In this activity, students use a square grid of 100 to revisit the meaning of tenths and hundredths and to make sense of the decimal notation for these fractions. They begin to make connections between the familiar representations of a fraction—using a diagram, fraction notation, and words—and the newly introduced decimal notation, and to notice similarities in their structure (MP2, MP7). It is important for students to consistently hear numbers read as decimals, for example 1.7 as one and 7 tenths, so that they can connect decimal notation to visual representations and fraction notation. Later, in the Lesson Synthesis, the connections between the decimal notation and numbers in base-ten will begin to be made explicit.

Students may begin to notice that there are different ways to write decimals that represent the same fraction. It is not essential to discuss this in depth, as students will look at equivalent decimals more closely in upcoming activities.

• Invite students to share the decimals for the diagrams in the first problem. Record their responses for all to see.
• “How are the diagrams in the last problem different from those in the first problem?” (They represent numbers greater than 1.)
• “How did you figure out how to write each fraction in decimal notation?”
• If not mentioned in students’ responses, point out that we can think of as . The 1 whole goes in the ones place, to the left of the decimal point, and the 20 hundredths goes to the right of the decimal point.
• “The decimal 1.20 can be read ‘one and 20 hundredths’. The decimal 1.33 can be read ‘one and 33 hundredths’.”

In this activity, students practice representing and writing decimals given another representation (fraction notation or a diagram). The idea that two decimals can be equivalent, just like two fractions can be equivalent, is made explicit here. When students make connections between quantities expressed in word form, decimal notation, and fraction notation, they reason abstractly and quantitatively (MP2).

• Ask students to use words and decimal notation to express each amount in the first problem.
• Clarify that 0.02 can be named “two hundredths” and 0.22 can be named “twenty-two hundredths” and so on.
• Select students to share their representations for and 1.6 and how they reasoned about them.
• Display 1.07 and 1.6. “How would you say these decimals in words?” (One and seven hundredths or one point zero seven for 1.07, and one and sixth tenths or one point six for 1.6.)