How to do addition and subtraction on the place value chart (HTO chart)

Written by ValerieW. Posted in 2nd Grade

Second Grade Math

How to do addition and subtraction on the place value chart (HTO chart)


48 + 24 = ________

  1. DRAW the numbers in base 10 (meaning, lines for the tens, and circles or dots for the ones) on the place value chart.  Ask your child to organize the numbers; tens like tally marks, ones like dots on a ten frame, as shown below).  The two numbers are placed in middle part of mat, the first number above the second one. (The answer will be placed below the line.) We start out by adding up the ones.  Ooops!  There are too many ones for the ones column (there are 12).



  1. Take a red pen, and circle a group of 10 ones (you are composing them into a group of ten).



  1. With the red pen, draw an arrow over to the tens column, where you will be putting your group of ten.  Remember to cross off the circle of ones, so you don’t count it twice.



  1. Now add them all up, and DRAW the answer (the sum) at the bottom of the table in base ten (lines and circles).  Fill in the number sentence at the bottom.  You are finished!



When we subtract, we are actually looking at two quantities to see the difference between them, that is, we are trying to figure out how much more one group has than the other.

Before human beings had numerals with which to subtract symbolically, they could figure out which of two groups was bigger by taking away one from one group, one from the other, and so on, till one group disappeared and the larger group remained. 

In the example below, we have butterflies and flowers. We have taken away one from the group of flowers, and one from the group of butterflies.  

Crossing off one from the bottom, one from the top, we continue until the smaller group (butterflies) is entirely crossed off.  We see that the group of flowers still has 14 flowers. It is larger by 14.  The difference between the two groups is 14. 


When we subtract, we use the above rationale. 


  1. DRAW 35 and 19 in base ten on the place value chart.


  1. We know that 35 is the larger of the two numbers, but we don’t know by how much.  We can see that there are only 5 ones in the top part of the table – – not enough to be able to successfully cross off all those 9 ones in the bottom number!   We need to break 35 apart (decompose 35) in such a way that there will be enough ones in the top group to be able to successfully cross off all those 9 ones in the bottom group.  So, with a red pen we’ll take a group of ten, cross off that ten (so we don’t accidentally count it later), draw an arrow to the ones column, and draw 10 ones in red in the ones column.



  1. Now in red we will cross off the 9 ones (from the 19), and also cross off 9 ones (from the 35).  (Remember the procedure from “what’s the difference?“)


  1. Now we will cross off 1 ten (from 19), and also 1 ten (from 35). (Remember “what’s the difference?“) Finally we draw what is left in base ten:  (1 line and 6 circles), and we write that number in the number sentence: 35 – 19 = 16



If we teach our students the shortcut (the traditional algorithm of “carrying” and “borrowing”) for doing addition and subtraction without previously giving them the rationale for their actions, learning this shortcut will be meaningless to them.

But by understanding the rationale behind addition and subtraction, these operations become meaningful, and easy to visualize and understand.  The traditional algorithm will come later.

If you have any questions please don’t hesitate to ask us!

The Second Grade Team