Chapter 48: Cartesian Plane
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Cartesian Plane in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Cartesian plane (A Cartesian plane uses horizontal and vertical axes to locate points with ordered pairs.)
- x-axis (x-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- y-axis (y-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Origin (Origin is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Ordered pairs (Ordered pairs is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Quadrant I (Quadrant I is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
48.1 Cartesian plane
A Cartesian plane uses horizontal and vertical axes to locate points with ordered pairs. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Cartesian plane. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.2 x-axis
x-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about x-axis. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.3 y-axis
y-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about y-axis. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.4 Origin
Origin is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Origin. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.5 Ordered pairs
Ordered pairs is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Does the point (2, 3) satisfy x + y ≤ 6?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 2
Problem: Does the point (4, 4) satisfy x + y ≤ 6?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: No
Worked Example 3
Problem: Does the point (1, 5) satisfy x + y < 8?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 4
Problem: Does the point (3, 6) satisfy y ≥ 5?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 5
Problem: Does the point (7, 2) satisfy x < 5?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: No
Worked Example 6
Problem: Does the point (0, 0) satisfy x+y≥0?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 7
Problem: Does the point (-1, 4) satisfy y>2?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 8
Problem: Does the point (5, 1) satisfy x≤5?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Worked Example 9
Problem: Does the point (2, 2) satisfy x+y>5?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: No
Worked Example 10
Problem: Does the point (6, 3) satisfy x-y≥2?
- Substitute the x- and y-values into the inequality.
- Evaluate both sides.
- Decide whether the statement is true.
Very beginner explanation: Testing an ordered pair tells whether that point belongs to the solution set.
Answer: Yes
Practice Exercise
Create one new Grade 6 problem about Ordered pairs. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.6 Quadrant I
Quadrant I is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Quadrant I. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.7 Quadrant II
Quadrant II is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Quadrant II. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.8 Quadrant III
Quadrant III is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Quadrant III. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.9 Quadrant IV
Quadrant IV is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Quadrant IV. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.10 Plotting points
Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Plotting points to analyze the values 8 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Plotting points to analyze the values 16 and 20. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Plotting points to analyze the values 23 and 3. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Plotting points to analyze the values 21 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Plotting points to analyze the values 2 and 3. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Plotting points to analyze the values 9 and 5. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Plotting points to analyze the values 13 and 7. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Plotting points to analyze the values 18 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Plotting points to analyze the values 16 and 18. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Plotting points to analyze the values 22 and 18. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Plotting points. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.11 Reading coordinates
Reading coordinates is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Reading coordinates. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.12 Horizontal and vertical distance
Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Horizontal and vertical distance to analyze the values 3 and 12. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Horizontal and vertical distance to analyze the values 3 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Horizontal and vertical distance to analyze the values 28 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Horizontal and vertical distance to analyze the values 7 and 19. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Horizontal and vertical distance to analyze the values 29 and 6. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Horizontal and vertical distance to analyze the values 12 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Horizontal and vertical distance to analyze the values 2 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Horizontal and vertical distance to analyze the values 14 and 6. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Horizontal and vertical distance to analyze the values 28 and 13. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Horizontal and vertical distance to analyze the values 11 and 12. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Horizontal and vertical distance. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
48.13 Coordinate problems
Coordinate problems is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Where is the point (2, 3) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Worked Example 2
Problem: Where is the point (-4, 5) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 3
Problem: Where is the point (-3, -2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 4
Problem: Where is the point (6, -1) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 5
Problem: Where is the point (0, 4) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 6
Problem: Where is the point (5, 0) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: on an axis
Worked Example 7
Problem: Where is the point (-7, 2) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant II
Worked Example 8
Problem: Where is the point (1, -6) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant IV
Worked Example 9
Problem: Where is the point (-2, -8) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant III
Worked Example 10
Problem: Where is the point (8, 7) located?
- Read x first: move horizontally.
- Read y second: move vertically.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y), horizontal coordinate first.
Answer: Quadrant I
Practice Exercise
Create one new Grade 6 problem about Coordinate problems. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
30 Review Questions and Answers
Q1. What is important to understand about Cartesian plane?
Answer: A Cartesian plane uses horizontal and vertical axes to locate points with ordered pairs.
Q2. What is important to understand about x-axis?
Answer: x-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q3. What is important to understand about y-axis?
Answer: y-axis is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q4. What is important to understand about Origin?
Answer: Origin is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q5. What is important to understand about Ordered pairs?
Answer: Ordered pairs is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q6. What is important to understand about Quadrant I?
Answer: Quadrant I is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q7. What is important to understand about Quadrant II?
Answer: Quadrant II is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q8. What is important to understand about Quadrant III?
Answer: Quadrant III is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q9. What is important to understand about Quadrant IV?
Answer: Quadrant IV is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q10. What is important to understand about Plotting points?
Answer: Plotting points is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q11. What is important to understand about Reading coordinates?
Answer: Reading coordinates is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q12. What is important to understand about Horizontal and vertical distance?
Answer: Horizontal and vertical distance is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q13. What is important to understand about Coordinate problems?
Answer: Coordinate problems is a Grade 6 mathematics idea in Cartesian Plane. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q23. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q24. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q25. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q26. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q27. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q28. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q29. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q30. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.