Lesson objective: Use absolute value to find distance between points

Students bring prior knowledge that the number line can show both distance and direction, and that a number's distance from zero is called the number's absolute value from 6.NS.C.7c. This prior knowledge is extended to students using absolute value to find the distance between points. A conceptual challenge students may encounter is thinking that one must *always *add absolute values to determine distances on the coordinate plane.

The concept is developed through work with points on the same side and opposite sides of the axes, which allows students to concretely see cases when they can add absolute values to determine distances across axes and when subtracting absolute values is the appropriate course of action when points lie within the same qudrant.

This work helps students deepen their understanding of what the absolute value of a number is because they can plainly see how they're using the distance from zero to help them find distances on the coordinate plane.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they apply their knowledge of coordinate pairs and absolute value to determine distances on the coordinate plane.

**Key vocabulary:**

- absolute value
- coordinate plane
- perimeter

**Special materials needed: **graph paper is helpful, not required