Equation Balancing

Source: I designed this activity to work with a virtual manipulative I found on the Illuminations website: http://illuminations.nctm.org/ActivityDetail.aspx?ID=26

Introductory information necessary: Knowledge of addition, subtraction, multiplication and division facts; basic information regarding number sentences.

Link to MN State Math Standards: Grade 3: Algebra: Use number sentences involving multiplication and division basic facts and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

3.2.2.1: Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences.

For example: The number sentence 8 × m = 24 could be represented by the question "How much did each ticket to a play cost if 8 tickets totaled $24?"

3.2.2.2: Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.

For example: Find values of the unknowns that make each number sentence true

6 = p ÷ 9 24 = a × b 5 × 8 = 4 × t.

Materials Required: Computers with internet access for each student or group of students.

Procedure/Description of Activity: This activity would be used to help students understand numerical equations.

Students would first be given time to work with the virtual manipulative on their own, to get a feel for how it works. The main idea is to enter different expressions on both sides of the scale (the red pan and the blue pan) that are equal. When an expression is entered into either side, the pans move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation is entered into the “Balanced Equation” side of the screen. Students can reset the balance to remove the expressions from the pans.

After the students have had enough time to get a good idea of how the manipulative works, the teacher would read a realistic math problem to the class. The students would discuss how they could go about creating an equation to solve it, and then test their solutions on the scale manipulative. An example of a math problem would be “Charlie is planning a birthday party. He is inviting 5 friends. The cupcakes he has purchased came in a pack of 18. How many cupcakes will each person get? (hint: be sure to include the birthday boy in your equation!)” A balanced equation would be 6x3=18. A situation such as this could be made more difficult by adding something like “The dog got into the cupcakes and ate six of them. How many cupcakes would each person get?” A balanced equation in this situation would be 6x12=18-6.

At which grade level would this activity be appropriate? This virtual manipulative would be perfect for third grade students, as it ties into the Minnesota math standard 3.2.2.1 and 3.2.2.2, which deal with interpreting and solving number sentences.

How will you engage students with different learning styles? This activity will naturally appeal to students with a variety of learning preferences. The manipulative provides a tactile activity and will also appeal to students that enjoy learning visually, and auditory learners will respond well to the discussion of the problem. For students that enjoy working with others, it would be appropriate to have them work in pairs or small groups.

How does this activity connect to the real world for students? By creating realistic math problems for the students to solve, they will clearly see how equations can help them in the real world.

Why is this activity with its concepts important for student learning? The virtual manipulative helps strengthen students’ understanding of numerical expressions and equality. By being able to see how the two sides of the equation need to balance, students can actually see when the equation works. And, as stated on the Illuminations website, “in understanding equality, one of the first things students must realize is that equality is a relationship, not an operation. Many students view ‘=’ as ‘find the answer.’ For these students, it is difficult to understand equations such as 11 = 4 + 7 or 3 × 5 = 17 – 2.”

What are your comments on this activity? Would you use it in your classroom? I love this activity! I like that it utilizes technology, which students seem to respond very well to, I like the visual aspect of the activity, which definitely aids in the students’ understanding of equality, and I like that it allows students them to try a variety of solutions to problems. I would definitely use it in my classroom.