Lower Elementary:
Question: Sally is making a card for Valentine’s day. She is going to decorate the border with different colored hearts in a pattern. Starting in the upper left corner and going clockwise, the pattern is red, orange, yellow, green, blue, purple, red, orange, yellow, green, blue, purple, and so on. What color will the 34th heart be in the pattern?
Answer: Green
Solution: There are 6 colors in the pattern, so the pattern repeats every 6 colors. So the 6th color is purple, the 12th color is purple, the 18th color is purple, the 24th color is purple, and the 30th color is purple. Now we continue the pattern from here: the 31st is red, the 32nd is orange, the 33rd is yellow, and the 34th is green. So the 34th heart is green.
Upper Elementary:
Question: Billy buys a box of chocolates to give to his secret admirer. Half of the chocolates are milk chocolate, a quarter are dark chocolate, and the remaining 6 pieces are white chocolate. How many total chocolates did Billy give his secret admirer?
Answer: 24 chocolates
Solution: First we need to find the fractional part that the white chocolate represents. Half are milk chocolate and a quarter are dark chocolate. That means that the rest of the chocolates are white chocolate. To find the fractional part, subtract the other parts from the whole. 1 – ½ – ¼ = ½ – ¼ = ¼. So the white chocolate makes up ¼ of the chocolate. Since 6 pieces are ¼ of the chocolate, the whole would be 4 × 6 = 24 chocolates. There are a total of 24 chocolates.
Middle School:
Question: If 12 roses costs $51, how much would 5 roses cost?
Answer: $21.25
Solution: Unit price method:
Let’s find the price of 1 rose. To find the cost of 1 rose, divide the total cost of 12 roses by 12 to get the price of 1 rose. 51 ÷ 12 = $4.25. Multiply the cost of 1 rose by 5 To find the cost of 5 roses. 4.25 × 5 = $21.25.
Proportions method:
Set up a proportion of roses over cost. Let r be the cost of 5 roses. The proportion will be:
12/51 = 5/r
We can reduce the 12/51 by 3.
4/17 = 5/r
Cross multiply.
4r = 85
Divide by 4.
r = 21.25
5 roses cost $21.25
Algebra and Up:
Question: Amy wrote 52 Valentine’s Day cards for her friends. Half of the cards are blue and the other half are red. Each card has either a silver or a gold wrapped piece of chocolate. There are 32 silver wrapped candies and 20 gold wrapped candy. 5 blue cards have gold wrapped candy. What is the probability of receiving a blue card with a silver wrapped candy?
Answer: 21/52
Solution: There are a total of 52 Valentine’s Day cards to pick from. We know that half of the cards are blue, so there are 26 total blue cards to pick from. 5 blue cards have gold wrapped candy, which means the remaining 21 blue cards have a silver wrapped candy. So the probability of drawing a blue card with a silver wrapped candy is 21/52.
