Algebraic Equations

Katharine Borg

Source: My own Activity
“What’s my rule?” http://www.schoolinyourhome.com/math/whats-my-rule.htm

Mathematical Topic: The Origin of Algebraic Equations

Grade Level: 4-6

Minnesota Standards
Algebra: Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.
Algebra: Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

National Standard
Numbers and Operations: Instructional programs from prekindergarten through grade 12 should enable all students to understand numbers, ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and how they relate to one another; and compute fluently and make reasonable estimates.
Algebra: understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various concepts.
Problem Solving: build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving.
Connections: recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

Applications to the Math Classroom
- Begin to explain how to solve a problem with a missing variable. First explain to them what a variable is, then move on to algebraic equations with independent and dependent variables and constants. Explain how solving a problem with missing variables means solving the equations backwards.
- Begin with an activity to have students try to solve problems without using function notation first to introduce functions. After giving examples and they see how difficult it is, explain how to find functions by beginning with domain and range, and then move onto the f(x), using the “What’s my Rule?” game to show students how to find the output. Have the students compare using functions and not using functions.
- “What’s My Rule?” To play this math game, you simply think of a formula and have the student guess input values. After each input value you supply an output value. The student has to guess the rule. For example, you think of the rule y = 2x + 1. The student guesses 0, and you reply 1. The student guesses 1, and you reply 3. The student guesses 3 and you reply 7. The student then guesses the rule "double the number and add one", which would be correct.
- Note: This is a good way to teach equivalence of algebraic expressions. For example, the rule "double the number and add two" i.e. 2x+2 is equivalent to "add one to the number and then multiply this amount by two" i.e. 2(x+1).
- A variation on this game is to allow the student to come up with the rule. The student will enjoy trying to stump the teacher!
-What introductory information is necessary for children to have prior to starting this activity?
Students will need to know how to add, subtract, multiply, and divide.

-What grade level/s is appropriate for this activity? Please use appropriate justification for your answers here.
I would teach this activity to grades 4th through 6th grade. I think this activity is great for introducing algebraic equations. Teaching this activity at a later grade level is helpful to the teacher and the students. Students will better be able to understand these concepts of algebra and will have a great grasp on addition, subtraction, multiplication, and division. When students understand these things better it means less re-teaching of these concepts.

-How will you engage students with different learning styles?
For this activity I could use many different teaching techniques to engage my students with different learning styles in the activity. One thing I would do is use visuals in this activity so the students can easily see the rule that is being used. I also could let students work with partners to talk through the equations to find the rule being used.

-How does this activity connect to the real world for students? Be specific.
Algebraic equations can be used in many different ways. An example that I have is if you were to put $10 in the bank and keep it there for 5 years with 5% interest rate annually. How much money will you have in five years? 5(10)+.05(5)=the amount of money you will have total after 5 years.

-Why is this activity with its concepts important for student learning? Be specific.
This activity is a great introduction to algebraic equations. Students need to know and understand these algebraic equation concepts because they are the basis for future algebraic equations and formulas. Students will use this basic understanding of algebraic equations to further their knowledge in algebra.

-What are your comments on this activity? Would you use it in your classroom?
I really like this activity because it introduces algebraic equations through a whole classroom activity. I taught this activity to students about two years ago and it went really well. The students had been introduced to algebraic equations and this activity I was using as a review for them to prepare them for their test. The students really enjoyed it cause they thought they would be able to think of equations that would stump me