In this activity, students encounter both fraction and decimal notation for tenths and hundredths and are asked to arrange them in order by size. They need to rely on their knowledge of equivalent fractions and of the relationship between these two ways of expressing values. Students look for and make use of structure (MP7), for instance, by identifying the digits that tell us about the ones, tenths, and hundredths in each number.

• “How did you decide how to order the numbers from least to greatest?”
• “Which fractions would be helpful to think about as decimals (or the other way around)? How can that help you to order the entire set of numbers?”

• Select students to share their ordered collection of 10 cards. Invite the class to agree or disagree with the arrangement.
• “What was the first thing you did or looked at to start ordering? What was the next thing? What came after that?” (We first looked at the digit in the ones place. Next, we decided to write the decimals with the same whole number as fractions and ordered the fractions.)

In this activity, students compare and order decimals and fractions to solve problems about distances. They practice reasoning about tenths and hundredths expressed in different notations. Some of the distances are written to the tenths of a meter and others are written to the hundredths, prompting students to attend to the size of the decimals.

When students interpret and order the distances, they reason abstractly and quantitatively (MP2).

• See Lesson Synthesis.