Read non-unit fractions as repeated unit fractions in strip models.
Teaching companion · Version 2.0.0
Distinguish all equal parts from the selected parts in a strip.
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 has six equal parts and four are shaded. Name the shaded fraction and explain the two numbers.
Look for: 4/6 (equivalent to 2/3): four selected pieces out of six equal parts in one whole.
If you observe: Writes 6/4 or uses the two unshaded pieces as the denominator.
Respond: Circle the entire six-part whole, then mark only the four shaded pieces with counters. Ask which count names the size of one piece.
Rotate a strip showing 2/3 by a quarter turn. Has its fraction changed?
Look for: No. It still has two of three equal parts shaded.
If you observe: Renames the fraction when the strip becomes vertical.
Respond: Rotate the actual paper without cutting or shading it. Recount all parts and selected parts.
Check independently: A whole has eight equal parts, five shaded. What fraction is shaded and what fraction is unshaded?
5/8 is shaded and 3/8 is unshaded.
Use the whole size short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives 2/3 for two shaded parts out of three equal parts. e2 also meets its criterion: e2 says the denominator tells how many equal parts make one whole.
Continue to the linked next lesson. Transfer the same numerator and denominator roles from shaded pieces to equal distances.
Next lesson: Number Line Launche1 does not yet meet this criterion: e1 gives 2/3 for two shaded parts out of three equal parts.
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 says the denominator tells how many equal parts make one whole.
Have the learner label “all equal parts” and “shaded parts” directly on e1, then use those labels to explain the denominator in e2.
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 4 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 6 equal parts; 5 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.
Strip model: 1 same-sized whole, each divided into 8 equal parts; 7 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 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 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; 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.
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.
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: 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.
Look for in the response:
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Look for in the response:
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.
Look for in the response:
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.
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?
Draw strips with thirds, fourths, sixths and eighths. Shade a different number of parts.
Cover the labels. A partner names the shaded amount and explains the denominator.
Uncover labels and repair mismatches using the equal-part count.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Name two shaded parts in a strip of three equal parts. What does the denominator tell a strip detective?
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.
2 parts of size 1/4 represent 2/4.
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.
4 parts of size 1/6 represent 4/6.
1 parts of size 1/3 represent 1/3.
1 parts of size 1/2 represent 1/2.
2 parts of size 1/3 represent 2/3.
1 parts of size 1/4 represent 1/4.
3 parts of size 1/4 represent 3/4.
A vertical or horizontal strip with three equal parts and two shaded shows 2/3.
The denominator counts all six parts; the numerator counts four shaded parts.
Shade five of eight equal sections; three eighths stay unshaded.
Four equal sections; three are shaded and one is not.
Two thirds are shaded.
It tells how many equal parts make the whole.
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. Read non-unit fractions as repeated unit fractions in strip models.
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.