Chapter 7: Powers, Squares, and Square Roots
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Powers, Squares, and Square Roots with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- 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.
7.1 Base
Base is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Base 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: Base 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 Base 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: Base 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 Base 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: Base 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 Base 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: Base 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 Base 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: Base 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 Base. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.2 Exponent
An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent .
Answer: 100
Worked Example 6
Problem: Explain Exponent 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: Exponent 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 Exponent 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: Exponent 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 Exponent 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: Exponent 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 Exponent 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: Exponent 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 Exponent 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: Exponent 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 Exponent. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.3 Power
Power is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Power 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: Power 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 Power 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: Power 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 Power 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: Power 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 Power 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: Power 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 Power 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: Power 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 Power. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.4 Repeated multiplication
A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
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 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication .
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Repeated multiplication. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.5 Evaluating powers
Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Evaluating powers 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: Evaluating powers 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 Evaluating powers 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: Evaluating powers 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 Evaluating powers 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: Evaluating powers 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 Evaluating powers 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: Evaluating powers 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 Evaluating powers 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: Evaluating powers 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 Evaluating powers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.6 Powers of 10
Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Powers of 10 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: Powers of 10 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 Powers of 10 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: Powers of 10 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 Powers of 10 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: Powers of 10 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 Powers of 10 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: Powers of 10 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 Powers of 10 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: Powers of 10 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 Powers of 10. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.7 Square numbers
Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 2².
- 2×2=4.
Very beginner explanation: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4
Worked Example 2
Problem: Find 3².
- 3×3=9.
Very beginner explanation: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Find 4².
- 4×4=16.
Very beginner explanation: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Find 5².
- 5×5=25.
Very beginner explanation: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25
Worked Example 5
Problem: Find 10².
- 10×10=100.
Very beginner explanation: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Square numbers 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: Square numbers 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 Square numbers 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: Square numbers 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 Square numbers 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: Square numbers 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 Square numbers 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: Square numbers 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 Square numbers 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: Square numbers 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 Square numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.8 Perfect squares
Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 2².
- 2×2=4.
Very beginner explanation: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4
Worked Example 2
Problem: Find 3².
- 3×3=9.
Very beginner explanation: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Find 4².
- 4×4=16.
Very beginner explanation: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Find 5².
- 5×5=25.
Very beginner explanation: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25
Worked Example 5
Problem: Find 10².
- 10×10=100.
Very beginner explanation: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Perfect squares 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: Perfect squares 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 Perfect squares 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: Perfect squares 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 Perfect squares 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: Perfect squares 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 Perfect squares 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: Perfect squares 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 Perfect squares 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: Perfect squares 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 Perfect squares. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.9 Square roots
A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
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 √4.
- 2×2=4.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
Answer: 2
Worked Example 2
Problem: Find √9.
- 3×3=9.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
Answer: 3
Worked Example 3
Problem: Find √16.
- 4×4=16.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
Answer: 4
Worked Example 4
Problem: Find √25.
- 5×5=25.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
Answer: 5
Worked Example 5
Problem: Find √100.
- 10×10=100.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots .
Answer: 10
Worked Example 6
Problem: Explain Square roots 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: Square roots 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 Square roots 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: Square roots 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 Square roots 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: Square roots 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 Square roots 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: Square roots 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 Square roots 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: Square roots 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 Square roots. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.10 Estimating square roots
A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
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 √4.
- 2×2=4.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
Answer: 2
Worked Example 2
Problem: Find √9.
- 3×3=9.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
Answer: 3
Worked Example 3
Problem: Find √16.
- 4×4=16.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
Answer: 4
Worked Example 4
Problem: Find √25.
- 5×5=25.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
Answer: 5
Worked Example 5
Problem: Find √100.
- 10×10=100.
Very beginner explanation: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots .
Answer: 10
Worked Example 6
Problem: Explain Estimating square roots 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: Estimating square roots 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 Estimating square roots 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: Estimating square roots 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 Estimating square roots 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: Estimating square roots 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 Estimating square roots 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: Estimating square roots 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 Estimating square roots 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: Estimating square roots 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 Estimating square roots. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.11 Cube numbers introduction
Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Cube numbers introduction 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: Cube numbers introduction 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 Cube numbers introduction 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: Cube numbers introduction 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 Cube numbers introduction 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: Cube numbers introduction 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 Cube numbers introduction 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: Cube numbers introduction 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 Cube numbers introduction 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: Cube numbers introduction 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 Cube numbers introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.12 Exponent patterns
An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns .
Answer: 100
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Exponent patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
7.13 Real-life applications of powers
Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. 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: Evaluate 2^3.
- Multiply 2 by itself 3 times.
Very beginner explanation: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8
Worked Example 2
Problem: Evaluate 3^2.
- Multiply 3 by itself 2 times.
Very beginner explanation: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 9
Worked Example 3
Problem: Evaluate 4^2.
- Multiply 4 by itself 2 times.
Very beginner explanation: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 16
Worked Example 4
Problem: Evaluate 5^3.
- Multiply 5 by itself 3 times.
Very beginner explanation: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 125
Worked Example 5
Problem: Evaluate 10^2.
- Multiply 10 by itself 2 times.
Very beginner explanation: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 100
Worked Example 6
Problem: Explain Real-life applications of powers 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: Real-life applications of powers 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 Real-life applications of powers 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: Real-life applications of powers 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 Real-life applications of powers 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: Real-life applications of powers 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 Real-life applications of powers 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: Real-life applications of powers 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 Real-life applications of powers 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: Real-life applications of powers 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 Real-life applications of powers. 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
- Create and solve a new question about Base . Show your reasoning and check your answer.
- Create and solve a new question about Exponent . Show your reasoning and check your answer.
- Create and solve a new question about Power . Show your reasoning and check your answer.
- Create and solve a new question about Repeated multiplication . Show your reasoning and check your answer.
- Create and solve a new question about Evaluating powers . Show your reasoning and check your answer.
- Create and solve a new question about Powers of 10 . Show your reasoning and check your answer.
- Create and solve a new question about Square numbers . Show your reasoning and check your answer.
- Create and solve a new question about Perfect squares . Show your reasoning and check your answer.
- Create and solve a new question about Square roots . Show your reasoning and check your answer.
- Create and solve a new question about Estimating square roots . Show your reasoning and check your answer.
- Create and solve a new question about Cube numbers introduction . Show your reasoning and check your answer.
- Create and solve a new question about Exponent patterns . Show your reasoning and check your answer.
Common Mistakes
- Ignoring place value or signs.
- Using an operation before checking what the question asks.
- Skipping estimation and accepting an unreasonable result.
- Forgetting the correct order of operations.
30 Review Questions and Answers
Q1. What is important to remember about Base?
Answer: Base is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Exponent?
Answer: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent.
Q3. What is important to remember about Power?
Answer: Power is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Repeated multiplication?
Answer: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Repeated multiplication.
Q5. What is important to remember about Evaluating powers?
Answer: Evaluating powers is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Powers of 10?
Answer: Powers of 10 is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Square numbers?
Answer: Square numbers is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Perfect squares?
Answer: Perfect squares is an important Grade 7 idea in Powers, Squares, and Square Roots. 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 Square roots?
Answer: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Square roots.
Q10. What is important to remember about Estimating square roots?
Answer: A square root (a number that multiplied by itself gives the original number) reverses squaring. This topic focuses on Estimating square roots.
Q11. What is important to remember about Cube numbers introduction?
Answer: Cube numbers introduction is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Exponent patterns?
Answer: An exponent (a small raised number showing repeated multiplication) tells how many times the base is used as a factor. This topic focuses on Exponent patterns.
Q13. What is important to remember about Real-life applications of powers?
Answer: Real-life applications of powers is an important Grade 7 idea in Powers, Squares, and Square Roots. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and 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.