Question 1: A spaceship has a fuel tank that contains 3/4 of its full capacity. If the spaceship consumes 2 times this amount during a mission, how much fuel is used? Use a visual model to illustrate your calculation.

Answer: 1.5 (or 3/2)

Question 2: Construct a visual model on the grid to represent 2 × (1/3) of the moon’s surface area, where the total area is divided into 3 equal parts.

Answer: The model should show 2 parts out of 3, representing 2/3.

Question 3: A satellite orbits Earth 5/6 of the time in a day. If it spends 3 hours in orbit during this time, how many hours does it spend in orbit in a full day? Show your reasoning with a visual model.

Answer: Approximately 4.5 hours

Question 4: A telescope observes 3/4 of a galaxy’s stars in a specific region. If the total number of stars in that region is 2400, how many stars does the telescope observe? Use a visual model to support your answer.

Answer: 1800

Question 5: A planet’s surface area is divided into 8 equal sectors. If an astronomer models observing 3 × (1/8) of the surface, how many sectors does this represent? Draw your visual model.

Answer: 3 sectors

Question 6: Problem Solving: A space station uses a fuel supply that is 5/6 full at the start of a mission. If the station consumes 2 times this amount during the mission, how much fuel is used? Illustrate with a visual model and explain your reasoning.

Answer: The station consumes 10/6 or 5/3 of the full capacity.

Question 7: Challenge: An asteroid field covers 7/8 of a certain region of space. An explorer models 3 × (7/8) of this region. How much of the region is modeled? Draw and justify your visual model.

Answer: 21/8 or 2 5/8 (more than the entire region, indicating a modeling extension)

Question 8: Mixed Review: Use visual models to find the product of 2/5 and 4. Show your model and calculation.

Answer: 8/5

Question 9: Error Analysis: A student models 3 × (2/3) but represents it as 3/2 on the grid. Identify the mistake and correct the visual model.

Answer: Incorrectly multiplying numerator and denominator; the correct model should show 3 times 2/3, which is 2.

Question 10: Construct a visual model to represent 4 × (1/4). What does this model demonstrate about multiplying by 1?

Answer: It demonstrates that multiplying by 1 leaves the quantity unchanged.