The purpose of this activity is for students to apply conservation of length by measuring with a tool that does not start at 0. Until now, students have focused on measuring by lining up the edge of an object with 0. In this activity, students consider how the units on a ruler, and in later lessons, a number line, can help us solve problems and measure even when we are not starting at 0. It is important for students to recognize that the tick marks show a consistent distance between numbers, so any part of the ruler can show a specific number of units. The Activity Synthesis focuses on how addition (counting on from the starting number) and subtraction can be used to find the length of an object. The teacher records students’ thinking with an equation and a question mark for the unknown.

It is recommended that students use rulers to measure the length of smaller objects (2–10 inches) in this activity. This smaller number range helps students connect what they notice about measuring starting at different numbers on the ruler to familiar addition and subtraction equations within 20. However, this activity can be adapted to use measuring tapes or yardsticks to measure longer objects if they are available.

When students measure objects starting at different non-zero spots on the ruler and observe what stays the same (the difference) and what changes (the starting and ending spots), they observe a structure which repeats itself no matter which starting spot they use on the ruler to begin the measurement (MP7, MP8).

• Invite selected students to share their measurements and their reasoning.
• Write equations that correspond to the students’ thinking using a question mark to represent the unknown value.
• “¿Por qué creen que obtienen la misma medida todas las veces, aunque empiecen a medir desde un lugar distinto?” // “Why do you think you get the same measurement each time, even if you measure starting from a different place?” (The object didn't change, so the length has to stay the same. The total length in inches is still the same between the number that you start with and end with.)

In this activity, students apply the methods they used in the first activity to solve a similar problem independently. They write equations to represent each problem. Students may write an equation with an unknown to represent the problem or a complete equation after they have solved. Students make connections to addition and subtraction as they count on or subtract to determine the length of objects when measuring with a torn tape measure. In the Activity Synthesis, students compare 2 different equations that could represent the problem.

• Invite previously selected students to share the equations they used to find the length of the short side of the desk or display:
• “¿Ambas ecuaciones representan una forma en la que Lin podría encontrar la longitud del lado corto de su pupitre? ¿Cómo lo saben?” // “Do both of these equations represent how Lin could find the length of the short side of her desk? How do you know?”