Tenths to Hundredths
Connect tenths to equivalent hundredths and decimal notation.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Write 0.3 as a fraction.
c2. Write 30/100 as a decimal.
c3. Compare 0.4 and 0.40. Choose <, =, or >. The wholes are the same size.
c4. 7/10 = ?/100. Enter the numerator.
c5. Write 0.09 as a fraction.
c6. Compare 0.6 and 0.60. Choose <, =, or >. The wholes are the same size.
c7. Calculate 3/10 + 4/100. Show a model or your reasoning.
c8. Write 0.25 as a fraction.
e1. Compare 0.3 and 0.30. Choose <, =, or >. The wholes are the same size.
e2. Why can a zero be added at the end of 0.3?
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
- Partition a strip into tenths and shade three.
- Split each tenth into ten hundredths without moving the shaded endpoint.
- Write 3/10, 30/100, 0.3 and 0.30; explain why each names the same value.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Partition a strip into tenths and shade three.
Split each tenth into ten hundredths without moving the shaded endpoint.
Write 3/10, 30/100, 0.3 and 0.30; explain why each names the same value.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 0.3 and 0.30. Choose <, =, or >. The wholes are the same size. Why can a zero be added at the end of 0.3?
Watch for this misconception
Treating an extra trailing zero as a larger quantity.
Name the place values and compare the shaded endpoint.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Write 0.3 as a fraction.
Three tenths is thirty hundredths.
c2. Write 30/100 as a decimal.
Thirty hundredths is 0.30.
c3. Compare 0.4 and 0.40. Choose <, =, or >. The wholes are the same size.
0.4 = 0.40. Rename them as equal-sized parts or place them on the same unit number line.
c4. 7/10 = ?/100. Enter the numerator.
Each tenth is ten hundredths.
c5. Write 0.09 as a fraction.
Nine hundredths is 9/100.
c6. Compare 0.6 and 0.60. Choose <, =, or >. The wholes are the same size.
0.6 = 0.60. Rename them as equal-sized parts or place them on the same unit number line.
c7. Calculate 3/10 + 4/100. Show a model or your reasoning.
3/10 + 4/100 = 17/50. Use equal-sized parts before combining or removing them.
c8. Write 0.25 as a fraction.
Twenty-five hundredths is one quarter.
s1. Write one tenth as a decimal.
One tenth is 0.1.
s2. Write two tenths as a decimal.
Two tenths is 0.2.
s3. Write 0.10 as a fraction.
Ten hundredths is one tenth.
s4. Compare 0.2 and 0.20. Choose <, =, or >. The wholes are the same size.
0.2 = 0.20. Rename them as equal-sized parts or place them on the same unit number line.
h1. Explain why 0.3 = 0.30 with repartitioning.
Each tenth is ten hundredths, so three tenths is thirty 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. Does 0.03 equal 0.3? Use place value.
No. Three hundredths is a tenth of three tenths.
- 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. Show 0.47 as tenths plus hundredths.
Four tenths plus seven hundredths equals forty-seven 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.
h4. Invent a pair of decimals with different written lengths and equal value.
0.5 and 0.50 both mean one half.
- 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 0.3 and 0.30. Choose <, =, or >. The wholes are the same size.
0.3 = 0.30. Rename them as equal-sized parts or place them on the same unit number line.
e2. Why can a zero be added at the end of 0.3?
It expresses tenths as hundredths without adding any value.
- 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. Write one tenth as a decimal.
s2. Write two tenths as a decimal.
s3. Write 0.10 as a fraction.
s4. Compare 0.2 and 0.20. Choose <, =, or >. The wholes are the same size.
e1. Compare 0.3 and 0.30. Choose <, =, or >. The wholes are the same size.
e2. Why can a zero be added at the end of 0.3?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain why 0.3 = 0.30 with repartitioning.
h2. Does 0.03 equal 0.3? Use place value.
h3. Show 0.47 as tenths plus hundredths.
h4. Invent a pair of decimals with different written lengths and equal value.
e1. Compare 0.3 and 0.30. Choose <, =, or >. The wholes are the same size.
e2. Why can a zero be added at the end of 0.3?
Teaching notes & lesson sources
Designed for Grade 4. Connect tenths to equivalent hundredths and decimal notation.
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.