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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

Instructor:
*Shannon Orr*

Because mental math is a very useful life skill, there are many different concepts. This lesson is designed to define what counting on means. It will also give strategies for helping students understand and have the ability to use counting on in addition.

When you learn to read, you are taught to start at the beginning of the sentence. When you learn to write, you are taught to start at the beginning of the paper. No surprise that when you are taught how to count, you are told to start at the beginning. There are songs, poems, and pictures that clearly show that counting always starts at the number 1. Now imagine first grade students walking into their classroom, sitting at their desk, and you, the teacher, announcing that they will begin counting from another number. Another number? This can't be real. Can't you just picture the terror on the faces of the little people looking back at you?

As an adult, the idea of counting on may seem pretty clear but to a child who has always started at the number 1, this idea may seem ridiculous and unbearable. **Counting on** is a mental math skill where, when adding two numbers, you begin counting from the largest number and add the second number to it. Counting on helps us figure out how many more we need of something and how many we will have once more is added.

Being able to count starting at any number is important for two main reasons. One reason is that it shows how well a student understands numerical order. For example, when students use **rote counting** or counting in order, teachers can't really determine how well they understand number order. Every day, Sally may be able to count from 1 to 20 without ever skipping a number. It may appear that Sally understands what number comes first, next, and so on until she reaches 20. The real test comes when the teacher asks Sally to start at number 7 and count to 20. If Sally only knows her numbers starting at 1, she hasn't truly grasped numerical order.

Another reason counting on is important is because it is the beginning steps for teaching students how to add. If Tony understands that after the number 11 there is 12, 13, 14, and so on, he has the foundation to be able to compute 11 + 3 = 14. Until students understand the numerical order, they may have a difficult time understanding how to add.

One strategy that students have to understand before counting on is introduced is identifying which number is larger when comparing two numbers. The definition for counting on states that counting begins with the largest number and goes on. If Emily can't determine which number, 3 or 7, is larger, the concept of counting on will be difficult. Teachers can help students understand which number is bigger by using models. If Emily's teacher shows her 3 balls and 7 balls and asks her which is more, Emily is likely to be able to choose the 7 balls. Then the teacher would explain that more means the number is larger. Making this connection between vocabulary words will help students when they are identifying the largest number.

Once students understand how to identify the largest number, the next step is to teach how to count on or add the second number to the first. The teacher should verbally remind students to always start with the largest number because it will make counting on much easier since the second number is smaller than the first. If the teacher asks Billy what is 2 + 8, Billy must first acknowledge that 8 is the larger number then he can add two more to figure out that the answer is 10.

**Counting on** is when you are adding two numbers and you begin counting from the largest number and add the second number to it. It is an important mental math skill that we use every day. In order for students to be able to properly use the technique, they need to understand numerical order as well as be able to figure out which number is larger.

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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

- What are the Different Types of Numbers? 6:56
- What Is The Order of Operations in Math? - Definition & Examples 5:50
- How to Find the Prime Factorization of a Number 5:36
- How to Find the Greatest Common Factor 4:56
- How to Find the Least Common Multiple 5:37
- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Estimation Problems using Fractions 7:37
- How to Solve Complex Fractions 5:20
- Calculations with Ratios and Proportions 5:35
- What is a Percent? - Definition & Examples 4:20
- Changing Between Decimals and Percents 4:53
- Changing Between Decimals and Fractions 7:17
- Mathematical Sets: Elements, Intersections & Unions 3:02
- Ruler Postulate: Definition & Examples 5:19
- What is a Fact Family? - Definition & Examples 6:09
- What is a Multiple in Math? - Definition & Overview 6:02
- What is a Positive Integer? - Definition & Examples 3:56
- Basic Arithmetic: Rules & Concepts 5:02
- How to Do Double Digit Multiplication: Steps & Practice Problems 4:27
- How to Teach Double Digit Multiplication
- Double Digit Multiplication Strategies 5:10
- Counting On in Math: Definition & Strategy
- Go to Basic Math Review: Help and Review

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