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Chapter 30: Coordinate Plane

Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 7Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Coordinate Plane with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Estimate (a close approximation used to check whether an answer is reasonable)
  • Solution (a value or result that satisfies the problem)
  • Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
  • Reasonableness (whether an answer makes sense in the context of the problem)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

30.1 Cartesian plane

Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Cartesian plane: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Cartesian plane: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Cartesian plane: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Cartesian plane: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Cartesian plane: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Cartesian plane in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Cartesian plane becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Cartesian plane and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Cartesian plane becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Cartesian plane using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Cartesian plane becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Cartesian plane problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Cartesian plane becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Cartesian plane could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Cartesian plane becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Cartesian plane. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.2 x-axis

x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Explain x-axis in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: x-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy x-axis and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: x-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show x-axis using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: x-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a x-axis problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: x-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where x-axis could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: x-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about x-axis. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.3 y-axis

y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Explain y-axis in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: y-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy y-axis and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: y-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show y-axis using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: y-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a y-axis problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: y-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where y-axis could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: y-axis becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about y-axis. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.4 Origin

Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Explain Origin in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Origin becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Origin and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Origin becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Origin using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Origin becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Origin problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Origin becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Origin could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Origin becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Origin. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.5 Ordered pairs

Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Explain Ordered pairs in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Ordered pairs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Ordered pairs and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Ordered pairs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Ordered pairs using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Ordered pairs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Ordered pairs problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Ordered pairs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Ordered pairs could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Ordered pairs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Ordered pairs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.6 Quadrant I

Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Quadrant I. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.7 Quadrant II

Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Quadrant II. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.8 Quadrant III

Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Quadrant III. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.9 Quadrant IV

Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Quadrant IV. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.10 Plotting points

A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Plotting points: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Plotting points: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Plotting points: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Plotting points: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Plotting points: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Plotting points in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Plotting points becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Plotting points and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Plotting points becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Plotting points using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Plotting points becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Plotting points problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Plotting points becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Plotting points could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Plotting points becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Plotting points. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.11 Reading coordinates

Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates .

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Reading coordinates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.12 Distance along horizontal and vertical lines

Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find supplementary angle to 35°.

  1. Supplementary angles total 180°.

Very beginner explanation: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 145°

Worked Example 2

Problem: Find supplementary angle to 48°.

  1. Supplementary angles total 180°.

Very beginner explanation: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 132°

Worked Example 3

Problem: Find supplementary angle to 67°.

  1. Supplementary angles total 180°.

Very beginner explanation: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 113°

Worked Example 4

Problem: Find supplementary angle to 72°.

  1. Supplementary angles total 180°.

Very beginner explanation: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 108°

Worked Example 5

Problem: Find supplementary angle to 110°.

  1. Supplementary angles total 180°.

Very beginner explanation: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 70°

Worked Example 6

Problem: Explain Distance along horizontal and vertical lines in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance along horizontal and vertical lines becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Distance along horizontal and vertical lines and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance along horizontal and vertical lines becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Distance along horizontal and vertical lines using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance along horizontal and vertical lines becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Distance along horizontal and vertical lines problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance along horizontal and vertical lines becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Distance along horizontal and vertical lines could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance along horizontal and vertical lines becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Distance along horizontal and vertical lines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

30.13 Coordinate word problems

Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Locate (2,3).

  1. Move 2 units right.
  2. Move 3 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Answer: Quadrant I

Worked Example 2

Problem: Locate (-4,5).

  1. Move 4 units left.
  2. Move 5 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Answer: Quadrant II

Worked Example 3

Problem: Locate (-3,-2).

  1. Move 3 units left.
  2. Move 2 units down.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Answer: Quadrant III

Worked Example 4

Problem: Locate (6,-1).

  1. Move 6 units right.
  2. Move 1 units down.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Answer: Quadrant IV

Worked Example 5

Problem: Locate (0,4).

  1. Move 0 units right.
  2. Move 4 units up.

Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems .

Answer: on an axis

Worked Example 6

Problem: Locate (2,3) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant I

Worked Example 7

Problem: Locate (-4,5) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant II

Worked Example 8

Problem: Locate (-3,-2) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant III

Worked Example 9

Problem: Locate (6,-1) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: Quadrant IV

Worked Example 10

Problem: Locate (0,4) on the coordinate plane.

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.

Answer: on an axis

Practice Exercise

Create one new question about Coordinate word problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

  • Read the complete question before choosing an operation, formula, graph, or model.
  • Write technical words together with their meaning until you are comfortable using them.
  • Show all important steps so another student can follow your reasoning.
  • Keep units, labels, signs, axes, variables, and mathematical symbols clear.
  • Estimate before or after calculating when an estimate can help check reasonableness.
  • For real-life problems, explain what the final number means in the situation.

Extra Practice

  1. Create and solve a new question about Cartesian plane . Show your reasoning and check your answer.
  2. Create and solve a new question about x-axis . Show your reasoning and check your answer.
  3. Create and solve a new question about y-axis . Show your reasoning and check your answer.
  4. Create and solve a new question about Origin . Show your reasoning and check your answer.
  5. Create and solve a new question about Ordered pairs . Show your reasoning and check your answer.
  6. Create and solve a new question about Quadrant I . Show your reasoning and check your answer.
  7. Create and solve a new question about Quadrant II . Show your reasoning and check your answer.
  8. Create and solve a new question about Quadrant III . Show your reasoning and check your answer.
  9. Create and solve a new question about Quadrant IV . Show your reasoning and check your answer.
  10. Create and solve a new question about Plotting points . Show your reasoning and check your answer.
  11. Create and solve a new question about Reading coordinates . Show your reasoning and check your answer.
  12. Create and solve a new question about Distance along horizontal and vertical lines . Show your reasoning and check your answer.

Common Mistakes

  • Combining unlike terms.
  • Changing only one side of an equation.
  • Forgetting to distribute to every term.
  • Using a pattern rule that works only for the first few terms.
  • Writing code without tracing variable values.
  • Using a mathematical model without stating assumptions.
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30 Review Questions and Answers

Q1. What is important to remember about Cartesian plane?

Answer: Cartesian plane is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about x-axis?

Answer: x-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about y-axis?

Answer: y-axis is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Origin?

Answer: Origin is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Ordered pairs?

Answer: Ordered pairs is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q6. What is important to remember about Quadrant I?

Answer: Quadrant I is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Quadrant II?

Answer: Quadrant II is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Quadrant III?

Answer: Quadrant III is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Quadrant IV?

Answer: Quadrant IV is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q10. What is important to remember about Plotting points?

Answer: A point marks an exact location and has no length, width, or height. This topic focuses on Plotting points.

Q11. What is important to remember about Reading coordinates?

Answer: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Reading coordinates.

Q12. What is important to remember about Distance along horizontal and vertical lines?

Answer: Distance along horizontal and vertical lines is an important Grade 7 idea in Coordinate Plane. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Coordinate word problems?

Answer: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate word problems.

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 prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, 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, check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer you obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.

Q26. How should you study this chapter?

Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.

Q27. When is a calculator useful?

Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.

Q28. Why compare more than one strategy?

Answer: Different strategies can make a problem easier and provide a way to verify the result.

Q29. What is a mathematical model?

Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.

Q30. Why should assumptions be stated?

Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.