Question 1: Use visual models to calculate: ⅖ × 3. (Draw three copies of the ⅖ model and find the total shaded area.)

Answer: 3/5

Question 2: A rectangle is divided into 4 equal parts with 2 shaded. If this rectangle is replicated 5 times, what is the total number of shaded parts? Use visual models to justify your answer.

Answer: 10/4 or 5/2

Question 3: Visualize ⅗ multiplied by 4 using a grid. How many parts are shaded in total?

Answer: 12/5

Question 4: Construct a visual model showing ½ × 6. How many segments are shaded? Write your answer as a fraction.

Answer: 3

Question 5: Plot the graph of y = ⅓ x on the provided grid. How does the visual model help understand this relationship?

Answer: The graph shows how multiplying by ⅓ scales down the value, visualized by shading one-third of each unit.

Question 6: A visual model shows ⅖ shaded in each of 4 identical rectangles. What is the total shaded in all four? Show your work.

Answer: 8/5 or 1⅗

Question 7: Identify the common mistake: A student models ⅓ × 5 by shading ⅓ of a rectangle 5 times but concludes the answer is 5/3. What is the correct interpretation?

Answer: The total shaded parts should be 5 times ⅓, which is 5/3, so the student’s answer is correct; the mistake might be misreading the fraction or the total segments.

Question 8: Using visual models, explain why ⅘ × 2 equals ⅚.

Answer: Two copies of ⅘, each with 4 shaded parts out of 5, total 8 shaded parts out of 10, which simplifies to 4/5 × 2 = 8/10 = 4/5.

Question 9: Challenge: Construct a visual model for ⅖ × 7. How many parts are shaded in total? Express your answer as a simplified fraction.

Answer: 14/5 or 2⅚

Question 10: A visual model shows ⅗ shaded in each of 3 rectangles. Another rectangle is shaded in ½. Which is greater: ⅗ × 3 or ½? Use the visual models to compare and explain.

Answer: ⅗ × 3 = 9/5; ½ = 2/4; 9/5 = 1.8 which is greater than ½, so ⅗ × 3 is larger.