Chapter 52: Coordinates in the First Quadrant
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Coordinates in the First Quadrant with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Cartesian plane basics (a Grade 5 idea used in this chapter)
- x-axis and y-axis (a Grade 5 idea used in this chapter)
- Origin (a Grade 5 idea used in this chapter)
- Ordered pairs (a Grade 5 idea used in this chapter)
- Plotting first-quadrant points (a Grade 5 idea used in this chapter)
- Reading coordinates (a Grade 5 idea used in this chapter)
- Using different coordinate scales (a Grade 5 idea used in this chapter)
- Graphing points from a table (a Grade 5 idea used in this chapter)
- Describing translations between points (a Grade 5 idea used in this chapter)
- Coordinate-grid word problems (a Grade 5 idea used in this chapter)
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.
52.1 Cartesian plane basics
Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Cartesian plane basics?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Cartesian plane basics?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Cartesian plane basics.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Cartesian plane basics problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Cartesian plane basics.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Cartesian plane basics can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Cartesian plane basics in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Cartesian plane basics 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 basics and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Cartesian plane basics 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 basics using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Cartesian plane basics 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 basics problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Cartesian plane basics 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 basics could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Cartesian plane basics 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 basics. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.2 x-axis and y-axis
x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of x-axis and y-axis?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about x-axis and y-axis?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for x-axis and y-axis.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a x-axis and y-axis problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for x-axis and y-axis.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: x-axis and y-axis can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain x-axis and y-axis in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: x-axis and 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 x-axis and y-axis and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: x-axis and 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 x-axis and y-axis using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: x-axis and 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 x-axis and y-axis problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: x-axis and 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 x-axis and y-axis could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: x-axis and 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 x-axis and y-axis. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.3 Origin
Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Origin?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Origin?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Origin.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Origin problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Origin.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Origin can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Origin in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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?
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
52.4 Ordered pairs
Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Ordered pairs?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Ordered pairs?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Ordered pairs.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Ordered pairs problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Ordered pairs.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Ordered pairs can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Ordered pairs in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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?
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
- Read the definition of the topic.
- Use the definition to build the response.
- 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.
52.5 Plotting first-quadrant points
Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Plotting first-quadrant points?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Plotting first-quadrant points?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Plotting first-quadrant points.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Plotting first-quadrant points problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Plotting first-quadrant points.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Plotting first-quadrant points can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Locate (2,3) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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 Plotting first-quadrant points. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.6 Reading coordinates
Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Reading coordinates?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Reading coordinates?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Reading coordinates.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Reading coordinates problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Reading coordinates.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Reading coordinates can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Locate (2,3) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
52.7 Using different coordinate scales
Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Using different coordinate scales?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Using different coordinate scales?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Using different coordinate scales.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Using different coordinate scales problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Using different coordinate scales.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Using different coordinate scales can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Locate (2,3) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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 Using different coordinate scales. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.8 Graphing points from a table
Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Graphing points from a table?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Worked Example 2
Problem: What should you identify first before solving a problem about Graphing points from a table?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Graphing points from a table.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Graphing points from a table problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Graphing points from a table.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Graphing points from a table can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Graphing points from a table in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Graphing points from a table 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 Graphing points from a table and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Graphing points from a table 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 Graphing points from a table using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Graphing points from a table 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 Graphing points from a table problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Graphing points from a table 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 Graphing points from a table could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Graphing points from a table 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 Graphing points from a table. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.9 Describing translations between points
Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Describing translations between points?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Describing translations between points?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Describing translations between points.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Describing translations between points problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Describing translations between points.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Describing translations between points can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Describing translations between points. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
52.10 Coordinate-grid word problems
Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Coordinate-grid word problems?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Coordinate-grid word problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Coordinate-grid word problems.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Coordinate-grid word problems problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Coordinate-grid word problems.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Coordinate-grid word problems can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Locate (2,3) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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.
- Move horizontally using x.
- Move vertically using y.
- 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-grid 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 question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Cartesian plane basics.
- Create and solve one original problem about x-axis and y-axis.
- Create and solve one original problem about Origin.
- Create and solve one original problem about Ordered pairs.
- Create and solve one original problem about Plotting first-quadrant points.
- Create and solve one original problem about Reading coordinates.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Cartesian plane basics?
Answer: Cartesian plane basics is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q2. What is the key idea in x-axis and y-axis?
Answer: x-axis and y-axis is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q3. What is the key idea in Origin?
Answer: Origin is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q4. What is the key idea in Ordered pairs?
Answer: Ordered pairs is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q5. What is the key idea in Plotting first-quadrant points?
Answer: Plotting first-quadrant points is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q6. What is the key idea in Reading coordinates?
Answer: Reading coordinates develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q7. What is the key idea in Using different coordinate scales?
Answer: Using different coordinate scales develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q8. What is the key idea in Graphing points from a table?
Answer: Graphing points from a table helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q9. What is the key idea in Describing translations between points?
Answer: Describing translations between points develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q10. What is the key idea in Coordinate-grid word problems?
Answer: Coordinate-grid word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 5 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Coordinates in the First Quadrant effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Coordinates in the First Quadrant effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Coordinates in the First Quadrant effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Coordinates in the First Quadrant effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Coordinates in the First Quadrant effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.