Trust your intuition. Did you know that even 4- and 5-year-olds can develop math intuition? One way is by building a sense of equality (the same) and inequality (more). And you don’t have to wait until they know how to count to teach these comparisons!

Corresponding Common Core Standards: K.CC.C.6, K.CC.B.4.A

## Step 1: Understanding equality and one-to-one matching

How can you teach students to compare when they can’t yet count the objects? Begin with a concrete approach using manipulatives. Build a tower using 2-5 uniform cubes (same size, shape, and color) and ask students to build a tower with “the same number”:

They can easily compare height to arrive at equality without having to count.

After students respond, reinforce the concept of “the same number” and the one-to-one match of cubes by comparing each cube of the two towers. Point with two fingers and say, “Same, same, same….”

If they respond incorrectly, you’ll get to a single cube and say, “…different.” For example, at Happy Numbers, we respond to incorrect answers by illustrating this difference:

Soon, students can take over the role of comparing aloud. This approach helps them move toward a counting comparison. They learn that the towers are the same height because they are made up of the same number of cubes. It also reinforces the vocabulary of “the same” and “different.”

## Step 2: Understanding inequality

Next, introduce the vocabulary “more.” By using familiar, uniform cube towers, you’ll build upon existing knowledge through scaffolding. Build two towers of differing height and ask which has “more” cubes:

Students understand the new term visually by comparing the height of the towers. They see that the two towers are different and learn that the term for the taller one is “more.”

Again, evaluate each response by pointing to cubes and saying, “Same, same, same, different” to reinforce visual one-to-one matching and to build the concepts of equality and inequality:

## Step 3: Using non-uniform objects

The next scaffolded step is to maintain the vertical alignment, familiar task, and familiar vocabulary while switching to non-uniform objects. Combine different sets of cubes (math counters, stringing beads, etc.) as long as they are roughly the same size:

Students learn that in determining “more,” it is the height that matters and not the appearance of the cubes. This is one of the first steps in transitioning to abstract thinking.

One way to add complexity to the task is by combining the concepts of “the same” and “more.” Build two towers of identical cubes and increase the number of answer options. Ask students whether one tower has more, the other tower has more, or they are the same:

Another way to increase complexity is by presenting two sets of scattered cubes. Give students the option to align them in towers if they want to. Those who are beginning to rely on counting or have a strong ability to match one-to-one can skip that step. Either way, using manipulatives during instruction helps students to adapt and strengthen their thinking.

If students choose not to align the cubes by building towers and answer incorrectly, prompt them to build the towers and answer again.

## Step 5: Applying the skill in a new environment

By now, students should have a good feel for “the same” and “more” and can apply this understanding in a new environment. Present familiar tasks (align objects and compare) using horizontal alignment and varied objects. This requires students to transfer skills and helps them avoid situated cognition.

Begin with uniform objects in a horizontal alignment — for example, at Happy Numbers we use train cars as kindergarteners like to build trains. After identifying “the same” and “more,” present scattered sets and have students align them horizontally to compare:

Next, try varying the objects by presenting different objects for the same task. Matchbox cars, Shopkins, or mini erasers all work well (as long as they are roughly the same size)! Again, give students the option of whether or not to align the objects before comparing:

If students answer incorrectly without first aligning the objects, prompt them to do so and then answer again. If the response is still incorrect, demonstrate one-to-one matching by pointing and saying, “Same, same, ….”:

1. Get online: HappyNumbers.com ←

HappyNumbers.com provides interactive, scaffolded lessons for use on PCs or tablets. The exercises discussed in this post are part of our kindergarten curriculum.

Yours,
Evgeny & Happy Numbers Team