Lower Elementary
Question: Frances and Joshua weigh a total of 210 pounds. If Joshua weights twice as much as Frances, how much does each person weigh?
Answer: Joshua weighs 140 pounds and Frances weighs 70 pounds
Note: Use guess and check method.
Upper Elementary
Question: 3/8 of a class of students like vanilla ice cream, 1/4 of the class likes chocolate ice cream, and the rest like strawberry ice cream. What fraction of the students in the class like strawberry ice cream?
Answer: 3/8 of the students
Note: Drawing a picture can help students visualize the solution.
3/8 of the class (people who like vanilla) + 1/4 of the class (people who like chocolate) + people who like strawberry = 1 whole class
3/8 + 1/4 + _______ = 1
Rename 1/4 = 2/8
3/8 + 2/8 + _______ = 8/8 (1 whole)
5/8 + _______ = 8/8 (1 whole)
The missing piece is 3/8.
Middle School
Question: Mike and Dustin had a total of 110 baseball cards. Mike gave 1/3 of his cards to his little brother and Dustin gave 10 of his cards to his cousin, so that Mike and Dustin now have the same number of cards. How many cards did Dustin have originally?
Answer: 50 cards
Note: One method for solving this problem is guess and check.
Algebraic solution:
x = Mike’s original number of cards
110 – x = Dustin’s original number of cards.
After each boy gives away their cards they have the same number of cards.
x – 1/3(x) = Mike’s cards after he gives 1/3 of them way
100 – x = Dustin’s cards after her gives 10 cards away
x – 1/3(x) = 100 – x
Simplify the left side, then solve for x.
x – 1/3(x) = 100 – x
2/3(x) = 100 – x (add x to both sides)
5/3(x) = 100 (multiply both sides by 3)
5x = 300 (divide both sides by 5)
x = 60
So Mike has 60 cards. That means Dustin had 50 (110 – 60) cards originally.
Algebra and Up
Question: The hypotenuse of a right triangle has endpoints (7, 8 ) and (4, 4). If each leg of the triangle has an integer side length, what is the perimeter of the triangle?
Answer: 12
Note: Draw a picture. Observe that the length of the two legs of the triangle are 3 and 4 respectively. That means the hypotenuse of the triangle is 5, because this forms a Pythagorean triple. You can also use the Pythagorean theorem or distance formula to verify the length of the hypotenuse is 5.
Pythagorean Theorem:
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c
3 + 4 + 5 = 12
