Match a fraction across strips, unit-fraction words, and number lines.
Teaching companion · Version 2.0.0
Match the same quantity across strips, words, and number-line distances.
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 strip shows two of three equal parts shaded. Where should its matching point lie on a 0–1 number line?
Look for: Two equal third-steps from zero, at 2/3.
If you observe: Places the point on the second tick including zero, at 1/3.
Respond: Align the strip with 0 and 1; transfer the shaded endpoint and count the two intervals beneath it.
A card says “two thirds” but shows two of four equal parts shaded. What can you change to make a match?
Look for: Relabel it two fourths (one half), or redraw three equal parts and shade two.
If you observe: Matches cards by the numerator two alone.
Respond: Read “thirds” as a part-size instruction and count how many such equal parts fill the whole.
Check independently: Match three shaded fourths with a line point and a word card.
The point is three quarter-steps from zero, at 3/4; the words are “three fourths.”
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 2/3 for the matching model. e2 also meets its criterion: e2 connects “thirds” with the equal-part size and three such parts per whole.
Continue to the linked next lesson. Critique a collection of representations and repair mislabeled exhibits.
Next lesson: Fraction Museume1 does not yet meet this criterion: e1 gives 2/3 for the matching model.
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 connects “thirds” with the equal-part size and three such parts per whole.
Return to the two-thirds word card. Ask the learner to identify which word names the count and which names the part size, then label the e1 model.
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 3 equal parts; 2 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 4 equal parts; 3 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 6 equal parts; 4 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 8 equal parts; 3 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
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 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 6 equal intervals. The marked point is 4 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.
Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 3 equal parts; 1 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 3 equal parts; 2 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 4 equal parts; 1 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Watch for: Matches representations by one visible feature instead of the whole, part size, and selected amount together.
Try: Align a strip with the zero and one of a number line. Transfer its shaded endpoint to the line, then read the word card. Repair whichever card has a different part size or selected count; rotate the strip to check that orientation alone does not change its value.
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: Matches representations by one visible feature instead of the whole, part size, and selected amount together.
Try: Align a strip with the zero and one of a number line. Transfer its shaded endpoint to the line, then read the word card. Repair whichever card has a different part size or selected count; rotate the strip to check that orientation alone does not change its value.
Look for in the response:
Watch for: Counts pieces without checking equal area.
Try: Keep one rectangle fixed. Draw four unequal pieces beside four equal-area pieces. Ask which set lets every piece be called one fourth, then have the learner repair the unequal partition.
Watch for: Assumes equal fraction labels guarantee equal physical amounts even when the wholes differ.
Try: Compare half of a 12 cm strip with half of a 6 cm strip. Measure 6 cm and 3 cm. Keep the fraction label visible and ask what changed; then repeat the comparison using two equal-length strips.
Look for in the response:
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: 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.
Watch for: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole.
Try: Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
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?
Station 1: draw and label four strip cards using thirds or fourths.
Station 2: write each amount as a count of unit parts, such as two thirds.
Station 3: put the matching amount on a number line and explain the shared value.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Write a value that matches the point and strip. How do words describe the strip denominator?
Reverses the shaded count and the total equal-part count.
Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Teacher answer key. Open responses include a rubric and one valid sample.
2 parts of size 1/3 represent 2/3.
3 parts of size 1/4 represent 3/4.
4 parts of size 1/6 represent 4/6.
3 parts of size 1/8 represent 3/8.
2 parts of size 1/3 represent 2/3.
3 parts of size 1/4 represent 3/4.
4 parts of size 1/6 represent 4/6.
3 parts of size 1/8 represent 3/8.
1 parts of size 1/2 represent 1/2.
1 parts of size 1/3 represent 1/3.
2 parts of size 1/3 represent 2/3.
1 parts of size 1/4 represent 1/4.
Two shaded thirds, the words two thirds, and a point two third-steps from zero.
Both describe half of one unit.
A strip with three fourths shaded cannot match a line marked 1/4; change the point to 3/4.
Use the same whole, equal parts and the same counted amount.
Both represent two thirds.
Thirds names the size of each equal part.
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. Match a fraction across strips, unit-fraction words, and number lines.
3.NF.A.3a curriculum reference
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.