Decimal Number Line
Locate hundredths on a unit line and compare decimal distances.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Write the marked position as a decimal.
c2. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
c3. Compare 0.67 and 0.7. Choose <, =, or >. The wholes are the same size.
c4. Compare 0.25 and 0.2. Choose <, =, or >. The wholes are the same size.
c5. Compare 0.09 and 0.1. Choose <, =, or >. The wholes are the same size.
c6. Compare 0.80 and 0.8. Choose <, =, or >. The wholes are the same size.
c7. Compare 0.56 and 0.65. Choose <, =, or >. The wholes are the same size.
c8. Write the marked position as a decimal.
e1. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
e2. How many hundredth steps equal one tenth?
Before the lesson
Recognize a whole and count equal parts.
Materials
- Pencil: 1 per student
- Plain paper sheets: 2 per student
- Projector: 1 per class (optional)
Activity
- Draw a line from zero to one with tenth marks. Zoom the segment from 0.4 to 0.5.
- Divide that segment into ten equal hundredth steps and locate 0.45.
- Partners locate a second decimal and compare distances from zero.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw a line from zero to one with tenth marks. Zoom the segment from 0.4 to 0.5.
Divide that segment into ten equal hundredth steps and locate 0.45.
Partners locate a second decimal and compare distances from zero.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size. How many hundredth steps equal one tenth?
Watch for this misconception
Spacing decimal points by their written digit count.
Use a fixed hundredth-length interval and count from zero.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Write the marked position as a decimal.
Forty-five hundredths from zero.
c2. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
0.45 < 0.5. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 0.67 and 0.7. Choose <, =, or >. The wholes are the same size.
0.67 < 0.7. Rename them as equal-sized parts or place them on the same unit number line.
c4. Compare 0.25 and 0.2. Choose <, =, or >. The wholes are the same size.
0.25 > 0.2. Rename them as equal-sized parts or place them on the same unit number line.
c5. Compare 0.09 and 0.1. Choose <, =, or >. The wholes are the same size.
0.09 < 0.1. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 0.80 and 0.8. Choose <, =, or >. The wholes are the same size.
0.80 = 0.8. Rename them as equal-sized parts or place them on the same unit number line.
c7. Compare 0.56 and 0.65. Choose <, =, or >. The wholes are the same size.
0.56 < 0.65. Rename them as equal-sized parts or place them on the same unit number line.
c8. Write the marked position as a decimal.
Thirty-two hundredths from zero.
s1. Name the point in decimal notation.
Count tenth-length intervals.
s2. Name the point in decimal notation.
Count tenth-length intervals.
s3. Name the point in decimal notation.
Count tenth-length intervals.
s4. Name the point in decimal notation.
Count tenth-length intervals.
h1. Explain why 0.45 lies between 0.4 and 0.5.
45 hundredths lies between 40 and 50 hundredths.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h2. Give three hundredth decimals between 0.6 and 0.7.
0.61, 0.65 and 0.69 fit.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h3. Why is a zoomed segment helpful?
Hundredth intervals can be spaced visibly while the unit remains specified.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h4. Repair a line that places 0.9 before 0.12.
0.9 is 90 hundredths and must lie farther from zero than 12 hundredths.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
e1. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
0.45 < 0.5. Rename them as equal-sized parts or place them on the same unit number line.
e2. How many hundredth steps equal one tenth?
Ten hundredth steps.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
s1. Name the point in decimal notation.
s2. Name the point in decimal notation.
s3. Name the point in decimal notation.
s4. Name the point in decimal notation.
e1. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
e2. How many hundredth steps equal one tenth?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain why 0.45 lies between 0.4 and 0.5.
h2. Give three hundredth decimals between 0.6 and 0.7.
h3. Why is a zoomed segment helpful?
h4. Repair a line that places 0.9 before 0.12.
e1. Compare 0.45 and 0.5. Choose <, =, or >. The wholes are the same size.
e2. How many hundredth steps equal one tenth?
Teaching notes & lesson sources
Designed for Grade 4. Locate hundredths on a unit line and compare decimal distances.
Version 1.0.0. Original, AI-assisted lesson content. Free local classroom use; public reuse terms have not yet been assigned.
These lessons have not yet been field-tested in classrooms. Use the exit ticket and student explanations to decide what to revisit.