Locate hundredths on a unit line and compare decimal distances.
Teaching companion · Version 2.0.0
Locate and compare hundredth distances using a fixed decimal unit.
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.
A line segment runs from 0.4 to 0.5 in ten equal intervals. What is each interval worth?
Look for: 0.01, or one hundredth of the original whole.
If you observe: Calls each interval 0.1 because there are ten intervals.
Respond: Write the segment length as 0.1, then divide that length into ten. Keep the original 0–1 unit visible beside the zoom.
Which is farther right on one increasing number line: 0.45 or 0.5?
Look for: 0.5, because 50 hundredths exceeds 45 hundredths.
If you observe: Places 0.45 farther right because 45 exceeds 5.
Respond: Rename the right endpoint 0.50 and count the five hundredth-steps from 0.45 to it.
Check independently: Name a point seven hundredth-steps after 0.6, and compare it with 0.7.
0.67; it is less than 0.70.
Use the intervals not points short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives < for 0.45 compared with 0.5. e2 also meets its criterion: e2 states that ten hundredth-steps equal one tenth.
Continue to the linked next lesson. Use the number-line positions to challenge decimal digit-count rules.
Next lesson: Decimal Detectivee1 does not yet meet this criterion: e1 gives < for 0.45 compared with 0.5.
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 states that ten hundredth-steps equal one tenth.
Ask the learner to move ten 0.01 steps from 0.4 to 0.5 and connect that movement to the ten-hundredths-per-tenth statement.
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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 100 equal intervals. The marked point is 45 intervals from zero.
Watch for: Counts tick marks, including zero, instead of equal intervals from zero.
Try: Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
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: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
Watch for: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
Watch for: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
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: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 100 equal intervals. The marked point is 32 intervals from zero.
Watch for: Counts tick marks, including zero, instead of equal intervals from zero.
Try: Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 10 equal intervals. The marked point is 1 intervals from zero.
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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 10 equal intervals. The marked point is 2 intervals from zero.
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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 10 equal intervals. The marked point is 5 intervals from zero.
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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 10 equal intervals. The marked point is 7 intervals from zero.
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.
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: Accepts uneven spacing on a fraction number line.
Try: Fold a paper strip into four equal lengths and transfer the fold positions to a 0–1 line. Compare every neighboring gap with the first gap before labeling fourths.
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: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
Look for in the response:
Watch for: Orders decimals by their digit strings or written length rather than place value.
Try: Rename 0.9 as 90 hundredths and 0.12 as 12 hundredths. Mark both on one 0–1 line, then compare the counts of the same hundredth-sized unit.
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:
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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?
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?
Counts tick marks, including zero, instead of equal intervals from zero.
Mark 0 and 1, then make four equal spaces. Draw one jump over each space and count four jumps despite five marks. Count jumps from zero to the target point, keeping zero as the starting position.
Teacher answer key. Open responses include a rubric and one valid sample.
Forty-five hundredths from zero.
0.45 < 0.5. Rename them as equal-sized parts or place them on the same unit number line.
0.67 < 0.7. Rename them as equal-sized parts or place them on the same unit number line.
0.25 > 0.2. Rename them as equal-sized parts or place them on the same unit number line.
0.09 < 0.1. Rename them as equal-sized parts or place them on the same unit number line.
0.80 = 0.8. Rename them as equal-sized parts or place them on the same unit number line.
0.56 < 0.65. Rename them as equal-sized parts or place them on the same unit number line.
Thirty-two hundredths from zero.
Count tenth-length intervals.
Count tenth-length intervals.
Count tenth-length intervals.
Count tenth-length intervals.
45 hundredths lies between 40 and 50 hundredths.
0.61, 0.65 and 0.69 fit.
Hundredth intervals can be spaced visibly while the unit remains specified.
0.9 is 90 hundredths and must lie farther from zero than 12 hundredths.
0.45 < 0.5. Rename them as equal-sized parts or place them on the same unit number line.
Ten hundredth steps.
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. 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.