Question 1: Use a visual model to find 2/3 × 3. Draw your model in the grid and write the answer.

Answer: 2

Question 2: Calculate 4/5 × 2 using visual models. Show your drawing and the calculation process.

Answer: 8/5 or 1 3/5

Question 3: A rectangle is divided into 5 equal parts. Shade 3/5 of it and then duplicate this shaded area 2 times to show 2 × 3/5. Write the total shaded parts as a fraction.

Answer: 6/5 or 1 1/5

Question 4: Plot the graph of y = (2/3) x in the grid. Label the points where x = 0, 1, 2.

Answer: Points at (0,0), (1,2/3), (2,4/3)

Question 5: Construct a triangle with sides representing 3/4, 1/2, and 5/8. Use the grid to draw and compare the lengths visually.

Answer: Approximate lengths; exact measurement depends on scale

Question 6: A piece of fabric is divided into 8 equal parts. Shade 5/8 of it. Then, multiply this shaded area by 3. Show your visual model and the answer.

Answer: 15/8 or 1 7/8

Question 7: In a word problem, a garden bed is 2/3 meters wide. If a gardener plans to plant 4 such beds, using visual models, find the total width.

Answer: 8/3 meters or 2 2/3 meters

Question 8: Identify and correct the mistake in this visual model: A student shaded 3/4 of a rectangle and then duplicated it 5 times, claiming the total shaded area is 15/4. Explain the error.

Answer: The mistake is that multiplying 3/4 by 5 gives 15/4, but it only applies if the shaded parts are independent. If the model is a repeated addition, it's correct; if not, the student may have misinterpreted the visual.

Question 9: A recipe calls for 1/2 cup of sugar. If you want to make 3 batches, use visual models to find the total sugar needed.

Answer: 3/2 or 1 1/2 cups

Question 10: Using visual models, compare the products of 2/3 × 4 and 4/3 × 2. Are the results the same? Explain your reasoning.

Answer: Yes, both are 8/3, because multiplication is commutative, and visual models show equal shaded areas.

Question 11: A common mistake is to add the numerators and denominators when multiplying fractions. Show an example with 2/3 × 3/4 and explain the error.

Answer: Incorrect: 2 + 3 / 4 + 4. Correct method: multiply numerators and denominators: (2×3)/(3×4)=6/12=1/2