Solving Equations and Balanced Hangers

Mrs. Nelson introduces a sixth-grade math lesson focused on writing and solving equations using balanced hangers. The lesson includes an activity where students connect diagrams to equations and solutions. Students learn to reason about weights using both diagrams and equations, ensuring balance by applying mathematical operations equally to both sides. The lesson emphasizes understanding through visual and equation-based reasoning.

What is the main objective of the lesson on balanced hangers?

• To learn about different types of hangers

• To write and solve equations representing balanced hangers

• To calculate the speed of a moving hanger

• To understand the history of hangers

In the context of balanced hangers, what does it mean when the left side equals the right side?

• The weights are balanced

• The hanger is too heavy

• The hanger is broken

• The weights are unequal

How can you express the equation for a balanced hanger with two identical weights labeled Y and a total weight of 12?

• Y - Y = 12

• Y + Y = 12

• Y / Y = 12

• Y * Y = 12

If a balanced hanger has a total weight of 11 and four identical weights labeled Z, what is the weight of each Z?

• 11

• 3

• 4

• 2.75

What is the weight of W if it balances with 13 and 4/5, and 3 and 4/5 is already accounted for?

• 12

• 8

• 5

• 10

What is the first step in solving the equation X + 3 = 8?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 3 from both sides

• Add 3 to both sides

When solving 2Y = 12, what operation should be performed to isolate Y?

• Subtract 2 from both sides

• Divide both sides by 2

• Add 2 to both sides

• Multiply both sides by 2

What is the inverse operation of multiplication when solving equations?

• Subtraction

• Division

• Addition

• Multiplication

Why is it important to perform the same operation on both sides of an equation?

• To change the equation's solution

• To keep the equation balanced

• To simplify the equation

• To make the equation more complex

What is the final step in solving an equation to find the weight of a piece labeled with a letter?

• Check if the solution satisfies the original equation

• Multiply all weights together

• Add all weights together

• Subtract all weights from each other