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Three Digit Subtraction with Regrouping Base Ten Blocks

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Three Digit Subtraction with Regrouping Base Ten Blocks
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Basics on the topic Three Digit Subtraction with Regrouping Base Ten Blocks

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Subtraction with Regrouping with Base Ten Blocks

Subtraction with large numbers can often be confusing. Luckily, there is help! You can visualize subtraction with 3 digit numbers using base ten blocks. This text teaches you how to use base ten blocks to conduct subtraction with regrouping.

Modeling Subtraction with Regrouping using Base Ten Blocks

Why use base ten blocks for three digit subtraction with regrouping? Modeling subtraction with regrouping with base ten blocks helps us see what is happening when we subtract. Rather than just moving digits, like in the standard algorithm, we can build and break apart numbers to see how values change. It is particularly helpful when we are regrouping. We build the first number in blocks to make the subtraction equation easier to regroup, or borrow from.

Subtraction with Regrouping with Base Ten Blocks – Example

Let’s solve six hundred seventy-one minus fifty-eight as our 3 digit subtraction equation with regrouping using base ten blocks.

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In a place value chart, represent the first number, six hundred seventy-one, with base ten blocks. The second number, fifty-eight, tells us how many to take away from six hundred seventy-one.

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Starting in the ones column, the second number tells us to take away eight blocks.We can't do that because there is only one block here.

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We need to regroup a set of ten from the tens place.There are now eleven blocks in the ones place that we can take eight away from. We are left with three blocks, so write three below. Now move to the tens place.The second number tells us to subtract five tens. Take away five from the six tens which leaves us with one ten. Write the number one below.

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Now move to the hundreds place.There are no hundreds to take away, so write the number six below. Six hundred seventy one minus fifty eight equals six hundred thirteen.

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Subtraction with Regrouping with Base Ten Blocks – Summary of Steps

These are the necessary steps you need to follow in order to conduct three digit number subtraction with regrouping using base ten blocks.

Step # What to do
1 Model the first number with base ten blocks in a place value chart.
2 Look at the second number and identify its ones place.
Begin taking away from the ones place first and regrouping
from the tens place, if needed. Write the answer below.
3 Move left to the next place value, repeating the process
to solve the equation.
4 If you need to regroup but there is a zero,
move left to the next place value until you can regroup!

Have you practiced yet? On this website, you can also find 3 digit subtraction with regrouping using base ten blocks worksheets and exercises.

Transcript Three Digit Subtraction with Regrouping Base Ten Blocks

"Dear Imani, I've had so much fun at summer camp!" "We have camp fires every night!" "The wood pile had six hundred seventy one logs, and we've burned fifty eight so far, so there are... erm" "What do I do?!" Let's help Mr. Squeaks by learning "Three Digit Subtraction with Regrouping-Base Ten Blocks.” We can use place value charts and base ten blocks to model subtraction with regrouping. These tools help us see what's happening when we regroup rather than just moving numbers around. We build the first number in blocks to make the subtraction equation easier to regroup, or borrow from. Let's use the campfire equation to practice. In a place value chart, represent the first number, six hundred seventy-one, with base ten blocks. The second number, fifty-eight, tells us how many to take away from six hundred seventy-one. Starting in the ones column, the second number tells us to take away eight blocks. We can't do that because there is only one block here. We need to regroup a set of ten from the tens place. There are now eleven blocks in the ones place that we can take eight away from. We are left with three blocks, so write three below. Now move to the tens place. The second number tells us to subtract five tens. Take away five from the six tens which leaves us with one ten. Write the number one below. Now move to the hundreds place. There are no hundreds to take away, so write the number six below. Six hundred seventy one minus fifty eight equals six hundred thirteen. Mr. Squeaks can write there are six hundred thirteen logs left for the campfires! Next, Mr. Squeaks writes that there were two hundred and three water balloons for a water balloon fight. By the end, one hundred eighty nine were thrown. Let's help calculate how many balloons were left. What is our first step? Use base ten blocks to represent two hundred and three. The second number, one hundred eighty-nine, tells us how many we take away from it. In the ones column, how many blocks will we subtract from three? ...According to the second number, we should subtract nine, but we can't do that because there are only three blocks. What can we do? We can regroup a set of ten from the tens place. But there are zero tens here! What should we do? Instead, we should move to the hundreds to regroup. Regroup one hundreds block from the hundreds and put it in the tens place. Now take a set of ten from here, regrouping it to the ones place. There are now thirteen blocks in the ones place that we can take nine away from. We have four blocks left, so write four below. Then, move to the tens place. The second number tells us to take eight tens away. Eight taken away from nine leaves us with one. Write one below. Now move to the hundreds place. We borrowed from here earlier, so there is only one hundred left. The second number tells us to take one hundred away which makes zero hundreds. Below, leave the hundreds place blank, so... two hundred three minus one hundred eighty nine equals fourteen. Mr. Squeaks writes that there were only fourteen water balloons left in the end! To subtract three digit numbers with regrouping, remember! Model the first number with base ten blocks in a place value chart. Next, look at the second number and identify its place. Begin taking away from the ones place first... and regrouping from the tens place, if needed. Write the answer below. Move left to the next place value, repeating the process to solve the equation. If you need to regroup but there is a zero, move left to the next place value until you can regroup! "That's weird...who uses real wood for a campfire?" "And throwing water!? How dangerous someone will definitely short circuit!"

Three Digit Subtraction with Regrouping Base Ten Blocks exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Three Digit Subtraction with Regrouping Base Ten Blocks.
  • How many marshmallows are left?

    Hints

    If there are not enough ones to subtract from, you can re-group a ten to the ones.

    We can see a ten has been re-grouped into the ones place, so we can now subtract 7 from 12.

    Use the base ten blocks to help you solve the rest of the problem.

    Solution

    At the end of day one they had 305 marshmallows left.

    362-57

    • First of all, we needed to subtract 7 from the ones place, however, there were only 2 ones so we re-grouped a ten from the tens place.
    • We therefore had 12 ones. 12 - 7 = 5 so we can write 5 in the ones place.
    • We then needed to subtract 5 from the tens place.
    • There were 5 tens in the tens place, so 5 - 5 = 0, so we can write 0 in the tens place.
    • We move to the hundreds place where there are three hundreds but nothing to subtract, so we write 3 in the hundreds place.
    • This gives us the answer: 305.

  • Which jar should the marshmallows go in?

    Hints

    Remember, re-group from the place value to the left if you don't have enough to subtract from.

    You can draw out your own base 10 blocks to help you solve the problem.

    Once we have subtracted the ones, we need to re-group a hundred to the tens column to be able to subtract 7 from 15 to get 8.

    Solution

    They have 81 marshmallows left so should store them in this jar!

    255 - 174

    • First of all, we need to subtract 4 from the ones.
    • 5 - 4 = 1, so we write 1 in the ones place.
    • We then need to subtract 7 tens but we only have 5 tens, so we re-group a hundred so then have 15 tens.
    • 15 - 7 = 8 so we write 8 in the tens place.
    • We now need to subtract a hundred from the hundreds where there is only one hundred left, so we are left with zero hundreds.
    • The answer is therefore 81.

  • How much food does the camp have left?

    Hints

    You can draw your own base ten blocks to help you solve the problems.

    Remember, you can re-group from the tens or hundreds if you need to.

    Solution

    Here are the amounts of each food they have left:

    672 - 484

    • We first need to subtract the ones but there are not enough, so we re-group a ten and have 12 ones.
    • 12 - 4 = 8, so write 8 in the ones column.
    • We then need to subtract the tens but there are not enough, so we re-group a hundred.
    • 16 - 8 = 8, so write 8 in the tens place.
    • We then subtract 4 hundreds from 5 hundreds to get 1 hundred, so write 1 in the hundreds place.
    • Therefore our answer is 188.
    312 - 199
    • First, we subtract the ones but need to re-group a ten to do so, giving us 12 ones.
    • 12 - 9 = 3, so we write 3 in the ones place.
    • We then subtract the tens but need to re-group a hundred to do so, giving us 10 tens.
    • 10 - 9 = 1, so we write 1 in the tens place.
    • We then have 2 hundreds - 1 hundred which equals 1 hundred, so we write 1 in the hundreds place.
    • Our answer is therefore 113.
    604 - 387
    • First, we subtract the ones but need to re-group a ten to do so, however there are zero tens so we re-group a hundred, then re-group a ten giving us 14 ones.
    • 14 - 7 = 7, so we write 7 in the ones place.
    • We then subtract the tens which we now have 9 of, after re-grouping the hundred earlier.
    • 9 - 8 = 1, so we write 1 in the tens place.
    • We then have 5 hundreds - 3 hundreds which equals 2 hundreds, so we write 2 in the hundreds place.
    • Our answer is therefore 217.
    407 - 197
    • First, we subtract the ones.
    • 7 - 7 = 0 so we write 0 in the ones place.
    • We then subtract the tens but need to re-group a hundred to do so, giving us ten tens.
    • 10 - 9 = 1. so we write 1 in the tens place.
    • We then have 3 hundreds - 1 hundred which equals 2 hundreds, so we write 2 in the hundreds place.
    • Our answer is therefore 210.

  • Solve the subtraction problems.

    Hints

    Remember, you can draw your own base ten blocks to help you solve the problems.

    Remember to re-group if needed.

    Solution
    • Dear Mr. Squeaks,
    We have had a great time at camp! We have been busy creating new robots! We started with 153 screens and have used 98. Now we have 55 left.

    • Altogether, we built 214 robots but unfortunately 137 short-circuited! Now we only have 77 left.
    • We tried to fix the ones that broke! We had 302 nails and ended up using 277! We only have 25 left now.
    • We also had an inventing competition! We were given 345 minutes to create something new. It took me 296 minutes to complete my creation so I had 49 minutes to spare!
    • It has been great! Looking forward to seeing you soon, Imani

    P.S. I think we need to do some shopping when we get home. We had 601 screws but I brought 474 with me so we only have 127 left now!

  • How many screws are left at Imani's camp?

    Hints

    To subtract the ones, you will need to re-group a ten like this.

    Can you subtract 28 from these base ten blocks?

    Solution

    They have 304 screws left.

    332 - 28

    • First of all, we need to subtract the ones but there are not enough, so we need to re-group a ten. We then have 12 ones.
    • 12 - 8 = 4, so we write 4 in the ones column.
    • We then have 2 tens left in the tens column. We need to subtract 2 tens, so 2 - 2 = 0, so we write 0 in the tens column.
    • We have no hundreds to subtract, so we write 3 in the hundreds column as 3 - 0 = 3.
    • Therefore our answer is 304.

  • How many logs are left now?

    Hints

    There are multiple subtraction problems to solve here. Solve them one at a time, re-grouping where needed.

    You can draw out your own base ten blocks to help you.

    Solution

    There are 289 logs left after day three.

    • They started with 902 logs and burned 183 on day one.
    • 902 - 183 = 719.
    • We then need to subtract 234 (logs burned on day two) from 719.
    • 719 - 234 = 485.
    • On day three they burned 196 logs.
    • 485 - 196 = 289.