Fraction Classroom · 2.0.0 · Teacher answers & responses
Fraction Strip Detective: teaching companion
Distinguish all equal parts from the selected parts in a strip. Student pages include two diagnostic probes, a reteaching check, and the original exit ticket. The teacher copy includes the complete lesson preparation, teaching sequence, diagnostic responses, all original question guides, and updated rubrics.
Complete lesson preparation
Grade 3 · 45 minutes. Read non-unit fractions as repeated unit fractions in strip models.
materials. Materials: Pencil: 1 per student; Plain paper sheets: 2 per student; Projector: 1 per class (optional).
activity-1. Draw strips with thirds, fourths, sixths and eighths. Shade a different number of parts.
activity-2. Cover the labels. A partner names the shaded amount and explains the denominator.
activity-3. Uncover labels and repair mismatches using the equal-part count.
phase-1. 5 min · warmup: Look at the first model or task. What is the whole? What do you notice?
Answer: Students: Sketch an initial prediction and explain it to a partner.
phase-2. 8 min · model: Draw strips with thirds, fourths, sixths and eighths. Shade a different number of parts.
Answer: Students: Follow the model; label the whole and the equal parts.
phase-3. 10 min · partner: Cover the labels. A partner names the shaded amount and explains the denominator.
Answer: Students: Work in pairs. One models, the other checks; switch roles.
phase-4. 7 min · discussion: Uncover labels and repair mismatches using the equal-part count.
Answer: Students: Compare two solutions and explain the relationship.
phase-5. 10 min · practice: Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Answer: Students: Solve independently, then compare the reasoning.
phase-6. 5 min · exit: Name two shaded parts in a strip of three equal parts. What does the denominator tell a strip detective?
Answer: Students: Complete the two exit questions independently.
Diagnostic probes
Explain or draw your reasoning. Your teacher will use these responses to choose what to revisit.
d1. A strip has six equal parts and four are shaded. Name the shaded fraction and explain the two numbers.
Answer: 4/6 (equivalent to 2/3): four selected pieces out of six equal parts in one whole.
Teacher response: If the learner writes 6/4 or uses the two unshaded pieces as the denominator. Circle the entire six-part whole, then mark only the four shaded pieces with counters. Ask which count names the size of one piece.
d2. Rotate a strip showing 2/3 by a quarter turn. Has its fraction changed?
Answer: No. It still has two of three equal parts shaded.
Teacher response: If the learner renames the fraction when the strip becomes vertical. Rotate the actual paper without cutting or shading it. Recount all parts and selected parts.
Check after reteaching
Complete this check independently after discussing the model.
r1. A whole has eight equal parts, five shaded. What fraction is shaded and what fraction is unshaded?
Answer: 5/8 is shaded and 3/8 is unshaded.
Exit ticket
Complete both original exit questions independently. Use a drawing or explanation when asked.
e1. Name two shaded parts in a strip of three equal parts. Strip model: 1 same-sized whole, each divided into 3 equal parts; 2 parts are shaded altogether.
Answer: 2/3
Teacher response: 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.
e2. What does the denominator tell a strip detective?
Answer: It tells how many equal parts make the whole.
Look for:
- State that the denominator counts equal parts in one whole.
- Distinguish this total from the shaded count.
- Connect the denominator to part size, such as three equal parts making thirds.
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. 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.
Focused reteach
Distinguish all equal parts from the selected parts in a strip.
teach-1. Outline the whole before counting any shaded pieces.
teach-2. Label the total equal-part count below the fraction bar and the selected count above it.
teach-3. Turn the model and cover one shaded part temporarily; distinguish a change in orientation from a change in selected amount.
Use the exit evidence
A wrong answer invites a follow-up probe; it does not by itself establish a particular misconception. Check e1 and e2 separately.
next-1. 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.
Teacher response: Continue to the linked next lesson. Transfer the same numerator and denominator roles from shaded pieces to equal distances. Next original lesson: /lessons/number-line-launch/.
next-2. e1 does not yet meet this criterion: e1 gives 2/3 for two shaded parts out of three equal parts.
Teacher response: 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. Short intervention: /interventions/whole-size/.
next-3. e1 meets its criterion, but e2 does not yet show this evidence: e2 says the denominator tells how many equal parts make one whole.
Teacher response: Have the learner label “all equal parts” and “shaded parts” directly on e1, then use those labels to explain the denominator in e2. Short intervention: /interventions/whole-size/.
Original question guide and updated rubrics
Use these question-specific teaching responses alongside the original lesson. Accept other mathematically valid open responses that meet the criteria. The original question wording and mathematical answers are retained; model descriptions below make their references readable offline.
c1. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 3 equal parts; 2 parts are shaded altogether.
Answer: 2/3
Teacher response: 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.
c2. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 3 parts are shaded altogether.
Answer: 3/4
Teacher response: 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.
c3. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 2 parts are shaded altogether.
Answer: 2/4
Teacher response: 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.
c4. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 6 equal parts; 5 parts are shaded altogether.
Answer: 5/6
Teacher response: 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.
c5. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 8 equal parts; 3 parts are shaded altogether.
Answer: 3/8
Teacher response: 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.
c6. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 8 equal parts; 7 parts are shaded altogether.
Answer: 7/8
Teacher response: 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.
c7. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 6 equal parts; 4 parts are shaded altogether.
Answer: 4/6
Teacher response: 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.
c8. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 3 equal parts; 1 parts are shaded altogether.
Answer: 1/3
Teacher response: 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.
s1. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Answer: 1/2
Teacher response: 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.
s2. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 3 equal parts; 2 parts are shaded altogether.
Answer: 2/3
Teacher response: 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.
s3. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 1 parts are shaded altogether.
Answer: 1/4
Teacher response: 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.
s4. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 3 parts are shaded altogether.
Answer: 3/4
Teacher response: 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.
h1. Draw 2/3 in two different orientations.
Answer: A vertical or horizontal strip with three equal parts and two shaded shows 2/3.
Look for:
- Draw two representations with different orientations.
- Partition each whole into three equal-area parts.
- Shade exactly two parts in each and label both 2/3.
Teacher response: Matches representations by one visible feature instead of the whole, part size, and selected amount together. 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.
h2. A strip has six equal parts, four shaded. Explain why 6/4 is the wrong label.
Answer: The denominator counts all six parts; the numerator counts four shaded parts.
Look for:
- Identify six as the total number of equal parts.
- Identify four as the number shaded.
- Replace 6/4 with 4/6, accepting 2/3 as an equivalent value.
Teacher response: 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.
h3. Draw a strip for 5/8 and describe the unshaded amount.
Answer: Shade five of eight equal sections; three eighths stay unshaded.
Look for:
- Partition a strip into eight equal parts.
- Shade exactly five and label the shaded fraction 5/8.
- State or label the three unshaded parts as 3/8.
Teacher response: Finds the missing count to one without retaining the fractional unit. 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.
h4. Make a clue for a strip showing 3/4 without using the fraction name.
Answer: Four equal sections; three are shaded and one is not.
Look for:
- Describe four equal parts in one whole.
- Specify that three parts are selected or shaded.
- Keep the clue interpretable as 3/4 without using the fraction name.
Teacher response: 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.
e1. Name two shaded parts in a strip of three equal parts. Strip model: 1 same-sized whole, each divided into 3 equal parts; 2 parts are shaded altogether.
Answer: 2/3
Teacher response: 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.
e2. What does the denominator tell a strip detective?
Answer: It tells how many equal parts make the whole.
Look for:
- State that the denominator counts equal parts in one whole.
- Distinguish this total from the shaded count.
- Connect the denominator to part size, such as three equal parts making thirds.
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. 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.
Teaching notes
- Teaching supplement version 2.0.0. Original lesson questions and PDF materials remain version 1.0.0. Original PDFs contain their original teaching notes and rubrics; use this supplement for the updated diagnostic guidance.
- Short intervention: /interventions/whole-size/. Use its model for the identified difficulty, then return to this lesson’s check and exit ticket.
- Next original lesson: /lessons/number-line-launch/. Transfer the same numerator and denominator roles from shaded pieces to equal distances.
- Open responses are reviewed by a teacher using the specific criteria. These materials have not been field-tested in classrooms.