Two-Digit Addition

In this lesson and the next, we will use the grid to visualize the methods used to do arithmetic with two-digit numbers. For today, we’ll be looking at addition.

How many small green squares are on the grid to the left? Enter this number in the first input box. Then click the first Next button to see the next example on the grid. Continue to do this for each row in the table. (Hint: The grid is 10 squares tall.)

The first addition problem in this table is illustrated on the grid to the left. How many green squares are there? Type in your answer, and continue to the following rows, clicking each Next button in turn.

The example on the top grid represents an addition problem of the type you just solved. In the first row of this table, complete that problem. Then continue to the next row, by clicking its Next button. Enter the new addition problem shown on the top grid. The problem you type in will be shown on the bottom grid. You can switch between input boxes by pressing the tab key. Fill in each row in this way.

In each row of this table, click the Next button and then enter the addition problem that the example on the top grid represents. These problems involve slightly larger numbers than in the last question, but you do not have to solve them. Again, the problem you type in will be shown on the bottom grid.

The first addition problem in this table is illustrated on the grid to the left. How many green squares are there? Click the first Rearrange button to move the squares around without changing how many there are, making it easier to count them. Enter your answer, and then click the Next button to continue to the second row.

Solve these addition problems in the standard way (by adding one column at a time), without using the grid.

	$36$
$+$	$21$
$=$

	$47$
$+$	$32$
$=$

Again, how many green squares are there? Use the Rearrange button in each row.

Now solve these addition problems in the standard way, without using the grid.

	$54$
$+$	$39$
$=$

	$38$
$+$	$43$
$=$

Notice that, in the two last sets of questions, you were doing exactly the same thing both times you solved each addition problem! That is, adding in columns is just like using the Rearrange button on the grid.