Lower Elementary:
Question: Penny likes to collect beads. She starts off with 12 beads. She finds 10 more at her granny’s house. She then gives half of the beads to her younger sister. How many beads does Penny have left?
Answer: 11 beads
Solution: Penny starts with 12 beads and finds 10 more beads at her granny’s house. This means she has a total of 22 beads (12 + 10 = 22). She gives half of them to her sister. Half of 22 = half of 20 + half of 2 = 10 + 1 = 11. Penny has 11 beads left.
Upper Elementary:
Question: Ryan bought 20 apples for $1.50 each. He then resells all the apples for $2.00 each. How much profit does Ryan make?
Answer: $10.00
Solution: One way to solve this problem is to see how much money Ryan spent on the apples, find how much he earned selling the apples, and then find the difference between the two. Ryan bought 20 apples for $1.50. That means he spend $30 buying the apples (20 × $1.50 = $30). He resells all the apples for $2. That means he earned $40 selling the apples (20 × 2 = 40). Ryan earned $40 selling the apples and spent $30 buying the apples. That means Ryan made $10 in profit (40 – 30 = 10).
Alternatively, we can find the profit of one apple and multiply it by the total number of apples. Ryan makes a 50¢ profit for each apple (2.00 – 1.50 = 50¢). Since Ryan bought and sold 20 apples, he made a $10 profit (20 × 50¢ = $10).
Middle School:
Question: Point A is plotted at (2, –4). Point A is translated down 3 and right 8 and then is reflected across the x-axis. This new point is called A’. What are the coordinates of A’?
Answer: (10, 7)
Solution: To translate a point down, we subtract the value from the y-coordinate. –4 – 3 = –7. After translating down, the point is now at (2, –7). To translate to the right, we add the value to the x-coordinate. 2 + 8 = 10. After translating to the right, the point is now at (10, –7). When a point is reflected across the x-axis, the y-coordinate changes its sign. After reflecting across the x-axis, point A’ is now at (10, 7).
Algebra and Up:
Question: A username must have 6 characters. The first four characters are letters and the last two characters are numbers. No value can be repeated. Write a numerical expression to calculate how many possible usernames can be created (you do not have to multiply out your answer)?
Answer: 26 × 25 × 24 × 23 × 10 × 9, or 32,292,000 possible usernames
Solution: The first four characters of the username have to be letters. There are 26 letters to choose from for the first character. Since there are no repeats, the second character can be one of the remaining 25 letters. Likewise, we have 24 letters to choose for the third character and 23 letters to choose from for the fourth character. The fifth and sixth characters have to be numbers. There are 10 digits to choose from for the fifth character. Since the numbers cannot repeat either, we have 9 digits to choose from for the sixth character. Multiplying all of the possibilities together, we have 26 × 25 × 24 × 23 × 10 × 9, or 32,292,000, possible usernames.
(925) 292-8854
