Determine the approximate number of objects in each group and compare them. There are circles and diamonds in the picture. They are arranged in 5 rows with 5 shapes in each. But two shapes are missing in the lowest row. That is why we can say there are fewer diamonds than circles without counting them.

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When we estimate the number, we assume how many objects there are without counting them. We calculate items only to check if we were right.

We apply estimation when the exact number of objects doesn’t matter or when we can't denote it. For example, how many windows are in the skyscraper? We may know there are 10 windows on the first floor, and the number of floors is 30. In this case, there are about 300 windows in total. But we do not know if there are some other windows which we haven’t counted. We just suppose and guess there are about 300 windows.

With the help of estimation, we can compare objects. Imagine you need to choose one jar of candies among the two. You will compare the total number of candies and choose the one with more sweets.

How does estimation help us? Are there other ways to find the precise number? Let’s look at the example. Here are the rows of figures with ten items in each.

We might think there are more shapes on the right because they take more place. But it’s wrong. The shapes on the right and the left are arranged in 3 rows with 10 items in each. It means the number of triangles is the same as the number of circles. Thus, the groups are equal.

Now, look at how the picture has changed?

The number of triangles hasn’t changed. There are still 3 rows with 10 figures in each, but the number of diamonds has become less. There are no 10 but 7 shapes in the third row, which makes two rows of 10 shapes and 7 diamonds in total. Three rows of 10 shapes are greater than two rows of 10, aren’t they? So, there are more triangles than diamonds.

To compare the groups of items without counting, look at how they are arranged. Let’s compare stars and frames. Which group has more items?

Look at the shapes in the top row. How many shapes can we see there? Firstly, 5 stars and then 5 ones nearby them. We can find their number without counting, as we already know what 5 shapes look like and that 5+5=10, so we can say there are 10 shapes in one row.

And how many rows with 10 shapes are there? We can see four rows with stars and the same number of rows with frames. These are 4 full rows with 10 shapes in both.

Does the number of stars equal the number of frames? We may guess so, as their number is approximately equal. To find it out, look at the lowest row that contains less than 10 shapes. 

There are 4 stars and 3 frames. 4 is greater than 3, so the number of stars is greater. Our assumption was right, the approximate number of shapes is equal. But it’s more correct to say the number of stars is greater than the number of frames.

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