To begin the lesson, place a number line from 0 - 200, on the board. The line should be partitioned into intervals of 10 with the ones marked in smaller hash marks. The online Number Line Generator is a great tool to create this, as it will allow you to annotate the 10s while showing ticks for 1s, and allows you to create lines larger than an 8.5 x 11 sheet of paper.
Prompt the students to come up and show how they might move from 0 to 75 in three jumps. Then from 0 to 140 in two jumps.
Practice with different end numbers and number of jumps until you feel they are comfortable with these directions.
Next, ask the students to turn and talk about what the "most efficient" way to jump from 0 to 173 might be, using exactly three jumps. If someone notices that it is 100 + 70 + 3, explain that we call that expanded notation.
This lesson is about exploring using the number line as a tool, so don't worry about pushing the expanded notation yet. Allow students to make their own sense in determining the number of their jumps.
To explore and practice, give the students a set of number lines and direct them to solve several situations. For example: 0-155 in 3 jumps, 0-100 in 5 jumps, 0-175 in 2 jumps, 0-180 in 2 jumps.
While students work, watch and listen for strategies that are accurate and efficient. Prompt your students to explain their thinking and write the matching equations to their jumps. Students will have different methods, so work with each as a way of making meaning.
The student in this clip worked with her knowledge of doubles to get her started. She knew 70+70=140 and would get her close to her end mark. She then figured out the remaining amount to jump.
These next two clips show students using their understanding of quarters and the combination of 25, 50, 75 as a way to get down the line.
This student understands expanded form and uses it with ease.
To close the lesson, the students share their pages with partners and compare strategies and why they chose the "jumps" on their number line. This is another time where students will listen to another's ideas and see that many strategies can be used to solve a problem. It is also a nice way to critique work and revise thinking.
After sharing, let the students know tomorrow that they will practice using expanded form to solve "big" math problems.