Missing Endpoint / Missing Midpoint

This routine is based on one routine called “Is This the End?” from the book Daily Routines to Jump-Start Math Class, Middle School: Engage Students, Improve Number Sense, and Practice Reasoning by John J. SanGiovanni and Eric Milou. If you don’t have it, check it out!

Missing Midpoint

The “Missing Midpoint” Routine, involves a number line with two endpoints and a missing midpoint. This routine encourages students to find the midpoint by thinking about dividing the number line into equal parts. This is foundational for understanding the relative magnitude of numbers and developing fraction concepts and understanding. Use whole numbers, fractions, or decimals. Here are a few examples with fractional midpoints.

Missing Midpoint Extension Questions:

What numbers would not fit on this number line?

Change one of the endpoints, then ask, do the placements of the other numbers change?

Choose an endpoint, then ask, what other numbers are near this point? How do you know?

Missing Endpoint

The “Missing Endpoints” Routine, involves the opposite; a number line with a midpoint labeled and missing endpoints. This routine encourages some great mathematical discourse since these answers will vary. When students give their ideas and justify their answers, ensure that students’ answers are equidistant from the midpoint. Use whole numbers, fractions, or decimals. Here are a few examples with fractions.

Missing Endpoint Extension Questions:

Can you think of several answers? How many?

Who can find the closest endpoints? How do you know?

Are you interested in trying out these awesome Number Sense Routines in your class? Sign up below to receive a Valentine’s Day themed Missing Midpoint/Missing Endpoint FRACTION routine to your inbox. These are most appropriate for grades 3-5. Check them out.