need some sugar.
So then the ones goes to the hundreds (house) to ask for sugar but they also have zero cups. Now that house also wants to make cookies.
Finally, go to the thousands house to ask for sugar. They finally have "1" cup of sugar! But they are the thousands place so this really means that they have 1,000 cups!
So the ones place takes the "1" cup of sugar and shares it with the neighbors in between. She gives the hundreds house the 1,000 cup but that becomes a 9 (or 900) because she has to then give the tens house some making it a 9, then finally she has 10 cups of sugar in her ones house to be able to subtract the 9.
My students LOVE this strategy. As we practice it, I will switch up what is being made as well as the ingredients. I will also have students come up with the story at times.
Remember-Not all Students Learn the Same
Remember that all of your students are capable of finding the answer when subtracting large numbers that require regrouping. However, they may all use different ways to get to that answer. It is always so interesting when I have students come up and teach each other how they got their answer using Cognitively Guided Instruction. I love to see how differently everyone’s brain works!