Solving Equations by Balancing

Overview: Students will solve equations using visual representations of mobiles.

Curriculum Expectation(s):

• Number Sense and Algebra: simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations

Learning Goal(s):

• Students will explore how to solve equations by balancing
• Students will represent a mobile puzzle with an algebraic expression

Timing and Sequencing:  This is a 75min activity. This is can be used as an introduction to solving equations,but students should be familiar with simplifying algebraic expressions.

Classroom Constructs: Students in groups of 3

Materials:

• Computer and projector

Description:

Open up the solveme mobiles puzzle website, and project it for students to see.

Explain to students that they are going to solve a puzzle in the form of a balance, where both sides of the balance have to be equal, and/or where both sides of the balance have to add up to a certain value.

e.g.

Students are reminded that they may not shout out answers or raise their hand until all students have had time to think of their solution (30-60s).  This gives all students time to work through the problem, without interrupting their thinking.

Ask a student to share their answer and how they came up with their solution. Ask if other students if they thought of the puzzle/problem in the same way, or if they had a different strategy.

Do 5-6 puzzles in this manner.

Now, students are going to write down an algebraic equation to represent the next puzzle. Then solve the puzzle.

Ask students to share their expressions and their strategies for solving the problem/equation. This can be done as a whole class, or in their small groups of 3.

E.g.

15 =  H + 12

H = 3

Do another 5-8 puzzles like this, where students have to write down an equation for each mobile puzzle, and then solve.

In groups of 3, students work on Vertical Non-Permanent Surfaces (ie. white-boards or black boards on a wall).

Students will draw their own mobile puzzle to represent an algebraic equation that the teacher gives to them verbally (and/or in writing). Students then solve the mobile/equation.

E.g. 3T - 4 = 5