Extend unit fractions past one on a number line.
Teaching companion · Version 2.0.0
Keep one fixed whole and one fixed step size while counting past one.
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.
Starting at zero, take five steps of size 1/4. Where do you land?
Look for: 5/4, or 1 1/4.
If you observe: Writes 1/5 or restarts at 1/4 after reaching one.
Respond: Label every landing 0/4 through 5/4. Leave 4/4 = 1 visible while taking the fifth identical step.
A line marks 0, 1, and 2. If there are four equal intervals in each whole, how many quarter-steps reach 2?
Look for: Eight quarter-steps; 2 = 8/4.
If you observe: Calls the whole 0–2 line one unit and uses eighths.
Respond: Bracket 0–1 as one whole and 1–2 as another equal whole; count four quarters in each bracket.
Check independently: What fraction names six quarter-steps from zero? What does its denominator count?
6/4 = 1 1/2; the denominator counts four quarter-steps in each one whole.
Use the beyond one short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 labels the point beyond one as 5/4. e2 also meets its criterion: e2 states that the whole length and equal step size stay unchanged after one.
Continue to the linked next lesson. Compare distances by the number of shared-size fractional steps.
Next lesson: Same Denominator Racee1 does not yet meet this criterion: e1 labels the point beyond one as 5/4.
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 the whole length and equal step size stay unchanged after one.
Ask the learner to compare the step immediately before and after one, then explain why the denominator remains four at 5/4.
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 2; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 5 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 6 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 7 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 2 equal intervals. The marked point is 3 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 4 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 5 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 6 equal intervals. The marked point is 9 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 8 equal intervals. The marked point is 10 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 2 equal intervals. The marked point is 2 intervals from zero.
Watch for: Does not recognize that b copies of 1/b make one whole.
Try: Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 2 equal intervals. The marked point is 3 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 4 intervals from zero.
Watch for: Does not recognize that b copies of 1/b make one whole.
Try: Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 5 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Look for in the response:
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Look for in the response:
Watch for: Does not recognize that b copies of 1/b make one whole.
Try: Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Look for in the response:
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Look for in the response:
Number line: 0 to 2; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 5 intervals from zero.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Watch for: Restarts the fraction count or changes the denominator after passing one.
Try: Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
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?
Make a floor number line from 0 to 2 with four equal steps per unit.
Walk five fourth-length steps from zero and record the landing point.
Repeat with thirds and halves; check that each unit stays the same length.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Label the marked point beyond one. What stays the same when you pass one?
Restarts the fraction count or changes the denominator after passing one.
Place two equal-length unit strips end to end, both split into fourths. Label 0/4, 1/4, …, 8/4 continuously. Circle 4/4 at one and take one more unchanged quarter-step to 5/4.
Teacher answer key. Open responses include a rubric and one valid sample.
5 parts of size 1/4 represent 5/4.
6 parts of size 1/4 represent 6/4.
7 parts of size 1/4 represent 7/4.
3 parts of size 1/2 represent 3/2.
4 parts of size 1/3 represent 4/3.
5 parts of size 1/3 represent 5/3.
9 parts of size 1/6 represent 9/6.
10 parts of size 1/8 represent 10/8.
2 parts of size 1/2 represent 2/2.
3 parts of size 1/2 represent 3/2.
4 parts of size 1/4 represent 4/4.
5 parts of size 1/4 represent 5/4.
Shade one full strip and one of four parts of a second strip.
One is 4/4 and two is 8/4; seven fourths lies between them.
2/2 and 4/4 are both at one.
The step size is 1/4, and five steps make 5/4.
Five fourths lie one fourth beyond one.
Each unit keeps the same length and the same equal step size.
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 3. Extend unit fractions past one on a number line.
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.