Connect tenths to equivalent hundredths and decimal notation.
Teaching companion · Version 2.0.0
Rename tenths as hundredths while preserving value and digit place.
The original lesson PDFs remain version 1.0.0. This supplement adds diagnostic probes, teaching responses, and question-specific rubrics. Use the supplement below for the updated guidance.
Ask for an explanation or drawing before choosing a response. A wrong answer alone does not identify its cause.
Use hundredths to explain whether 0.3 and 0.30 are equal.
Look for: They are equal: three tenths are thirty hundredths.
If you observe: Says 0.30 is larger because 30 exceeds 3.
Respond: Shade three columns of a hundred-grid and count the thirty cells without changing the shaded area.
Does 0.03 equal 0.3? Name the value of the digit three in each.
Look for: No. It represents three hundredths in 0.03 and three tenths in 0.3.
If you observe: Drops the zero after the decimal point as though it were a final zero.
Respond: Shade three cells beside three columns and name 3/100 versus 30/100.
Check independently: Rename 0.7 in hundredths, then compare it with 0.07.
0.7 = 70/100 = 0.70, which is greater than 0.07 = 7/100.
Use the equivalent factors short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives = for 0.3 compared with 0.30. e2 also meets its criterion: e2 explains that a final zero renames three tenths as thirty hundredths without changing the value.
Continue to the linked next lesson. Locate tenths and hundredths as distances on the same unit line.
Next lesson: Decimal Number Linee1 does not yet meet this criterion: e1 gives = for 0.3 compared with 0.30.
Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on.
Open the linked short interventione1 meets its criterion, but e2 does not yet show this evidence: e2 explains that a final zero renames three tenths as thirty hundredths without changing the value.
Use the equivalent-factors intervention for the repartitioning idea, then return to the decimal grid and have the learner explain the specific final zero in 0.30.
Open the linked short interventionUse these as follow-up prompts, then examine the learner’s model or explanation. Open responses may differ from the sample while satisfying the criteria.
Strip model: 1 same-sized whole, each divided into 10 equal parts; 3 parts are shaded altogether.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Watch for: Combines numerator counts before making the fractional units alike.
Try: Overlay thirds and fourths on the same whole to make twelfths. Rename 1/3 as 4/12 and 1/4 as 3/12; combine seven twelfths. Ask which original amount would change if only its denominator were replaced.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Look for in the response:
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Look for in the response:
Watch for: Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Try: Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Look for in the response:
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Look for in the response:
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Watch for: Thinks a final decimal zero changes value, or inserts a zero into a different place.
Try: Repartition three tenths into thirty hundredths on the same square. Write 0.3 = 0.30, then shade 0.03 separately to show why moving the 3 into the hundredths place changes its value.
Look for in the response:
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Eight core questions and a two-question exit ticket. Print one set per student.
Recognize a whole and count equal parts.
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?
Confuses tenths and hundredths or drops the zero that fixes a digit’s place.
Use a 100-cell square. Shade three complete columns for 0.3 and three cells for 0.03. Name these 30 hundredths and 3 hundredths before writing the decimals.
Teacher answer key. Open responses include a rubric and one valid sample.
Three tenths is thirty hundredths.
Thirty hundredths is 0.30.
0.4 = 0.40. Rename them as equal-sized parts or place them on the same unit number line.
Each tenth is ten hundredths.
Nine hundredths is 9/100.
0.6 = 0.60. Rename them as equal-sized parts or place them on the same unit number line.
3/10 + 4/100 = 17/50. Use equal-sized parts before combining or removing them.
Twenty-five hundredths is one quarter.
One tenth is 0.1.
Two tenths is 0.2.
Ten hundredths is one tenth.
0.2 = 0.20. Rename them as equal-sized parts or place them on the same unit number line.
Each tenth is ten hundredths, so three tenths is thirty hundredths.
No. Three hundredths is a tenth of three tenths.
Four tenths plus seven hundredths equals forty-seven hundredths.
0.5 and 0.50 both mean one half.
0.3 = 0.30. Rename them as equal-sized parts or place them on the same unit number line.
It expresses tenths as hundredths without adding any value.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
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.