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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn how to write equations using symbols.

### New York State Common Core Math Grade 8, Module 4, Lesson 1

Common Core Math Grade 8, Module 4, Lesson 1 Worksheets (pdf)

### Lesson 1 Student Outcomes

Lesson 1 Summary

Begin all word problems by defining your variables. State clearly what you want each symbol to represent.

Written mathematical statements can be represented as more than one correct symbolic statement.

Break complicated problems into smaller parts or try working them with simpler numbers.

Classwork

Discussion

Compare the mathematical statement to the equation.

Example 1

Express the following statement using symbolic language:

1 a) A whole number has the property that when half the number is added to fifteen, we get back the number itself.

1 b) A whole number has the property that when the square of half the number is subtracted from five times the number, we get back the number itself.

Example 2

Express the following statement using symbolic language:

Paulo has a certain amount of money. If he spends six dollars, then he has 1/4 of the original amount left.

Example 3

Write the following statement using symbolic language:

When a fraction of 57 is taken away from 57, what remains exceeds 2/3 of 57 by 4.

Example 4

Express the following statement using symbolic language:

The sum of three consecutive integers is 372.

Example 5

Express the following statement using symbolic language:

The sum of three consecutive odd integers is 93.

**Exercises 1–5**

Write each of the following statements using symbolic language.

1. The sum of four consecutive even integers is -28.

2. A number is four times larger than the square of half the number.

3. Steven has some money. If he spends nine dollars, then he will have 3/5 of the amount he started with.

4. The sum of a number squared and three less than twice the number is 129.

5. Miriam read a book with an unknown number of pages. The first week she read five less than 1/3 of the pages. The second week she read 171 pages and finished the book. Write an equation that represents the total number of pages in the book.

**Problem Set**

Write each of the following statements using symbolic language.

1. Bruce bought two books. One book costs four dollars more than three times the other. Together, the two books cost him $72.

2. Janet is three years older than her sister Julie. Janet’s brother is eight years younger than their sister Julie. The sum of all of their ages is 55.

3. The sum of three consecutive integers is 1.623.

4. One number is six more than another number. The sum of their squares is 90.

5. When you add 18 to 1/4 of a number, you get the number itself.

6. When a fraction of 12 is taken away from 17, what remains exceeds one-third of seventeen by six.

7. The sum of two consecutive even integers divided by four is 189.5.

8. Subtract seven more than twice a number from the square of one-third of the number to get zero.

9. The sum of three consecutive integers is 42. Let x be the middle of the three integers. Transcribe the statement accordingly.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn how to write equations using symbols.

• Students write mathematical statements using symbols to represent numbers.

• Students know that written statements can be written as more than one correct mathematical sentence.

Lesson 1 Summary

Begin all word problems by defining your variables. State clearly what you want each symbol to represent.

Written mathematical statements can be represented as more than one correct symbolic statement.

Break complicated problems into smaller parts or try working them with simpler numbers.

Classwork

Discussion

Compare the mathematical statement to the equation.

Example 1

Express the following statement using symbolic language:

1 a) A whole number has the property that when half the number is added to fifteen, we get back the number itself.

1 b) A whole number has the property that when the square of half the number is subtracted from five times the number, we get back the number itself.

Example 2

Express the following statement using symbolic language:

Paulo has a certain amount of money. If he spends six dollars, then he has 1/4 of the original amount left.

Example 3

Write the following statement using symbolic language:

When a fraction of 57 is taken away from 57, what remains exceeds 2/3 of 57 by 4.

Example 4

Express the following statement using symbolic language:

The sum of three consecutive integers is 372.

Example 5

Express the following statement using symbolic language:

The sum of three consecutive odd integers is 93.

Write each of the following statements using symbolic language.

1. The sum of four consecutive even integers is -28.

2. A number is four times larger than the square of half the number.

3. Steven has some money. If he spends nine dollars, then he will have 3/5 of the amount he started with.

4. The sum of a number squared and three less than twice the number is 129.

5. Miriam read a book with an unknown number of pages. The first week she read five less than 1/3 of the pages. The second week she read 171 pages and finished the book. Write an equation that represents the total number of pages in the book.

Write each of the following statements using symbolic language.

1. Bruce bought two books. One book costs four dollars more than three times the other. Together, the two books cost him $72.

2. Janet is three years older than her sister Julie. Janet’s brother is eight years younger than their sister Julie. The sum of all of their ages is 55.

3. The sum of three consecutive integers is 1.623.

4. One number is six more than another number. The sum of their squares is 90.

5. When you add 18 to 1/4 of a number, you get the number itself.

6. When a fraction of 12 is taken away from 17, what remains exceeds one-third of seventeen by six.

7. The sum of two consecutive even integers divided by four is 189.5.

8. Subtract seven more than twice a number from the square of one-third of the number to get zero.

9. The sum of three consecutive integers is 42. Let x be the middle of the three integers. Transcribe the statement accordingly.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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