Locate fractions from 0 to 1 by counting equal intervals.
Teaching companion · Version 2.0.0
Read a fraction as an equal distance from zero, counting intervals.
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 0–1 line has five equally spaced marks including its endpoints. What is the size of one interval?
Look for: 1/4: five marks bound four equal intervals.
If you observe: Answers 1/5 by counting the marks.
Respond: Draw one curved jump over each gap. Start the first jump at zero and count four jumps to one.
On that line, a point is three intervals from zero. Name the point and justify the denominator.
Look for: 3/4; three quarter-steps from zero, with four equal intervals per whole.
If you observe: Answers 4/5 by counting both boundary marks.
Respond: Place a counter at zero without counting a step, then move and count only completed intervals.
Check independently: A 0–1 line has six equal intervals. What point is four intervals from zero?
4/6, equivalent to 2/3.
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 labels the marked point 3/4. e2 also meets its criterion: e2 explains that spaces represent equal lengths and tick marks represent positions.
Continue to the linked next lesson. Continue the same interval size and count beyond the point labeled one.
Next lesson: Beyond One Walke1 does not yet meet this criterion: e1 labels the marked point 3/4.
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 explains that spaces represent equal lengths and tick marks represent positions.
Ask the learner to demonstrate one jump and one mark on e1, then explain why only a completed jump adds to the numerator.
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 4 equal intervals. The marked point is 1 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 3 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 2 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 6 equal intervals. The marked point is 1 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 6 equal intervals. The marked point is 5 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 8 equal intervals. The marked point is 3 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 8 equal intervals. The marked point is 7 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 2 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 2 equal intervals. The marked point is 1 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 3 equal intervals. The marked point is 1 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 1 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.
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 2 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: 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.
Look for in the response:
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.
Look for in the response:
Watch for: Treats different fraction names as different positions despite equal distance from zero.
Try: Align the zero and one of a halves strip and a fourths line. Transfer the halfway endpoint to the line and label the same point 1/2 and 2/4.
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.
Look for in the response:
Number line: 0 to 1; one whole is the distance from 0 to 1. Each whole has 4 equal intervals. The marked point is 3 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: 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.
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 0 to 1. Mark four equal intervals, not four interior points.
Place a paper counter at each fourth. Say the distance from zero.
Partners draw thirds and sixths and label the marked locations.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
What fraction is at the marked point? Explain why we count spaces instead of tick marks.
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.
1 parts of size 1/4 represent 1/4.
3 parts of size 1/4 represent 3/4.
2 parts of size 1/3 represent 2/3.
1 parts of size 1/6 represent 1/6.
5 parts of size 1/6 represent 5/6.
3 parts of size 1/8 represent 3/8.
7 parts of size 1/8 represent 7/8.
2 parts of size 1/4 represent 2/4.
1 parts of size 1/2 represent 1/2.
1 parts of size 1/3 represent 1/3.
1 parts of size 1/4 represent 1/4.
2 parts of size 1/4 represent 2/4.
Four equally spaced intervals connect zero to one.
Intervals are the spaces between neighboring tick marks.
Both are halfway from zero to one.
Space all four intervals equally between zero and one.
Count three quarter-length intervals from zero.
Each space is one equal unit fraction; a point itself has no length.
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. Locate fractions from 0 to 1 by counting equal intervals.
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.