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Regrouping in Subtraction

This is a complete lesson about how to teach regrouping in subtraction (borrowing) step-by-step with 2-digit numbers, meant for 2nd grade. The lesson contains a teaching video, instruction with visual models, and many exercises.

In the video below, I explain an idea of breaking down the concept of regrouping (borrowing) so that students can see what actually happens in it. For example, to subtract 52 − 38, we write 52 as 50 + 2 (breaking it down into its tens and ones). Then, regrouping means that 50 + 2 becomes 40 + 12. This makes the process totally transparent.


Subtraction with regrouping (YouTube video)




We will now study regrouping
(also called "borrowing") in subtraction.

As a first step, we study breaking
a ten-pillar into ten little cubes.
This is called regrouping,
because one ten "changes
groups" from the tens group
into the ones.

Break
a ten.

4 tens 5 ones

 

3 tens 15 ones

First we have 45. We
"break" one ten-pillar
into little cubes.
  Now we have 3 tens and
15 ones. It is still 45, but
written in a different way.
Here is another example. First
we have 5 tens 3 ones. We
"break" one ten-pillar into
10 little cubes. We end up with
4 tens 13 ones.
Break
a ten.

5 tens 3 ones

 

4 tens 13 ones

1. Break a ten into 10 ones. What do you get? Draw or use manipulatives to help.

a. 
   3  tens    0  ones ___tens ____ones
b. 
___ tens ____ones ___ tens ____ones
c. 
___ tens ____ones ___tens ____ones
d. 
___ tens ____ones ___ tens ____ones
e. 

___ tens ____ones ___tens ____ones
f. 
___ tens ____ones ___ tens ____ones


Let's study subtraction. The pictures
on the right illustrate 45 − 17.

First, a ten is broken into 10 ones.
So, 4 tens 5 ones becomes
3 tens 15 ones.

After that, cross out (subtract)
1 ten 7 ones.

Break
a ten.

4 tens 5 ones

 

3 tens 15 ones

Cross out 1 ten 7 ones (from the second picture).

What is left?  ____ tens ____ ones

The pictures on the right
illustrate 52 − 39.

First, a ten is broken into 10 ones.
So, 5 tens 2 ones becomes
4 tens 12 ones.

After that, cross out (subtract)
3 tens 9 ones.

Break
a ten.

5 tens 2 ones

 

4 tens 12 ones

Cross out 3 tens 9 ones (from the second picture).

What is left?  ____ tens ____ ones

2. Fill in. Always subtract (cross out some) from the second picture.

Break
a ten.

3 tens   6 ones

 

2 tens   16 ones

a. Subtract 8 ones (from the second picture).

What is left? ____ tens ____ ones

Break
a ten.

___ tens ___ ones

 

___ tens ___ ones

b.  Subtract 2 tens 7 ones.

What is left? ____ tens ____ ones

Break
a ten.

___ tens ___ ones

 

___ tens ___ ones

c.  Cross out 2 tens 5 ones.

What is left? ____ tens ____ ones

Break
a ten.

___ tens ___ ones

 

___ tens ___ ones

d.  Cross out 4 tens 4 ones.

What is left? ____ tens ____ ones



3. First, break a ten. Then subtract ones and tens separately. Look at the example.

a.

5 tens 5 ones

 

   4  tens

  15 ones

3   tens 7   ones
   1  ten

 8  ones

 b.

7 tens 2 ones

 

  ___ tens

 ___ ones

3   tens 5   ones

  ___ tens

___ ones

c.

6 tens 0 ones

 

  ___ tens

 ___ ones

2   tens 7   ones
  ___ tens

___ ones

d.

6 tens 4 ones

 

  ___ tens

 ___ ones

3   tens 8   ones
  ___ tens

___ ones

e.

7 tens 6 ones

 

  ___ tens

 ___ ones

4   tens 7   ones
  ___ tens

___ ones

f.

5 tens 0 ones

 

  ___ tens

 ___ ones

2   tens 2   ones
  ___ tens

___ ones

g.

8 tens 1 one

 

  ___ tens

 ___ ones

6   tens 5   ones
  ___ tens

___ ones

h.

6 tens 3 ones

 

  ___ tens

 ___ ones

2   tens 8   ones
  ___ tens

___ ones

4. Jessica had 27 colored pencils and her brother and sister had none. Then Jessica gave
   10 of them to her brother, and four to her sister.

    a.How many pencils does Jessica have now?
 

    b. How many more pencils does Jessica have than her brother?
 

    c. How many more pencils does Jessica have than her sister?



This lesson is taken from Maria Miller's book Math Mammoth Add & Subtract 2B, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.



Math Mammoth Add & Subtract 2-B

A self-teaching worktext for 2nd grade that covers mental addition and subtraction with two-digit numbers, and regrouping in addition and subtraction (carrying & borrowing).

Download ($5.65). Also available as a printed copy.

=> Learn more and see the free samples!

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