Fraction Match Stations: 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. Station 1: draw and label four strip cards using thirds or fourths.

activity-2. Station 2: write each amount as a count of unit parts, such as two thirds.

activity-3. Station 3: put the matching amount on a number line and explain the shared value.

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: Station 1: draw and label four strip cards using thirds or fourths.

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

phase-3. 10 min · partner: Station 2: write each amount as a count of unit parts, such as two thirds.

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

phase-4. 7 min · discussion: Station 3: put the matching amount on a number line and explain the shared value.

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: Write a value that matches the point and strip. How do words describe the strip denominator?

Answer: Students: Complete the two exit questions independently.

d1. A strip shows two of three equal parts shaded. Where should its matching point lie on a 0–1 number line?

Answer: Two equal third-steps from zero, at 2/3.

Teacher response: If the learner places the point on the second tick including zero, at 1/3. Align the strip with 0 and 1; transfer the shaded endpoint and count the two intervals beneath it.

d2. A card says “two thirds” but shows two of four equal parts shaded. What can you change to make a match?

Answer: Relabel it two fourths (one half), or redraw three equal parts and shade two.

Teacher response: If the learner matches cards by the numerator two alone. Read “thirds” as a part-size instruction and count how many such equal parts fill the whole.

r1. Match three shaded fourths with a line point and a word card.

Answer: The point is three quarter-steps from zero, at 3/4; the words are “three fourths.”

e1. Write a value that matches the point and strip. 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.

Answer: 2/3

Teacher response: Treats different fraction names as different positions despite equal distance from zero. 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.

e2. How do words describe the strip denominator?

Answer: Thirds names the size of each equal part.

Look for:

• Connect a denominator word such as “thirds” with equal-part size.
• Explain that three such parts fill the whole.
• Distinguish the part name from the number of parts selected.

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.

teach-1. Align a third-partitioned strip directly above a 0–1 line.

teach-2. Shade two parts and move a vertical guide from the shaded endpoint to the line.

teach-3. Write “two thirds,” 2/3, and two third-steps beside the same amount; repair one deliberately mismatched card.

next-1. 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.

Teacher response: Continue to the linked next lesson. Critique a collection of representations and repair mislabeled exhibits. Next original lesson: /lessons/fraction-museum/.

next-2. e1 does not yet meet this criterion: e1 gives 2/3 for the matching model.

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/intervals-not-points/.

next-3. e1 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.

Teacher response: 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. Short intervention: /interventions/intervals-not-points/.

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 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.

c4. 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.

c5. Write the fraction at the marked point. 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.

Answer: 2/3

Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. 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.

c6. Write the fraction at the marked point. 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.

Answer: 3/4

Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. 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.

c7. Write the fraction at the marked point. 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.

Answer: 4/6

Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. 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.

c8. Write the fraction at the marked point. 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.

Answer: 3/8

Teacher response: Counts tick marks, including zero, instead of equal intervals from zero. 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.

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; 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.

s3. 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.

s4. 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.

h1. Make a strip, words, and number-line set for 2/3.

Answer: Two shaded thirds, the words two thirds, and a point two third-steps from zero.

Look for:

• Show a strip divided into three equal parts with two shaded.
• Write the words “two thirds.”
• Place the line point two equal third-steps from zero on the same unit.

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. Why do 2/4 and 1/2 match the same number-line point?

Answer: Both describe half of one unit.

Look for:

• Identify both fractions as half of one unit.
• Use a common 0–1 interval or equal-length strips.
• Explain that two quarter-steps and one half-step end together.

Teacher response: Treats different fraction names as different positions despite equal distance from zero. 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.

h3. Create a deliberately mismatched card and repair it.

Answer: A strip with three fourths shaded cannot match a line marked 1/4; change the point to 3/4.

Look for:

• Create two cards that actually represent different values.
• Identify the precise mismatch in the shaded count, partition, words, or line point.
• Repair a card so all representations describe the same value.

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.

h4. Write a rule for checking all three stations.

Answer: Use the same whole, equal parts and the same counted amount.

Look for:

• Check the whole or 0–1 unit across the stations.
• Check equal-sized parts or intervals.
• Check that the words, selected count, and point all name the same amount.

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. Assumes equal fraction labels guarantee equal physical amounts even when the wholes differ. 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.

e1. Write a value that matches the point and strip. 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.

Answer: 2/3

Teacher response: Treats different fraction names as different positions despite equal distance from zero. 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.

e2. How do words describe the strip denominator?

Answer: Thirds names the size of each equal part.

Look for:

• Connect a denominator word such as “thirds” with equal-part size.
• Explain that three such parts fill the whole.
• Distinguish the part name from the number of parts selected.

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.