Fraction Museum: teaching companion

prepare. Before starting: Recognize a whole and count equal parts.

materials. Materials: Pencil: 1 per student; Plain paper sheets: 2 per student; Projector: 1 per class (optional).

activity-1. Create a small exhibit with a labeled strip and a matching number line.

activity-2. Exchange exhibits. Check equal partitions, labels and the whole.

activity-3. Write a curator note explaining one repair and one equivalent name.

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: Create a small exhibit with a labeled strip and a matching number line.

Answer: Students: Follow the model; label the whole and the equal parts.

phase-3. 10 min · partner: Exchange exhibits. Check equal partitions, labels and the whole.

Answer: Students: Work in pairs. One models, the other checks; switch roles.

phase-4. 7 min · discussion: Write a curator note explaining one repair and one equivalent name.

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: Compare 1/2 and 3/6. Choose <, =, or >. The wholes are the same size. Give one check you would use before displaying a model.

Answer: Students: Complete the two exit questions independently.

d1. One exhibit shades one of two equal parts; another shades three of six equal parts on an identical whole. Do they show the same amount?

Answer: Yes. Both show one half of the same-sized whole.

Teacher response: If the learner says three selected pieces must exceed one selected piece. Align the shaded endpoints and split each half into three sixths to connect the counts.

d2. An exhibit labeled 2/3 shows two of four equal parts shaded. What repair would make it accurate?

Answer: Change the label to 2/4 (or 1/2), or repartition into thirds and shade two.

Teacher response: If the learner keeps the label because two pieces are shaded. Ask the learner to name one piece from the whole’s partition before counting selected pieces.

r1. Would an uneven six-part picture be ready to display as 3/6 just because three pieces are shaded?

Answer: No. First verify or repair equal part areas; count alone does not establish sixths.

e1. Compare 1/2 and 3/6. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

e2. Give one check you would use before displaying a model.

Answer: Verify equal-sized parts and a label matching the shaded count.

Look for:

• Name a concrete pre-display check such as equal areas or label-to-count agreement.
• State what feature of the model is inspected, such as the part areas or selected count.
• Use a condition that establishes mathematical accuracy of the fraction exhibit.

Teacher response: Counts pieces without checking equal area. 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. 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.

teach-1. Prepare a valid half exhibit and a mislabeled two-of-four exhibit.

teach-2. Check the whole, equality of areas, total count, and selected count in that order.

teach-3. Pair equivalent exhibits by aligned endpoints, then write a precise curator note explaining one repair.

next-1. e1 meets its criterion: e1 gives = for 1/2 compared with 3/6. e2 also meets its criterion: e2 describes a concrete model check and what evidence would pass it, using its rubric.

Teacher response: Continue to the linked next lesson. Explain equivalent exhibits by repartitioning the same fixed whole. Next original lesson: /lessons/equivalent-strip-lab/.

next-2. e1 does not yet meet this criterion: e1 gives = for 1/2 compared with 3/6.

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/equivalent-factors/.

next-3. e1 meets its criterion, but e2 does not yet show this evidence: e2 describes a concrete model check and what evidence would pass it, using its rubric.

Teacher response: Present the mislabeled exhibit again. Ask the learner to apply the proposed e2 check and say exactly what would need repair. Short intervention: /interventions/equivalent-factors/.

c1. 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.

c2. 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.

c3. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 6 equal parts; 3 parts are shaded altogether.

Answer: 3/6

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.

c4. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 8 equal parts; 4 parts are shaded altogether.

Answer: 4/8

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.

c5. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c6. Compare 2/3 and 4/6. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c7. Compare 3/4 and 6/8. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

c8. Compare 2/2 and 3/3. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.

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: 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.

s2. 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: 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.

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: 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.

s4. 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.

h1. Design two exhibits for one half.

Answer: Shade one of two parts or two of four equal parts in equal-sized strips.

Look for:

• Create two different partitioned exhibits for one half.
• Use equal-sized wholes and equal parts within each exhibit.
• Show that both shaded amounts cover half, such as 1/2 and 2/4.

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

h2. Curate an exhibit labeled 2/3 on a strip with two of four parts shaded.

Answer: Change the label to 2/4, or redraw thirds and shade two.

Look for:

• Identify the mismatch between the 2/3 label and two of four shaded parts.
• Repair the label to 2/4 (or 1/2), or redraw thirds with two shaded.
• Explain why the repaired label now matches both total and shaded counts.

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. Write a museum note about whole fractions such as 3/3.

Answer: All three thirds are included, so the value is one whole.

Look for:

• Explain that 3/3 includes all three thirds.
• State that these equal parts fill one whole.
• Extend the note to fractions such as b/b rather than suggesting all fractions equal one.

Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.

h4. Give feedback on uneven partitions without rejecting the artist.

Answer: The shading is clear; equalize the partition sizes so the fraction label is accurate.

Look for:

• Identify uneven part areas as the mathematical issue.
• Give a specific revision that equalizes the partition sizes.
• Use feedback that addresses the model constructively and preserves an accurate fraction label.

Teacher response: Counts pieces without checking equal area. 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.

e1. Compare 1/2 and 3/6. Choose <, =, or >. The wholes are the same size.

Answer: =

Teacher response: Changes one part of a fraction without scaling numerator and denominator by the same factor. Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.

e2. Give one check you would use before displaying a model.

Answer: Verify equal-sized parts and a label matching the shaded count.

Look for:

• Name a concrete pre-display check such as equal areas or label-to-count agreement.
• State what feature of the model is inspected, such as the part areas or selected count.
• Use a condition that establishes mathematical accuracy of the fraction exhibit.

Teacher response: Counts pieces without checking equal area. 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. 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.