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Fraction Classroom · 2.0.0 · Teacher answers & responses

Fraction Strip Lab

Compare wholes, repartition fractions, add unlike units, and distinguish two meanings of division.

Explore, draw, and explain

Use the online model or draw a diagram. Label the whole and show your reasoning.

M1. Use 12 cm wholes. Show 2/3 on strip A and 4/6 on strip B. How many centimeters are shaded on each?

Answer: 8

Look for:

  • Both wholes are 12 cm. Two thirds and four sixths each measure 8 cm; both shaded endpoints agree.

Teacher response: If students are adding the same number to numerator and denominator. The centimeter labels make the whole explicit. Compare physical shaded lengths and fraction names separately. Use the sharing and counting tasks to name what the quotient measures.

M2. Use a 12 cm whole for A and a 24 cm whole for B. Shade 1/2 of A and 1/4 of B. How many centimeters are shaded on each?

Answer: 6

Look for:

  • One half of 12 cm is 6 cm; one quarter of 24 cm is also 6 cm. Different fractions can describe equal lengths when wholes differ.

Teacher response: If students are comparing fraction labels as physical amounts without checking the whole. The centimeter labels make the whole explicit. Compare physical shaded lengths and fraction names separately. Use the sharing and counting tasks to name what the quotient measures.

M3. Use 12 cm wholes. Shade 1/3 on A and 1/4 on B. What fraction of one 12 cm whole is their combined length?

Answer: 7/12

Look for:

  • The amounts measure 4 cm and 3 cm. Together they cover 7 of the twelve 1 cm units: 7/12, not 2/7.

Teacher response: If students are adding denominators as if thirds and fourths were the same-sized parts. The centimeter labels make the whole explicit. Compare physical shaded lengths and fraction names separately. Use the sharing and counting tasks to name what the quotient measures.

M4. Set A to a 12 cm whole with 1/2 shaded. Share that shaded half equally among 3 children. What fraction of the original whole does each child get?

Answer: 1/6

Look for:

  • Half of 12 cm is 6 cm. Three equal shares are 2 cm each: 2/12 = 1/6 of the original whole. Check: 3 × 1/6 = 1/2.

Teacher response: If students are treating the number of children as a serving size. The centimeter labels make the whole explicit. Compare physical shaded lengths and fraction names separately. Use the sharing and counting tasks to name what the quotient measures.

M5. Set A to a 12 cm whole partitioned into fourths. There are 3 whole strips. How many 1/4-strip pieces can you cut?

Answer: 12

Look for:

  • Each whole has four quarter-strip pieces. Three wholes have 3 × 4 = 12 pieces. Check: 12 × 1/4 = 3.

Teacher response: If students are sharing three wholes among four people instead of counting fourths. The centimeter labels make the whole explicit. Compare physical shaded lengths and fraction names separately. Use the sharing and counting tasks to name what the quotient measures.

Teaching notes