In this activity, students refresh what they know about equivalent fractions in tenths and hundredths. Students are given fractions in tenths and write equivalent fractions in hundredths, and vice versa. In one case, they encounter a fraction in hundredths that cannot be written as tenths and consider why this might be. The work here reminds students of the relative sizes of tenths and hundredths, and prepares students to add such fractions in upcoming activities.

• Select students to share their responses and their reasoning for the first set of problems. Display or record their responses.
• Discuss the fraction and what students wrote for its equivalent in tenths.
• Invite students to share the fractions they thought of for the last set of problems. Focus the discussion on how they know what fractions  are between and . 
• If not mentioned in students' explanations, ask: “Could that number be expressed in tenths? Why or why not?” (No, because there is not a whole number between 3 and 4.)
• Highlight explanations that show how expressing the and in hundredths would allow us to name the fractions between these given two fractions.

In this activity, students use jumps on number lines to visualize addition of tenths and hundredths and to find the values of such sums. Using diagrams helps to reinforce the relative sizes of tenths and hundredths. It provides a visual reminder that all tenths can be expressed in terms of hundredths, and that some hundredths can be written in tenths, which can in turn help with addition of these fractions.

This is the first activity in which students write expressions and equations to represent sums of fractions with different denominators. Initially, students will likely find it helpful to write equivalent fractions in the same denominator. Later, as students become more fluent in expressing tenths in hundredths and vice versa, they may perform the rewriting mentally rather than on paper. When students create and compare their own representations for the context, they reason abstractly and quantitatively (MP2).

• Invite students to share how they know which diagram represents Noah’s walk and their equations for the distances Noah and Jada walked.
• Given the number-line diagram for support, students are likely to write . Discuss why this is true.
• “How do you know that the sum of and is ?”
• Highlight that is equivalent to , and another makes .
• Consider displaying a number line that is partitioned into tenths and hundredths and shows as .