Year 2 Lesson 23 Lesson Plan - Problem
Solving: Rate - Time - Distance
- (5 min) Mental Math
- If grapes cost $2 per pound, how much will 3 pounds cost? [$6]
- If grapes cost $2 per pound, how much will a half-pound cost? [$1]
- At 40 miles per hour how far will I go in 4 hours? [160
miles]
- If I go 60 miles per hour, how far do I go in 10 minutes? [10 miles]
- If I go 30 miles per hour, how far do I go in 10 minutes? [5 miles]
- (5 min) Review of selected problems from previous lesson (no more
than 3 problems)
- (15 min) Setting up and solving rates problems
Many real-world problems ask you to deal with rates. Rates involve how
fast, how long, and how many of something happens. Rates are expressed as
"how many per how long" as in 10 miles per hour. Per means divide,
so 10 miles per hour is 10 miles/hour.
Write 10 miles so you can cancel units later
hour
You could also have "gallons per hour" or even "peanuts per minute". In
this lesson we are going to deal with distance (how many miles, feet,
inches) using the following formula where:
r is the rate t is the time and
d is the distance:
rt = d
This means that r = d/t and t = d/r. You can memorize all three formulas,
but I think it is easier to remember just one formula (r x t = d) and
then use algebra if you want to solve for r or t.
To find | Solve for | Units will
be |
How far | d |
miles, feet, km, etc. |
How fast | r |
miles per hour, feet per second, etc. |
How long | t |
hours, minutes, seconds, etc. |
- Example 1: A car goes 30 miles per hour for 2 hours. How far does
it go?
Start by writing the formula: rt = d. What are we asked for?
We are asked "how far." We must solve for d. So r = 30
miles/hour, t = 2 hours.
d = 30 miles x 2 hours = 60 miles
hour
Notice that the "hours" with t cancel with the denominator of
r so that the resulting units are just "miles".
- Example 2: I drove 1200 miles to Los Angeles in 20 hours. How fast
did I drive? We are asked "how fast". Solve for r. Here d = 1200 miles,
t = 20 hours.
rt = d
r x 20 hours = 1200 miles
r = 1200 miles / 20 hours = 60 miles / hour
- Example 3: I can walk 3 miles per hour. How long will it take for
me to walk 12
miles? Solve for t. r = 3 miles/hour and d = 12 miles
tr = d
t x 3 miles = 12 miles
hour
t = 12 miles x hours = 4 hours
3 miles
We write it like this so the miles will cancel and we are left with hours
for units.
- Finally, lets take a look at converting one rate to another.
Convert
3 inches per minute to feet per hour. Well 12 inches = 1 foot and 60
minutes = 1 hour, so we can set it up like this:
3 inches x 1 foot x 60 minutes
minute 12 inches hour
Cancel the inches and minutes and you get:
3 x 60 feet = 15 feet
12 hour hour
- (Remainder of class) In-class exercise
- Hand out homework as students successfully complete the in-class exercise.
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