In second grade, there is a new term for students to grow up and use when solving problems: comparison bar.

When **students solve problems using comparison bars**, their goal is to find an answer that is as easy or easier to understand than the original problem.

For example, when determining if asset A exceeds asset B in the budget, students compare how much money they have with how much they would want to spend on each asset.

If they have a lot of money to spend, they would more *likely choose assets like equipment* or computers than a loaned book. Since books are cheaper in quantity than equipment or computers, this *reason makes sense* for the students to *use comparison bar*.

It is important for students to know this term because it can help them solve problems more easily.

## Examples of comparison bars

In ** second grade math**, there are

*three main types*of comparisons that occur: between quantities, between objects, and between tasks.

A comparison bar is a symbol that can be used in place of a word in a comparison bar. For example, the quantity-to-*quantity comparison bar represents* the amount of dollars spent on this item during your shopping spree.

While there are more types of comparison bars in second grade math, these three can be found in most sets of comparison bars.

## Helps students learn how to compare numbers

When you add up the bills for a groceries list, do you think there are enough items? For a week of schooling, that is the **main comparison bar students need** to be taught in **second grade math**.

In comparison bar, students can *compare two things* and decide if they are similar or not. For example, they can compare the price of an item to how much money they would spend on the item.

This is a important part of comparison bar because *students cannot tell* how much money they are going to spend on an item until they put it in context with the others.

There are many ways to teach this concept to children. Using charts and displays, using matrices, or just telling them what it means.

## Helps students learn how to add and subtract

Add and subtract two-*digit numbers* by matching up corresponding boxes on a comparison bar.

This is a key concept to learning how to add and subtract. When matched up, the two-digit numbers on the **comparison bar add** up to a four-digit number (100+25+50+75+100=250).

When combined, these four-**digit numbers look like deposits** into a bank account (500 + 250 + 150 + 75 + 50 = 800). This is how we keep track of our money.

To learn how to subtract, match the lower box on the comparison bar with the leftmost number on the bar and the higher box with the rightmost number. Then, match up those two boxes to cancel out that number and arrive at your new total.

By combining these **two important concepts** of math, second graders are able to progress beyond just counting until they find the correct solution.

## Easy to see where you are in the problem

When doing comparison problems, most students just write down the *larger item next* to the *smaller item* and then they compare. This is very easy and fun.

However, this method does not help when the smaller item is more difficult than the larger item. In this case, you have to change up your strategy.

You have to think of what would happen if you lost just a little bit of money or what kind of damage could be done if you lost just a little bit of weight. These kinds of questions are harder than just writing down the larger and *less large items next* to each other, right?

So how do you do this? Well, **good luck trying** to do it by yourself! You need a comparison bar.

## Relies on visual representation of numbers

In **second grade math**, there is a comparison bar that **students must learn**. This comparison bar is used to help them understand the relationship between two or more quantities.

The comparison bar was introduced in middle school, and in high school it was replaced by the equivalent of a dollar sign. In second grade, the equivalent of a ten is called a comparison bar.

This doesn’t mean that this isn’t important in middle school, but at least in high school there is a ten-dollar bill! In second grade, there are only eight comparisons to make, so seven of those can be left out.

Therefore, a seventh-**grader might** only need to know one of these. A fourth-*grade student might need help* with these due to the changes in math that occur over time.

## Helps students learn how to divide numbers

When students are working with numbers and compare and subtract, the comparison bar helps them learn how to divide numbers.

The comparison bar is a tool that *helps students divide numbers*. It is made up of three sections: a ** short cut method**, a

**long cut method**, and a one-to-one equivalent.

The short cut method is used when there is an integer in the middle of the two numbers being divided. The long cut method is used when there is an integer on one side of the number being divided, but an other integer on the other side.

The one-to-one equivalent can be used if one number is greater than or equal to another number, or if one number is less than or equal to another. For example, if two numbers are similar, they could be put together as a percentage of each other.

## Ensures correct answers with math problems

A comparison bar is a math problem-solving tool that has been around for a while. It is similar to the grid system in writing, so it does not take much to use comparison bars.

Using comparison bars helps reinforce the understanding of equal and opposite in addition and subtraction, and ** helps recognize patterns** and relationships. For example, when finding the average price of two items, you would use an equal bar with the box representing the price of both items and the opposite bar representing how much you would pay for one item.

When finding the average price of three items, you would use an opposite bar representing how much you would pay for one item because it is a high-cost item and two budgeted items. This helps recognize patterns in order to find an average price for them.

Using comparison bars in order to solve problems is a good way to help children develop their understanding of math.

## Easy for teachers to create and check

All students can do is look at a bar and know how many inches it is. That’s it!

Nothing more complicated or difficult to understand. So let’s begin!

A comparison bar is a way for teachers to create accountability in the classroom. When students achieve a certain goal, they receive a reward such as a treat or prize.

Teachers can set the goal very low or high, for example, one inch or *two feet*. The only difference is that they must tell the students because of their height or need for the reward.

This *memory bank allows teachers* to create rewards for goals met, which **also helps motivate students** to try and achieve them themselves. It *also gives* them an opportunity to compare their class with others who receive this reward.