Understanding and Writing Equations

Lesson Plan - Get It!

Audio:

Before continuing this lesson, it would 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 term:

• equation
• variable

An equation is a mathematical statement or sentence that shows the relationship between two expressions.

For example, you could write an equation for a car ride you take with your parents. In your equation, you would compare the speed of the car and the distance the car travels, or the time it takes you to get from where you are to where you are going.

The table below is an example that could represent the drive you are taking with your family:

To learn how to write an equation that represents the relationship between the speed your car is going and the distance it is traveling, follow the steps below:

1. Look at the information in the table and find the pattern. For example, if your car is moving at a speed of 30 mph, it travels a distance of 90 miles. However, if it is moving at a speed of 35 mph, it travels a distance of 105 miles. It's time to figure out what the pattern is.
2. To do this, you can divide the distance by the speed. If you divide 90 by 30, your answer is 3. Do the same for the other values in the table. If you divide 105 by 35 your answer is 3. Is it the same for the other values? Yes it is! So now you know the pattern!
3. Take the pattern and write a mathematical sentence in words. You might say, "If my car is traveling at a speed of 30 mph for 3 hours, I will travel a distance of 90 miles."
4. Now take that mathematical sentence and write a shortened version: "Speed x 3 hours = Distance."
5. Now write your mathematical sentence in numbers: 30 x 3 = 90.
6. Notice that the last column of the table has an s in the Speed row and a d in the Distance row. The s and the d are variables. They are the numbers we are trying to find. You can now write your equation using the variables.
7. The s represents the speed and the d represents the distance. You know from step 4 that if you multiply the speed by 3 you get the distance. Therefore, your equation will look like this: s x 3 = d. Tada! You just wrote your first equation! Congratulations!
8. At this point, you could substitute a number for s and find the numerical value for d. For example, you could substitute 55 for s in your equation and find the distance your car travels in 3 hours. 55 x 3 = d (Do the multiplication) 55 x 3 = 165.
9. Try it for yourself. Substitute a number for s and find the answer for d.

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It would be great if every problem involving writing an equation came with a handy dandy table like the one above. However, that is not always the case. It is an important skill to learn how to set up your own table so you can then identify the pattern among the values and write your equation. Take a few minutes now and learn how to do that.

Mrs. Smith wants to take a vacation. The problem is, she has a dog and she only has $30 available to pay a kennel to board the dog for her while she is away. The local kennel charges $3 per day to board a dog. How many days can Mrs. Smith go on vacation and board her dog before her $30 runs out? Can she go on vacation for one week? Can she go on vacation for 2 weeks? Set up a table to show the relationship between the number of days the dog is boarded and the cost:

1. Your first step is to step up a table so you can illustrate the numerical values. Your table should have two rows (one for number of days and one for cost) and eight columns (one column for the titles of the rows and the other 7 columns for 7 days).
   

   # Days	1	2	3	4	5	6	7
   Cost

2. After reading the math problem above, you know the local kennel charges $3/day to board a dog. You can add that information into your table:
   

   # Days	1	2	3	4	5	6	7
   Cost	$3

3. Even though you only have a limited amount of information, you can still write an equation to help you fill in the rest of the chart and answer the questions above. You know that 1 day of boarding at the kennel costs $3. If you use the letter d to represent days and the letter c to represent cost, you can now set up your equation: D x 3(dollars) = C
4. Use your equation to fill in the rest of the values in the table. For example, 2 x 3(dollars) = 6(dollars)
5. Your completed table should look like the one below:
   

   # Days	1	2	3	4	5	6	7
   Cost	$3	$6	$9	$12	$15	$18	$21

6. Now you can go back to the original question and figure out the answer: How many days can she go on vacation? Discuss how you found your answer with your teacher.

The next section has opportunities for you to practice the skills you learned and strengthen your understanding.