Listening to Math Problems Flashcards

Listen to the math teacher: 'For this problem, first calculate the total cost of five notebooks that are $2.50 each. Then, determine the cost of three pens at $1.25 each. Finally, you need to find the difference between the cost of the notebooks and the cost of the pens.' What is the final step required to solve this problem?

Answer: Subtract the total cost of the pens from the total cost of the notebooks.

The teacher's final instruction is to 'find the difference between the cost of the notebooks and the cost of the pens.' The word 'difference' in mathematics indicates subtraction. Therefore, the last step is to subtract the smaller amount (cost of pens) from the larger amount (cost of notebooks).

A math teacher says: 'The graph shows the temperature in degrees Celsius every hour from 6 a.m. to 12 p.m. The x-axis represents the time, and the y-axis represents the temperature. I want you to identify the two-hour period where the temperature increased the most.' Which of the following describes what the students need to do?

Answer: Look for the steepest upward slope between any two points that are two hours apart.

The instruction is to find the 'two-hour period where the temperature increased the most.' On a line graph, the rate of increase is shown by the steepness of the line (the slope). A steeper upward slope over a two-hour interval on the x-axis indicates a larger temperature increase.

Listen to the instruction: 'Your task is to measure the perimeter of the rectangular table in the back of the room. Remember, the formula for the perimeter of a rectangle is two times the length plus two times the width. Please record your final answer in centimeters.' What information is essential for completing the task but was NOT explicitly stated by the teacher?

Answer: The actual length and width of the table.

The teacher provides the formula, identifies the object to be measured, and specifies the required units (centimeters). However, the actual measurements of the table's length and width are not given. The students must perform the action of measuring to find this missing information before they can use the formula.

The teacher explains a multi-step problem: 'First, divide 84 by 4. Take that result, which is the quotient, and subtract 9. After that, multiply the new number by 3. What is the value you should have just before the final multiplication step?'

Answer: 12

The question asks for the value *before* the final step. The steps are: 1) 84 ÷ 4 = 21. 2) 21 - 9 = 12. 3) Multiply by 3. The value just before the final multiplication step is the result of the second step, which is 12.

Listen to the teacher's review instruction: 'We have a triangle with angles A, B, and C. The measure of angle A is 40 degrees. The measure of angle B is 50 degrees. To find the measure of angle C, what fundamental geometric principle must you apply?'

Answer: The sum of the angles in any triangle is always 180 degrees.

The problem gives two angles of a triangle and asks how to find the third. The core principle required to solve this is knowing that the sum of the interior angles of any triangle always equals 180 degrees. By adding angles A and B (40+50=90) and subtracting from 180, one can find angle C.

A teacher gives the following word problem: 'A baker has 72 cookies to put into boxes. Each box must contain exactly 8 cookies. After filling as many boxes as possible, the baker gives the remaining cookies to his assistant. Which calculation is needed to find out how many cookies the assistant receives?'

Answer: The remainder of 72 divided by 8.

The problem is about division with a remainder. Dividing 72 cookies by 8 cookies per box (72 ÷ 8) tells you how many full boxes can be made. In this case, 72 ÷ 8 = 9 with no cookies left over. However, the question asks for the *calculation* needed to find the 'remaining' cookies. The mathematical operation that finds the amount left over after division is finding the remainder.