## Comparing Two-digit Numbers

#### Aligned To Common Core Standard:

**Grade 1 Numbers** - 1.NBT.3

How to Compare Two-digit Numbers - If you are familiar with comparing single-digit numbers, then you can easily use that knowledge to compare bigger numbers. Let's learn how you can do this. Two-digit numbers are 10 to 99 or values with tens and ones places. Some examples of of these values are 13, 23, 45, 77 and 81. You notice how all these numbers have two-digits? Comparing two-digit values is just like comparing single-digit values. In double-digit numbers, we compare the digits that belong to the same place values. The left integer holds more weight than the right integer, so we compare that first. If they are the same we compare the digits in the ones column. The bigger value wins. Here are some steps you can follow: Start from the left-hand side and then make your way to the right. Compare the digit left side digit of both numbers with each other, for example: 21 _ 73 You can already see that 2 is less than 7, which makes 73 already a bigger number than 21. But what if you have the same number on the left side of both the digits such as: 37 _ 32 Follow rule number, i.e. start from the left and then start moving to the right. In this case, both the digits have 3 on their left side. However, on the right side, we can clearly see that 7 is greater than 2. This makes 37 greater than 32. These worksheets introduce students to the concept of relative comparisons. We show students visualize what greater, less than, or equal means.

- Place Value Comparisons Step-by-step Lesson- We compare numbers by place value after clearly stating there position and value. We will explain each of the symbols of comparison and how to use them.
- Circle the Larger Number Worksheet- Find the bigger number in each set and circle and write it.
- Greater Than, Less Than, Equal To- A nice five-pack of problems. This will give you a bunch of different practice to get you going in the right direction.
- Words, Digits, and Pictures Guided Lesson - Walk through using greater than, less than, or equal in sentences, number form, and picture form. A trifecta!
- Breaking It Down Guided Lesson Explanation - Using the strategies we learned in the lesson, here is more detail for students.
- Compare Numbers of Shapes - You will look this one and say "What the! How does that relate to this standard?" I said the same when a colleague showed me this format. Throw this one in there to make sure the focus on the true use of the skill.
- Monster Strategy - We review a good strategy to follow when comparing numbers. You'll get the name after you view the worksheet.
- Use Your Sign - A straight up use of the symbols >, <, or =. I teach them to look for equal numbers, if not point to the smaller number.

- Guided Lesson 1 - We first looking for the largest and then smallest integer in a number series.
- Guided Lesson 2 - Which words makes this statement complete. This is leading us toward using symbols.
- Draw More or Less Guided Lesson 3 - This is where math and art fuse into one.
- Step-by-step Lesson 1 - We revisit the concept of being less than. Underline all numbers below that are bigger than 6?
- Step-by-step Lesson 2 - We get to the highest level of using this skill.
- Comparing Balloons Worksheet - Doesn't numbers on balloons just making every math problem more fun to do?
- Draw More or Less Worksheet - I kept the changes within four objects to make it not as cumbersome.
- Mark Numbers Worksheet - They describe a number and you put a check down for it.
- Compare Number Tables Worksheet - This is neat because you are really comparing ten numbers at once.

#### Guided Lessons

These really get students ready to start using symbols to simplify the language in number comparisons.

#### Practice Worksheets

I made these slightly more enjoyable by getting students to draw.

### The Applications of this Skill

While simply comparing the value of two integers does not seem like a critical math skill, it is the jump off point for too many applications to list. This allows you to order values from greatest to least and vice versa. When you evaluate a series of values it is simply a scalable version of the root skill. When we apply this to commerce, specifically purchasing something, this skill allows us to quickly evaluate which offer gives us the best deal. There are many professions and business sectors which at their core are entirely based on this fundamental skill. Many financial instruments are created by investment bankers and actuaries in an attempt to confuse their customer as to which the best deal is, but it really is still rooted in this simple concept and skill.

The core concept of comparing numbers has made its way into most of the machines we have created and the software that controls the behavior of those machines. The machine is often based on thresholds which tells the machine to constantly compare the current condition to a fixed value. A basic application of this would be a thermostat. Thermostats are those things in the walls that control the temperature of a room or several rooms. For instance, you may set the temperature to 70° (Fahrenheit) on the thermostat. This device then constantly compares the temperature value of the room to the 70° we set it at. If the temperature goes above or below that number, the air conditioning system, or heater are turned on.