# Medians Intersecting

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## Objective

SWBAT construct medians and show that medians in a triangle intersect to form a centroid.

#### Big Idea

Students will use coordinate geometry to discover the properties of medians and centroids.

## Do Now

10 minutes

This Do Now, serves two purposes. Taking time for this basic skills review is critical for students who may struggle and this also sets the stage for the lesson as students will be required to use them in problems involving centroids. First students review how to multiply by fractions, concentrating on 1/3 and 2/3  as well as review order of operations.

## Exploration 1

25 minutes

In this first Exploration, students will construct medians and then the centroid of a triangle using a compass and straightedge.  The steps to constructing are important since students following them incorrectly will not be able to determine the centroid (MP 5 and MP 6) and have an accurate calculation for the key relationship that a centroid divides a line from a vertex to the opposite side into a specific ratio, two to one.

To help ensure proper constructions you may want to put students in pairs checking each other's work, particularly before moving onto Steps 3 and 4.  Also, if you have access to a scanner or to an ELMO (a device that projects work on paper), you can have students check their work frequently with a peer's work (or your model) that is shared with the whole class.

30 minutes

15 minutes