This group of nuts has five almonds and five hazelnuts.

Grouping Objects

This is out last page before we start working on numbers, counting, and the rest of math. We just covered the way you observe and identify objects. The concept of grouping objects is part two to the ideas of observation. For example, if a question asks you about the blue balls in a bucket, you will need to mentally separate those balls from the group and start looking at their traits.

Grouping and Addition

When you study addition, addition is about putting groups together. Those groups may be made of one object or millions. In addition, the final group is larger than the two smaller groups.

A group of five pencils is combines with a group of four pencils.
5 + 4 = 9 (The final group has nine pencils.)

In addition, a group of three will combine with a group of four.

Grouping and Subtraction

Subtraction is the opposite of addition. You are taking one group away from another group when you subtract. The final group will be smaller that the first group.

Start with a group of eight candies. Take away a group of three candies.
8 - 3 = 5 (You finish with a smaller group of five candies.)

Grouping and Multiplication

When you get to the multiplication section, it will feel like addition. Instead of combining two groups, you are combining many groups. It's like asking yourself, "What happens if I have three groups of four objects?" You could add them, but that takes too long. You need to multiply to find out how large the final group is.

How many objects are in six groups of three?
Addition: 3 + 3 + 3 + 3 + 3 + 3 = 18
Multiplication: 6 x 3 = 18 (You finish with eighteen objects in the final group.)

Grouping and Division

Division is not the opposite of multiplication, but it is like a backwards version of multiplication. In division, you start with a big group and then your goal is to break it into equal parts. Looking at the previous example, a group of 18 can be broken into six groups of three. Ask yourself, "How many groups of this size can if get from this larger group?"

If I break this big group of twenty-four into three smaller groups, how many will be in each group?
24 ÷ 3 = 8 (You will have eight objects in each smaller group).

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