Going the Distance

Discovering Distance Formula (top of page 3 in student notes):

Students will follow the steps to discover the distance formula using the Pythagorean Theorem.  This is a great place to differentiate the lesson!  One suggestion would be to break students into pairs, and ask them to work on 2 steps at a time.  Once each pair is done, you can review the answers with students, and then let them continue on until they’ve completed the entire discovery activity.

This activity links directly with HSG. CO. A.1, in which students are required to know precise definitions of terms like distance.  By asking students to derive the formula from Pythagorean Theorem, we are also linking this concept with a host of other concepts like right angles and right triangles, and more specifically, an 8^th grade standard, G.B.6, which requires students to apply Pythagorean Theorem and its converse.

Pair-Share:  Application of Distance Formula

After discovering the distance formula, we can work on finding the distance of a line when given two points.  I’ve included a coordinate plane for students as well.  I find this helps students to predict our expected value for distance (see the cat comment in student notes) and also let’s students continue to connect to our standard (COA.1) the definition of distance and its connection to length.

Examples 3 and 4 in class notes ask students to preview and try to write the midpoint formula.  Students have established an understanding for midpoint in previous lessons, and this formula helps to formalize how we can find the midpoint when given coordinate points.  Many times, my students can’t write the formal formula for midpoint but can explain in words that we add the x’s together and then divide by 2 or some version of this.  You can present the formal formula for midpoint, and discuss how to apply this to examples on the next page of student notes.  

Activity/Homework:  Students will be asked to finish activity in class, and any questions that are not finished will become homework.

Exit Ticket:  Students will complete an exit ticket that asks students to find the perimeter of a triangle given 3 sides.  This is a longer exit ticket and may require students to work on it for 10 minutes.   I often collect student work for this question to get a sense what students know or don’t know about finding distance of points.