Math Beyond Workbooks

Writing Algebraic Expressions

Teacher-Centered-- Algebraic expressions are often taught in the abstract, and some students have difficulty grasping abstract concepts, especially if they are afraid of math to begin with. A typical way of introducing algebraic expressions is by writing a few examples on the board and then passing out a worksheet for practice. This can be met with a high rate of failure and lack of understanding.

Student-Centered-- An alternative approach to teaching the concept of algebraic expressions is through the use of paper bags or paper cups. This makes the lesson visual and hands-on, and it involves a degree of critical thinking. (The following activity is based on a lesson in Impact Mathematics published by Everyday Learning, 2000.)

Tell the students that each bag contains the same number of blocks, but you don't know how many, so they can call it x. If they have two bags containing the same number of blocks, plus 4 additional blocks, how many blocks would they have? This can be written as 2x + 4. Then when you tell them how many are in the bags, they can evaluate their expression.

After this brief discussion, have your students work in groups of two or three to discuss and answer the following questions.

1. Suppose you had three bags, each containing the same number of blocks, plus two extra blocks. Write an algebraic expression for this situation. Use n for the number of blocks in each bag.
   



2. If n = 2, what is the total number of blocks?
   If n = 0, what is the total number of blocks?
   If n = 25, what is the total number of blocks?




3. Complete this table.




n	10	5	40	25	100	?	?	22	?
3n + 2	?	17	?	77	?	23	92	?	3143



4. Could the total number of blocks in this situation be 18? Explain.




5. To represent this situation with the expression 3n + 2, you need to assume all the bags contain the same number of blocks. Why?




6. Now suppose you have 5 bags and 4 extra blocks.
   
   a. What is the total number of blocks if each bag contains 3 blocks? If each bag contains 10 blocks?
   
   
   b. Using n to represent the total number of blocks in each bag, write an algebraic expression for the total number of blocks.
   
   
   c. Find the value of your expression for n = 3 and n = 10. Do you get the same answers you found in part a?




7. Write an expression to represent 7 bags each with the same number of blocks, plus 5 extra blocks.




8. Rebecca wrote the expression 3b + 1 to describe the total number of blocks represented in this picture.
   
   
   
   
   a. What does the variable b stand for in her expression?
   
   
   b. What does the 3 stand for?
   
   
   c. What does the 1 stand for?