Grade 6 Math Flashcards

1. The table below shows changes in the area of several trapezoids as the lengths of the bases, b1 and b2, remain the same and the height, h, changes. Which formula best represents the relationship between A, the areas of these trapezoids, and h, their heights?

Answer: A=6h

The area of a trapezoid is given by the formula A = 0.5 * (b1 + b2) * h. Since b1 and b2 remain constant, their sum (b1 + b2) is also constant. For the formula A=6h to be correct, the term 0.5 * (b1 + b2) must equal 6, which means (b1 + b2) must be 12. This formula correctly represents a direct linear relationship between area and height when the bases are fixed.

2. This table shows lengths, widths, and areas of four rectangles. In each rectangle, the length remains 40 meters, but the width changes. Which formula best represents the relationship between P, the perimeters of these rectangles, and w, their widths?

Answer: P=2w+80

The perimeter of a rectangle is calculated using the formula P = 2 * (length + width). Given that the length remains 40 meters, we substitute this value into the formula. This results in P = 2 * (40 + w). Distributing the 2 gives us P = 80 + 2w, which can also be written as P = 2w + 80.

3. The drawing shows a protractor and a trapezoid. Which is closest to the measure of ?JNM?

Answer: 61°

To find the measure of angle JNM, one must align the protractor's baseline with one ray of the angle (e.g., NM) and its center with the vertex (N). Then, read the degree mark where the other ray (NJ) crosses the protractor's scale. Based on the visual representation (implied by the question), 61° is the closest reading for the angle.

4. Given the equation a^2+(2b-c)xd, solve for a=2, b=5, c=8, and d=4.

Answer: 12

To solve the expression a^2+(2b-c)xd, substitute the given values: a=2, b=5, c=8, and d=4. First, calculate a^2 = 2^2 = 4. Next, evaluate the parenthetical expression: (2*5 - 8) = (10 - 8) = 2. Finally, multiply this result by d and add it to a^2: 4 + (2 * 4) = 4 + 8 = 12.

5. Stephen researched the topic of solar-powered lights for his science project. He exposed 10 new solar lights to five hours of sunlight. He recorded the number of minutes each light continued to shine after dark in the list below. 63, 67, 73, 75, 80, 91, 63, 72, 79, 87 Which of these numbers is the mean of the number of minutes in Stephen's list?

Answer: 75

The mean of a set of numbers is found by summing all the values and then dividing by the total count of values. For the given list (63, 67, 73, 75, 80, 91, 63, 72, 79, 87), the sum is 750. Since there are 10 numbers in the list, the mean is 750 divided by 10, which equals 75.