8th grade Instructional Unit

Unit 2 – Exponents & Square Roots Review
Unit 3 – Pythagorean Theorem Instructional Unit

by
Nancy Perzel

Day 6 - Practice Finding 'c'

One of my favorite math comics - connection to the Pythagorean Theorem:

Building on the previous days lessons, students will practice using the Pythagorean Theorem to solve real-world problems.

 

Warm Up:

To get to the store from his house, Julio biked 5 km due west, then turned and biked 12 km due north.  On the way back he cut diagonally across a field taking the shortest route home.  How far did he bike total? 

Draw a picture of this problem, labeling the dimensions youÕve been given.  Solve.

 

Activity 1:

An extension of the warm-up using Google Maps. 

LetÕs say youÕre leaving Atlanta and you decide to take Highway 20 West to Birmingham.  Then, you turn North and drive on Highway 65 to Nashville.   How many miles would you have saved if you had driven directly from Atlanta to Nashville? 

Students will need to use www.googlemaps.com to find the following distances, by selecting ÔGet DirectionsÕ.  To create a multi-stop route you can ÔAdd DestinationsÕ to your directions.

Atlanta – Birmingham          ___________ miles

Birmingham – Nashville       ___________ miles

 

Using the Pythagorean Theorem, calculate your estimate of the direct distance from:

Atlanta – Nashville    __________ miles

*Students may use a calculator for this problem, but I suggest they also write down the steps and show their work in their math notebook.

Now, check by changing the route on Google Maps.  How close was your estimate?  Have you answered the original questionÉ?

 

Activity 2:

Students can explore the CCGPS Task below, in groups or individually.  The Acting Out GSP file incorporates the use of technology and would be a great mode of exploration for students. 

 

Extra practice/ Homework problems:

1)   A rectangle is 7cm. wide and 10cm. long.  What is the length of the diagonal?

2)   If the legs of an isosceles right triangle are 6 units long, find the length of the hypotenuse.

3)   A television set may be described in terms of the diagonal measure of its screen.  If a TV screen is 16 in. by 12 in., what is the length of the diagonal?

4)   The bases of a softball diamond are 60-feet apart.  How far is it from home plate to second base?

5)   A picket fence has a gate that is 48in. wide and 62 in. tall.  Find the length, to the nearest inch, of a diagonal brace for the gate.

6)   Cynthia drove 56 miles due south and 90 miles due west.  If she drives a straight line back to the point where she started, how far will she drive? – Have student do this with www.googlemaps.com.  Find the distances between two cities (making a right angle) and then calculate the direct distance

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