In this activity, students to share what they know about one tenth and one hundredth, and consider what they might know about one thousandth. Students make a poster showing what they know about these numbers and then discuss the different representations they made. If students show tenths, hundredths or thousandths on a number line or with base ten diagrams, highlight these representations in the Activity Synthesis, as they are familiar from IM Grade 4.

This activity is meant to be an invitational opportunity for students to bring their lived experience into the math classroom. Consider taking a walk through the community where your students live and noticing places that decimals are seen and used. Take pictures or notes that capture the details of your observations. Be prepared to share these artifacts with students during the Activity Synthesis.

• Invite students to share their posters.
• “What are some ways to represent 1 tenth?” (I can write it as a fraction or a decimal. I can divide a rectangle into 10 equal pieces. I can put it on the number line.)
• “What was challenging about representing 1 hundredth with a drawing or diagram?” (It was hard to divide something into 100 equal pieces because that’s a lot.)
• “What was challenging about representing 1 thousandth with a drawing or diagram?” (Dividing a rectangle into 1,000 pieces would take forever.)
• “In the next activity we will make and compare drawings of these numbers.”

• There are 10 tenths in a whole.
• There are 10 hundredths in a tenth.
• There are 10 thousandths in a hundredth.

This relationship can be seen when numbers are written as decimals or fractions. When students see this common relationship between the decimal place values they look for and make use of structure (MP7).

• Display the last image.
• “How many of the tiny shaded rectangles are there in the whole unit square? How do you know?" (1,000, because there are 10 in the small square and 100 of those squares in the whole.)
• “How much of the whole square is shaded?” (There is one tiny rectangle shaded and there are 1,000 of those in the whole. So,  is shaded. There is of shaded. That’s . There is because the hundredth is divided into 10 equal pieces.)
• “The number can also be written in decimal form as 0.001. Like the fraction, we call it ‘thousandth.’”
• “How do you think you would write as a decimal?” (0.004)