In this activity, students reason about the relative size of decimals by locating them on a number line. Students rely on their experience of locating fractions on a number line and the relationship of the decimal values relative to 0 and 1.

If desired and logistically feasible, consider carrying out the activity on a giant number line rather than on paper.

• Stretch a long strip of tape across a wall, at least 8 or 10 feet long. Partition the tape into 12 equal intervals, using shorter pieces of tape as tick marks. Label the locations of 0 and 1.
• Give each group of students 2–3 dot stickers, 4–5 sticky notes, and a thick marker.
• Ask each group to write (on sticky notes) labels for two of the tick marks, with one sticky note for each label.
• Assign each group one or two of the eight decimals in the second problem. Ask them to locate their assigned decimals on the number line, using dot stickers to mark the location and sticky notes to label them.

• “What do you notice about the numbers in the activity?”
• “What labels could we put on the number line to help us locate the decimals?”

• Select students to display their completed number lines (showing the locations of five additional decimals).
• Invite the class to agree or disagree with the locations of the point and discuss any disagreements.
• Select other students to share their comparison statements and how they know each statement is true.

In this activity, students continue to compare decimals to hundredths. They begin by reasoning with a number line and work toward generalizing their observations. Some students may compare two numbers by analyzing the value of the digits in the same place (for example, the tenths in one number and the tenths in the other). Comparing decimals by place value is a standard for grade 5 and is not expected at this point.

• See Lesson Synthesis.