*Contributor: Marlene Vogel. Lesson ID: 10845*

Rules rule, especially in algebra! A rule is an math expression that can be written in words and numbers. Using worksheets and online games, you will learn how to use tables of data to write rules!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Lion, Beaver

Grade Level

Intermediate (3-5)

Lesson Type

Dig Deeper

Before you continue, it will be good to learn or review some vocabulary words (All definitions can be found at A Maths Dictionary for Kids Quick Reference by clicking on the terms):

Algebra contains many *rules*. One way to make sure you understand the different rules you will learn in algebra is to write a rule yourself.

This lesson focuses on teaching you how to use tables of data to write *rules* or *expressions*. Your expressions will include a *variable*, an *operator*, and a *constant*. Review the vocabulary words above to make sure you understand what your expressions will look like. You will write your expressions in words first, then translate them into numbers.

*Write an expression describing the rule for the numbers in the sequence 6, 7, 8, 9, 10, and 11. Then give the 100 ^{th} number in the sequence.*

Term Number |
1 |
2 |
3 |
4 |
5 |
6 |

Number in Sequence |
6 |
7 |
8 |
9 |
10 |
11 |

Refer to the table above for this activity:

- The first step of writing an equation is to review and understand the information in the problem. Above is a table. This table includes the numbers in a sequence (6, 7, 8, 9, 10, 11) and the term number for each of the terms in the sequence (6 is the 1
^{st}term in the sequence, 7 is the 2^{nd}term in the sequence, etc.). - The next step is to find the rule used to find each number in the sequence. To do this, consider what you need to do to go from the term number 1 to the sequence number 6. How do you go from 1 to 6? Do you use addition, subtraction, multiplication, or division? You use addition. Exactly! In words, you would write "One plus five equals six." The numerical version of this math sentence would look like this: 1 + 5 = 6.
- Now take a look at the term number 2 and the sequence number 7. Again, write in words the rule of going from 2 to 7. Then rewrite it in numerical form (Two plus five equals seven; 2 + 5 = 7).
- I am sure you are noticing a pattern. It seems if you add 5 to the term number you get the sequence number. That is your rule! Written in words, it would look like this: "Add five to the term number." Written numerically, it would look like this:
*n*+ 5. The variable*n*represents the term number. In your numerical expression, you could substitute*n*with the number 1 or 2 or 3 or 4 or 5 or 6 . . . or even 100. In fact, that is the final step of this problem! - Now knowing that your expression is
*n*+ 5, use your expression to find the 100^{th}number in the sequence. To do this, simply substitute the number 100 for the variable*n*in your expression: 100 + 5 = 105. - 105 is the 100
^{th}number in the sequence!

In addition to being able to identifying the rule and writing the expression, you can also identify if the sequence is an *arithmetic* or a *geometric* sequence. The activity above is an example of an *arithmetic* sequence. Again, refer to the vocabulary at the beginning of the lesson to help your understanding of arithmetic and geometric sequences.

Term Number |
1 |
2 |
3 |
4 |
5 |
6 |

Number in Sequence |
6 |
7 |
8 |
9 |
10 |
11 |

Take a look at the second row of the table above. As labeled, those numbers are the numbers in the sequence. You can also see each number is one more than the number before it. This is an example of an arithmetic sequence. If you take the difference between consecutive numbers, the answer is always going to be the same: 1. This is characteristic of an arithmetic sequence. The same value is used between the consecutive numbers, the value 1 in this example.

Look at the table below:

Term Number |
1 |
2 |
3 |
4 |

Number in Sequence |
2 |
4 |
8 |
16 |

This table is an example of a *geometric* sequence. Focus only on the second row, the sequence numbers. If you use the same process as you did with the arithmetic sequence table, and take the difference of consecutive numbers, you can see that it is not an example of an arithmetic sequence. For example, 4 - 2 = 2 but 8 - 4 = 4. So you see, the same value is not used between consecutive numbers. In fact, if you pay close attention to the numbers in the bottom row, you can see a pattern.

Right! Each number is double the previous number: 4 is 2 doubled, 8 is 4 doubled, and so on.

Now that you have done an outstanding job on the lesson, it is time to practice and make sure your understanding of tables, equations, and arithmetic and geometric sequences is solid!

The* Got It?* section gives you some activities to do just that! Enjoy!