Life Skills:

• Thinking & Reasoning
• Communication

Time Frame:
1 class period that runs 45 minutes.

Group Size:
Large Groups

Summary:
This lesson will show how to distinguish algebraic terms. Like terms can be combined by adding or subracting the coefficients of each term...the variables themselves do not change.

Materials:
No materials are needed.

The students are the living materials needed. The boys can represent the y variables and the girls can represent the x variables.

However, signs for the students to wear that identify each person as an x or a y (or more variable if you wish), could be made; then some paper and tape would be all that is need.

Background For Teachers:
The teacher needs a basic understanding of numerical coefficients and variables.

Instructional Procedures:
One of the initial obstacles students face as they begin to learn basic algebra units is the concept of like terms and combining terms in an simple expression.

This unit will involve active participation by students. Ask for a dozen or so volunteers to come to the front of the room. Random order is fine.

Ask the class how they might categorize them. Boys vs. girls, blondes vs. brunettes, tall vs. short, etc.

Ask the students to describe the volunteer group as an expression using those names: EXAMPLE: 5 Blondes + 4 Brunettes or 3 blue jeans + 8 shorts, etc.

Be sure to show an example of a group like '5 girls + 3 girls' as well as a group of more than two items like '3 blondes + 5 brunettes + 1 red'.

Choosing the first example of boys vs. girls, ask them to describe the group with a mathematical expression--this time using variables instead of words.

EXAMPLE: Instead of Blondes...use L, instead of Brunettes...use B. (blue jeans...J, shorts...S, etc.).

If there were 6 girls and 4 boys in the front of the class, a student might decide to use '6g +4b'.

Allow for a variety of original expressions. Encourage creativity. EMPHASIZE THAT THE EXPRESSIONS GIVEN ARE CALLED ALGEBRAIC EXPRESSIONS.

Ask the students, 'What does 4b + 3b equal?' '5j + 10s + 2j = ?' 'Does 6g + 4b = 10gb?' WHY NOT? Explain your reasoning.

What conclusions can you draw from this? (Hopefully, the students will see that only like objects can be grouped together).

CONCLUSION: LIKE TERMS ARE TERMS THAT ARE ALIKE (identical variables). LIKE TERMS CAN BE ADDED AS LONG AS THE VARIABLES ARE ALIKE. COEFFICIENTS ARE ADDED, NOT VARIABLES.

Once it is clear that the students understand the addition examples, ask for another group to the front of the class.

Describe the group as an algebraic expression. Write the expression on the board for all to see (example: 5g + 4b).

REMOVE 2 OF THE SAME TYPE FROM THE GROUP. What operation represents the removal of the two? (SUBTRACTION) What algebraic expression can be written? (5g + 4b - 2g)

What is the net result of our actions? (3g + 4b). What equation can be written? (5g + 4b - 2g = 3g + 4b).

REPEAT THE PROCESS BY REMOVING OTHERS FROM THE GROUP. Use an example that removes the entire group.

Emphasize that 0g = 0...it isn't necessary to leave the variable when 0 is the numerical coefficient.

CONCLUSION: TERMS CAN BE SUBTRACTED AS LONG AS THEY ARE LIKE TERMS.

Extensions:
Have the students organize the class into more categories so that each student can be described as a combination of variable.

An example could be categories like blonde-blue eyed-boy, brunette-green eyed-girl, etc.

Assign different variables to each description. Write multi-variable expressions that describe each row, each half of the class, etc.

Students should be able to write expressions like 5afx + 4agy. Like terms can be recognized by their variable combinations.

ALSO, the students can describe their own families in three different ways. Have them explain the concepts learned to another family member and have the family member write an expression that describes the family.

Author:
KEVIN PEDERSEN

Created Date :
Jun 05 1997 13:09 PM