## Year 2 Lesson 23 Lesson Plan - Problem Solving: Rate - Time - Distance

1. (5 min) Mental Math
1. If grapes cost \$2 per pound, how much will 3 pounds cost? [\$6]
2. If grapes cost \$2 per pound, how much will a half-pound cost? [\$1]
3. At 40 miles per hour how far will I go in 4 hours? [160 miles]
4. At 40 miles per hour how far will I go in 30 minutes? [20 miles]
5. If I go 60 miles per hour, how far do I go in 10 minutes? [10 miles]
6. If I go 30 miles per hour, how far do I go in 10 minutes? [5 miles]

2. (5 min) Review of selected problems from previous lesson (no more than 3 problems)

3. 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:

r x t = 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 findSolve forUnits will be
How fard miles, feet, km, etc.
How fastr miles per hour, feet per second, etc.
How longt 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: r x t = 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.

r x t = 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

t x r = d

```t x 3 miles = 12 miles
hours

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.

4. 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```

5. (Remainder of class) In-class exercise

6. Hand out homework as students successfully complete the in-class exercise.