Lower Elementary
Question: Cameron had 25 action figures, then he lost 10 of them. If David had 20 action figures then bought 15 more, how many more action figures does David have than Cameron?
Answer: 20 action figures
Note: Cameron lost 10 of his 25 action figures. 10 less than 25 is 15 (25 – 10 = 15) so we know that Cameron now has 15 action figures. David had 20 action figures then bought 15 more (20 + 15 = 20 + 10 + 5 = 30 + 5 = 35) so now he has a total of 35 action figures. Finally, to find how many more action figures David has then Cameron we need to find the difference between 35 and 15. Subtracting gives, 35 – 15 = 20. You could also notice that 25 is 10 more than 15 and 35 is 10 more than 25.
10 + 10 = 20.
David has 20 more action figures than Cameron.
Upper Elementary
Question: Today Bill is twice as old as Jaime. In 3 years Jaime will be 19, how old is Bill today?
Answer: 32 years old
Note: 3 years from now Jaime will be 19, so today Jaime is 16 (19 – 3 = 16). Since Bill is twice as old as Jaime is today, we double Jaime’s age to find Bill’s age.
16 + 16 = 16 x 2 = 32
Middle School
Question: Jeremy wants to repaint the exterior walls of his house. His house is rectangular with a width of 100ft, a length of 45ft, and a height of 10ft. The front and back of his house both have two identical rectangular windows 6 feet high and 4 feet tall. If it costs 35 cents per square foot t paint, how much will Jeremy have to spend to paint his house?
Answer: $981.40
Note: First find the total surface area of the exterior of the house. Because a part is equal to the whole minus the other parts, subtract the area of the windows from the surface area of the entire house to find the surface area that needs to be painted.
SA = Perimeter • Height
SA = (2•100ft + 2•45ft) • 10ft
SA = 290ft • 10ft = 2900ft2
Let Aw equal the area of all four windows combined.
Aw = 4(6ft • 4ft) = 4(24ft2) = 96ft2
The area that needs to be painted is the entire surface area of the exterior of the house minus the area of the windows.
Let Ap equal the total area of the house that needs to be painted.
Ap = 2900ft2 – 96ft2 = 2804ft2
Lastly, because it cost 35 cents ($0.35) per square foot to paint the house, multiply 2804ft2 by $0.35.
2804ft2 • $0.35 per ft2 = $981.40
Algebra and Up
Question: Find the area of the trapezoid using the area of a trapezoid formula as well as summing up the area of each individual triangle. Set them equal to each other and simplify.
Answer: a2 + b2 = c2
Note: The two ways to solve for the area of the trapezoid are using the area of a trapezoid formula and finding the area of each individual triangle and summing them together.
Using the area of a trapezoid formula:
AT = ½(b1 + b2)h
AT = ½(a + b)(a + b)
AT = ½(a2 + 2ab + b2)
Summing up the area of each individual triangle:
A = ½bh
A1 = ½ab
A2 = ½ba
A3 = ½c2
AT = A1 + A2 + A3 = ½ab + ½ba + ½c2 = ½(2ab + c2)
Now set them equal to each other and simplify.
½(a2 + 2ab + b2) = ½(2ab + c2)
a2 + 2ab + b2 = 2ab + c2
a2 + b2 = c2
Congratulations you just proved the Pythagorean Theorem!
Fun Fact: The twentieth President of the United States came up with the proof of the Pythagorean Theorem 5 years before he became the President.
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