Question 1: Using visual models, represent the fraction 1/2 on a grid. Then, shade the same amount to show an equivalent fraction.

Answer: 1/2 is half of the grid; an equivalent fraction is 2/4, shading two parts out of four.

Question 2: Construct two rectangles divided into equal parts to visually show that 3/4 is equivalent to 6/8. Label each rectangle accordingly.

Answer: Correct diagram showing 3 shaded parts out of 4, and 6 shaded parts out of 8.

Question 3: A circle is divided into 12 equal sectors. Shade 4 sectors to represent 1/3. Then, shade an equivalent number of sectors to demonstrate 2/6.

Answer: 4 sectors shaded for 1/3; 4 sectors shaded again for 2/6, showing equivalence.

Question 4: Plot the graph of y=2x for x values from 0 to 5. Use the grid to draw the line accurately.

Answer: Line passing through (0,0), (1,2), (2,4), (3,6), (4,8), (5,10).

Question 5: Construct a triangle with sides 3cm, 4cm, and 5cm on the grid. Label the sides and verify the triangle is a right triangle.

Answer: Right triangle with hypotenuse 5cm, sides 3cm and 4cm, verified by Pythagoras (3^2 + 4^2 = 5^2).

Question 6: Identify the common mistake in shading to represent 2/3 and 4/6 in two different diagrams. Explain and correct it.

Answer: Mistake: Inconsistent shading; correct by shading same proportion of the whole in both diagrams.

Question 7: A baker divides a cake into 8 slices. Shade 3 slices to show 3/8. Then, draw an equivalent fraction using visual shading for 6/16.

Answer: Shade 3 of 8 slices, and for 6/16, shade 6 of 16 parts to show equivalence.

Question 8: Use visual models to solve: If 5/10 is equivalent to some fraction, what is it? Show your reasoning.

Answer: 5/10 is equivalent to 1/2, shown by shading half of the grid in both models.

Question 9: A rectangle divided into 10 equal parts has 4 parts shaded. Which fractions are equivalent to this shading? Use visual models to justify your answer.

Answer: Equivalent fractions: 4/10, and also 2/5, shown by shading 4 parts out of 10 and 2 out of 5 in different models.

Question 10: A visual model shows 3/4 shaded. Extend this model to illustrate a larger equivalent fraction with denominator 12. Explain your reasoning.

Answer: Multiply numerator and denominator by 3: 3/4 = 9/12, shade 9 parts out of 12.

Question 11: Identify and correct the mistake in the following visual fraction model, which claims 2/3 is not equivalent to 4/6.

Answer: Mistake: The shaded parts in both models are not proportional. Correct by ensuring equal shading relative to total parts.