The ideas in this borrowing lesson are taken from Add & Subtract 2-B ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Subtracting in columns - borrowing
Free lesson plan from ebook Adding & Subtracting in Columns 1

This lesson aims to explain the idea of borrowing. The student is first made to notice that sometimes when subtracting you don't have enough ones to do the 'taking away'. The solution is to break down one ten into ten ones.  This process is first practiced with pictures (or manipulatives).  

45 − 7 = ?     4 tens and 5 ones 3 tens and 15 ones   In the first picture, we can't cross out 7 ones, so we break down one ten-pillar. Now cross out 7 ones.  What is left? __ tens and __ ones =____

42 − 18 = ?     4 tens and 2 ones __ tens and __ ones   In the first picture, we can't cross out 1 ten and 8 ones, so we break down one ten-pillar.  Now cross out 1 ten 8 ones.  What is left? __ tens and __ ones =____

Example exercise types

These are just examples of the type of problems to do.  You should provide much more practice than is shown here.

1.  Break down a ten.  Draw ten-pillars and ones.  What do the numbers become?

43 4 tens 3 ones   3 tens 13 ones

36 __ tens __ ones   __ tens __ ones

Do it also without the pictures.

2.  Break down a ten first.  Then subtract ones and tens separately.  Write down the subtraction sentence.

5 tens 5 ones −  1 ten  7 ones

4 tens 15 ones −  1 ten    7 ones 3 tens   8 ones

55 − 17 = 38

After practicing for a while the process of breaking the ten into ten ones, it is time to introduce the standard form of subtracting in columns.

5 tens and 3 ones __ tens and __ ones Cross out 1 ten 6 ones.  What is left?     __tens __ ones tens 4 ones 13  5 3 −   1  6    3   7        The '5' in the tens-column changes into 4  because we 'broke one ten down'  OR BORROWED one ten into the  ones-column.  Now the ones-column has 13 instead of just 3.   Then we subtract the ones and  the tens separately.

4 tens  __ tens and __ ones Cross out 2 ten 8 ones.  What is left?     __tens __ ones tens   ones        −   2 8               We borrow a ten into the ones-column.   Now the tens-column has __ left, and ones-column has __ instead of just __.   Then we subtract the ones and the tens separately.

Example problems

1.   Fill in the table.  Break one ten down, then subtract.

2.  Subtract.  Borrow from the tens when needed.

Figure out the missing numbers in these subtraction    problems! You might need to borrow from the tens.       3  −  1   7   5    8       −    7  1   6         0  −  3    4   2         −  1  4 6   8    6   2  −     5   3

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