# IGCSE Mathematics Foundation: Working with Fractions

## Scheme of work: IGCSE Foundation: Year 10: Term 1: Coordinates

#### Prerequisite Knowledge

• Concept: Understanding how to plot and read coordinates in the first quadrant of the Cartesian plane.
• Example: $\text{Plot the point (3, 4) on the Cartesian plane and read the coordinates of the point.}$
2. Knowledge of the Number Line
• Concept: Understanding the concept of the number line, including positive and negative values.
• Example: $\text{Identify and plot numbers such as -2, 0, 3 on a number line.}$

#### Success Criteria

1. Using Conventions for Rectangular Cartesian Coordinates
• Objective: Students should understand and use conventions for rectangular Cartesian coordinates.
• Example: $\text{Plot the points (2,3) and (-1,4) on the Cartesian plane.}$
2. Plotting Points in Four Quadrants
• Objective: Students should be able to plot points $$(x, y)$$ in any of the four quadrants or locate points with given coordinates.
• Example: $\text{Plot the points (3,-2), (-4,1) on the Cartesian plane.}$
3. Determining Coordinates from Geometrical Information
• Objective: Students should be able to determine the coordinates of points identified by geometrical information.
• Example: $\text{Find the coordinates of the midpoint of a line segment with endpoints at (2,4) and (6,8).}$
4. Determining Midpoint Coordinates
• Objective: Students should be able to determine the coordinates of the midpoint of a line segment, given the coordinates of the two endpoints.
• Example: $\text{Midpoint of the segment joining (1, 3) and (5, 7) is } \left( \frac{1+5}{2}, \frac{3+7}{2} \right) = (3, 5).$

#### Key Concepts

1. Using Cartesian Coordinates
• Concept: Familiarity with the Cartesian coordinate system and the ability to plot and read points.
• Example: $\text{Plot the points (2, 3) and (-1, 4) on the Cartesian plane.}$
2. Plotting Points in Four Quadrants
• Concept: Knowing how to plot and locate points in all four quadrants of the Cartesian plane.
• Example: $\text{Plot the points (3, -2) and (-4, 1) on the Cartesian plane.}$
3. Geometrical Information
• Concept: Using geometrical properties to determine coordinates of points.
• Example: $\text{Find the coordinates of the midpoint of a line segment with endpoints at (2, 4) and (6, 8).}$
4. Midpoint Formula
• Concept: Applying the midpoint formula to find the midpoint of a line segment.
• Example: $\text{Midpoint of the segment joining (1, 3) and (5, 7) is } \left( \frac{1+5}{2}, \frac{3+7}{2} \right) = (3, 5).$

#### Common Misconceptions

1. Using Cartesian Coordinates
• Common Mistake: Students might plot points incorrectly by confusing the x and y coordinates.
• Example: Plotting (3, -2) as (2, -3). $\text{Incorrect: } (3, -2) \rightarrow (2, -3)$ $\text{Correct: } (3, -2) \rightarrow (3, -2)$
2. Plotting Points in Four Quadrants
• Common Mistake: Students might incorrectly plot points in the wrong quadrants.
• Example: Plotting (-4, 1) in the third quadrant instead of the second quadrant. $\text{Incorrect: } (-4, 1) \rightarrow \text{Third quadrant}$ $\text{Correct: } (-4, 1) \rightarrow \text{Second quadrant}$
3. Determining Coordinates from Geometrical Information
• Common Mistake: Students might miscalculate the coordinates of points using geometrical properties.
• Example: Finding the midpoint incorrectly by adding the coordinates instead of averaging them. $\text{Incorrect: Midpoint of (2, 4) and (6, 8) is } (8, 12)$ $\text{Correct: Midpoint of (2, 4) and (6, 8) is } \left( \frac{2+6}{2}, \frac{4+8}{2} \right) = (4, 6)$
4. Midpoint Formula
• Common Mistake: Students might apply the midpoint formula incorrectly by not dividing by 2 or by using incorrect coordinates.
• Example: Applying the midpoint formula incorrectly for points (1, 3) and (5, 7). $\text{Incorrect: Midpoint is } \left( \frac{1+5}{2}, 3+7 \right) = (3, 10)$ $\text{Correct: Midpoint is } \left( \frac{1+5}{2}, \frac{3+7}{2} \right) = (3, 5)$

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