Walk the equal spaces between 0 and 1 to connect a fraction denominator to distance, not tick marks.
The denominator counts equal intervals in one unit; the numerator counts intervals traveled from zero.
Materials: Paper and ruler; Pencil.
The second worked example, three unused practice tasks, and remaining transfer task are available for a follow-up session. Allow more time if the group needs to build the models.
Teaching move: Have the student touch a space while saying each count. Put a small arc over every interval and keep the mark at zero visibly separate from the first step.
Open an interactive number line →1 · Quick diagnosis
Use the answer notes to interpret what you hear. Choose a response for each question to get a suggested teaching step. These choices describe this brief check and are not a mastery score.
Explain with a drawing, objects, or words.
Answer or sample response: 4 equal intervals, although it has 5 marks.
Listen for this difficulty: Counting endpoint marks as fractional parts.
Try this response: Slide a finger across each gap, starting the first count after leaving zero.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The next mark is 1/6 because only one sixth-length interval has been traveled.
Listen for this difficulty: Including zero as a traveled step.
Try this response: Ask what distance has been traveled before taking the first step.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: No. Thirds require three equal-length intervals.
Listen for this difficulty: Treating any three consecutive gaps as thirds.
Try this response: Measure or copy the first gap to check whether it fits the other two.
Look for:
2 · Model together
Use one now. Ask the learner to explain each step before revealing the next part of your drawing.
Result: 3/4 is the endpoint after three fourth-length steps from zero.
Listen for this difficulty: Placing 3/4 at the third mark when zero is counted as mark one.
Try this response: Draw three travel arcs and read their endpoints: 1/4, 2/4, 3/4.
Look for:
Result: 2/6, equivalent to 1/3.
Listen for this difficulty: Using seven marks to claim sevenths.
Try this response: Underline the six gaps before writing a denominator.
Look for:
3 · Guided practice
Mix a calculation or drawing with an explanation or error repair. Keep the other tasks for another short session.
Explain with a drawing, objects, or words.
Answer or sample response: 4 marks.
Listen for this difficulty: Assuming the mark count equals the interval count.
Try this response: Start with the zero mark and add one endpoint for each of three steps.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 5/8.
Listen for this difficulty: Swapping the traveled steps and unit partition counts.
Try this response: Name the step size first, then count five copies.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 2/4, or 1/2.
Listen for this difficulty: Using five letters or labels as the denominator.
Try this response: Count the four gaps and mark the two that reach B.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Place the interior marks at 2 cm and 4 cm, making three equal 2 cm intervals.
Listen for this difficulty: Accepting unequal spacing when labels look correct.
Try this response: Compare all three gap lengths to the first gap.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: A unit split into three equal intervals with two arcs ending at 2/3.
Listen for this difficulty: Drawing two marks instead of traveling two intervals.
Try this response: Ask the learner to describe the length of each arc.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: No. The length of each step, or the number of equal steps in one whole unit, is also needed.
Listen for this difficulty: Using the numerator without a defined unit fraction.
Try this response: Compare three steps on a fourths line with three steps on an eighths line.
Look for:
4 · Independent transfer
Choose one task without coaching. Check the explanation against both criteria in its teaching notes; use the other task for a later check.
Explain with a drawing, objects, or words.
Answer or sample response: 5/6 is 10 cm from 0. Six 2 cm intervals require seven marks including the endpoints.
Listen for this difficulty: Using endpoint count to determine the denominator.
Try this response: Build the line with six 2 cm steps, then count endpoints separately.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The robot stops at 2/3. Three equal jumps make the unit, and two jumps have been completed.
Listen for this difficulty: Mixing the count of all marks with the count of reached marks.
Try this response: Have the student name what each number in 2/3 counts.
Look for:
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
Standards: 3.NF.A.2.a, 3.NF.A.2.b. Grade 3 alignment describes the mathematical work in this pack.
The tasks, worked examples, and teacher responses are original Fraction Classroom materials, version 2.0.0. The teaching approach draws on noticing the unit, moving between representations, and responding to student reasoning in the linked Illustrative Mathematics lesson. Its text and exercises are not reproduced here.