Word Problems
If Mimi drives 50 miles in 2 hours, what is her rate (speed per hour)?
What is 25 miles per hour
the pythagorean theorem is : __________
a2 + b2 = c2
Rewrite this equation in correct form: 2x + y = -12
y = 2x - 12 OR y = -12 + 2x
What is the difference between an open and closed problem?
open - decisions must be made by student before you can start
closed - no decisions, you need to start using math tools
What are the two methods we have used to solve systems of equations?
Graphing, setting equations equal to each other (algebraic solution)
Which is the better deal $20 for 5 t-shirts or $24 for 8 t-shirts
What is $24 for 8 t-shirts (rate of $3 per shirt)
When leg a = 6 and leg b = 8 then the hypotenuse = ?
10
+ = up and to the right
- = down and to the right
Is this problem open or closed? Why?
"Anna earns $12 in 3 hours. How much does she make in 5 hours?"
Closed, no decisions need to be made before starting.
By graphing, the solution to the system
y = 3x - 4
y = -3x + 2
(-1, 1)
Two boats leave the same marina. One heads due north, and the other heads due east. After some time, the northbound boat has traveled 12 miles, and the eastbound boat has traveled 16 miles. How far apart are the two boats?
20 miles
What are the pythagorean triples?
3 - 4 - ___
9 - ___ - 15
___ - 12 - 13
16 - ___ - 34
3 – 4 – 5
9 – 12 – 15
5 – 12 – 13
16 – 30 – 34
Graph the following equation. Include the y-intercept and 1 additional point.
y=(2/5)x
check graphed response
Is this an open or closed problem? Why?
"How long does it take to fill a recycling bin?"
Open - decisions must be made about context before starting.
Algebraically, find the solution to the system of equations:
y = 3x + 2
y = 6x - 4
x = 2, y = 8
The height of a right triangle is 4 inches less than the length of the base. The area is 30 square inches. What are the dimensions of the triangle?
Base = 10 in
Height = 6 in
A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance? Write the pythagorean equation for how you would solve for what c = ...
Find the value of x: 3x + 7 = 5x - 13
What is 10?
What are at least 3 reasonable decisions you might need to make before starting this problem?
"How should the animal shelter allocate space in its new wing?"
answers vary by group
e.g. size of new wing, stray population in current city, seasonal changes that lead to increase of stray dogs, do strays need medical attention, etc.
By graphing, the solution to the system
y = (1/3)x + 2
y = x - 2
(6,4)
The school theater group sells two types of tickets for the play. One price is for adults and the other price is for children. One family with two adults and three children paid $14 for their tickets. Another family with one adult and two children paid $8 for their tickets. What is the price of an adult ticket?
Adult = $4
The bottom of a ladder must be placed 3 feet from a wall. The ladder is 10 feet long. How far above the ground does the ladder touch the wall?
sqrt(91)
Graph the following equation. Include the y-intercept and 2 additional points.
y = 1/3x + 4
check graphed response
What are at least 3 reasonable decisions you might need to make before starting this problem?
"How long does it take to fill a recycling bin?"
Answers will vary by group
e.g. How big is the bin? Where is the it/who is using it -- an office or classroom would make a big difference. How often are people around it? Is it mixed recycling or a single material? What does "full" mean?
Solve the system of equations using graphical or algebraic methods.
4x = 3y + 5
x + 2y = - 7
(-1, -3)