Math 1 · Unit 11 · Lesson 2

Midpoint, Meeting in the Middle

Three tools, three questions, and this one is where is the middle. The midpoint is the point exactly halfway along a segment, splitting it into two equal pieces, a 1 to 1 ratio. On a number line, halfway between 2 and 8 is 5, the average. On the grid, average the x's for halfway across and average the y's for halfway up. Run it backward too: from the midpoint and one endpoint, find the other by taking the step one more time, or by setting the average equal and solving.

About 40 minutes Halfway across, halfway up

The big idea

The midpoint is the point exactly halfway along a segment. It bisects the segment into two equal halves, a 1 to 1 ratio. Halfway between two numbers on a number line is their mean, add and divide by 2, and the grid is the same thing in two directions: the midpoint's x is the average of the x's and its y is the average of the y's. The order of the endpoints does not matter because adding goes in any order. Every formula is a shortcut for something you can draw: half the step across and half the step up lands on the same point. Run it backward from the midpoint and one endpoint by taking the step from the endpoint to the midpoint one more time, or by setting each average equal to the midpoint's coordinate and solving the Unit 1 way.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Halfway across and halfway upThree tools, three questions: how steep (slope), how long (distance), where is the middle (midpoint). 3Backward: find the missing endpointNow the backward question. 4Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the number line idea, the midpoint formula as stacked averages, Jennifer and Jane, and both ways to find a missing endpoint. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Distance, the Pythagorean Theorem on the GridHow long is it? Next lesson: Perimeter and Area from CoordinatesDistance for every side, then add. And areas, with the height checked by slopes. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.G-GPE.6 (use coordinates to find the midpoint or an endpoint of a segment).