Geology Rocks! GSE Learning Plan 8th Grade Math

Open Ended

How can interpreting expressions and linear equations help us model real-world situations?

Multiple Choice

Which of the following best describes the significance of using algebraic reasoning in solving linear equations?

• It helps to find solutions systematically and justify each step.

• It is only useful for complex equations.

• It is not necessary for real-world problems.

• It makes equations more complicated.

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Multiple Choice

Based on the diagrams in both diagnostic assessment questions, what is the value of one candy bar in each scenario?

• $0.25 and $0.10

• $0.50 and $0.40

• $0.75 and $0.30

• $0.10 and $0.25

Fill in the Blank

What does x have to equal to make the scale balanced in the equation x + 2 = 4?

Multiple Choice

How do the diagrams with candy bars and coins relate to the diagrams with scales and variables? What mathematical concept connects them?

• They both show how to solve equations by balancing values

• They both show how to count objects

• They both show how to compare sizes

• They both show how to use money

Fill in the Blank

If the 3 x’s and 4 squares equal 10 squares, how many squares does each x represent?

Open Ended

Explain the concept of 'tare' and why it is important when using a scale.

Multiple Choice

Why is the scale not balanced when weighing a crate of 10 basketballs against 10 basketballs?

• The crate adds extra weight

• The basketballs are different sizes

• There are more basketballs on one side

• The scale is broken

Multiple Choice

What value of x will make the scale balanced in the equation 4 + 2x = 16?

• x = 6

• x = 8

• x = 4

• x = 2

Multiple Choice

How many rocks are inside each crate in the first balance scenario shown?

• 3

• 4

• 5

• 2

Open Ended

How does the concept of balancing scales relate to solving equations in algebra?

Multiple Choice

Which of the following equations correctly represents the second balance scenario with crates and rocks?

• 2x + 2 = 12

• 2x + 2 = 14

• 2x + 4 = 14

• 2x + 4 = 12

Open Ended

In the third balance scenario, what is the relationship between the number of crates and the number of rocks on each side of the scale?

Fill in the Blank

Fill in the blank: In the fourth scenario, the left side of the scale has two crates and ___ rocks.

Multiple Choice

If you remove one crate from each side of a balanced scale, what happens to the balance?

• The scale remains balanced.

• The left side becomes heavier.

• The right side becomes heavier.

• The scale tips randomly.

Multiple Select

Which of the following are steps you might use to solve a linear equation?

• Add or subtract the same value from both sides.

• Multiply or divide both sides by the same value.

• Change only one side of the equation.

• Keep both sides balanced throughout the process.

Open Ended

How does using manipulatives, such as crates of rocks, help you understand linear equations?

Fill in the Blank

A linear equation can be represented as a balanced ___ .

Multiple Choice

Which of the following best describes the relationship between balancing a scale and solving a linear equation?

• Both require keeping both sides equal by performing the same operation on each side.

• Balancing a scale is only about physical objects, while equations are about numbers.

• Solving a linear equation does not require balance.

• Balancing a scale always involves subtraction.

Open Ended

What do you notice about the scale in the image?

Open Ended

Is the scale in the first image balanced? How do you know?

Multiple Choice

In the second image, what does each 'X' represent if the scale is balanced?

• A number that makes both sides equal

• A box of rocks

• A single rock

• A variable with no value

Open Ended

Why is the scale not balanced in the third image?

Multiple Select

Which of the following statements about the crates and rocks in images 4 and 5 are true?

• Each crate represents the same value in all images

• The number of rocks on each side is always equal

• The scales are balanced when the total weight on both sides is equal

• Adding crates always makes the scale heavier

Open Ended

How can you use the idea of balancing scales to solve the equation 2(x + 4) = 16?

Fill in the Blank

Fill in the blank: In the equation 7x = 6 + 5x, the value of x is ___

Open Ended

How do you think algebraic reasoning can help you solve problems in real life?

Multiple Choice

Which of the following is NOT one of the learning goals for this lesson?

• I can use algebraic reasoning in describing the solutions to linear equations.

• I can interpret expressions and linear equations to model real-world situations.

• I can justify the steps to a linear equation.

• I can solve quadratic equations using factoring.

Open Ended

How does balancing a scale relate to solving a linear equation?