Strategic Solving

The triangle and the square below have equal perimeters.

Find the value of x.

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Determine the Strength of a Question.

Here below are a lot of equations:

(1). Without solving, identify 3 equations that you think would be least difficult to solve.

(2). Explain your reasoning.

(3). Choose 3 equations to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.

(a). Equation 1: (least difficult).

(b). Equation 2:

(c). Equation 3: (Most difficult).

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Predict the Sign of an Answer.

Without solving, identify whether the following equations have a solution that is positive, negative, or zero.

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Graph a Relationship from a Table of Values.

The table below gives some sample data for two quantities, and, that are in a proportional relationship. Complete the table.

(1). Write an equation that represents the relationship between and shown in the table.

(2). Graph the relationship on the axes below. Use a scale for the axes that shows all the points in the table.

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Mai gave half of her brownies, and then half a brownie more, to Kiran. Then she gave half of what was left, and half a brownie more, to Tyler. That left her with one remaining brownie.

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Solve each equation and check your solution.

(1).

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(2).

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(3).

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Elena said the equation 9+ 15 = 3+ 15 has no solutions because 9 is greater than 3. Do you agree with Elena? Explain your reasoning.