Chapter 2 REAL NUMBERS 40 Focus-on Mathematics Teacher’s Guide Grade 7 (Textbook Grade 7: P63) Suggested answer(s): 3.141592654 (π) … is not a rational number. It is an irrational number because it cannot be written as a fraction of two numbers. It is a non-repeating and non-terminating decimal, meaning that its decimal representation goes on infinitely without forming a pattern. As a result, π falls into the category of irrational numbers. Guide students to see Example 28 to make them understand more about set of real numbers and use them in operations of addition, subtraction, multiplication and division. Guide students to scan the QR codes of on page 63 for more online resources. Let students attempt Practice 2.5 (Textbook Grade 7: P64) and discuss about the answers with them. 2.6 Use of the Symbol <, >, ≤, ≥, =, ≠ Begin the lesson by introducing the concept of symbols in mathematics. Explain that symbols are marks or signs that represent ideas or relationships. In mathematics, symbols are used not only to represent quantities but also to indicate the relationship between two quantities. Help students understand commonly used mathematical symbols using the table shown on page 64. Practice 2.5 Answers: 1. 2. (a) 5.4 (b) –21 4 (c) 4√2 (d) –16 3. Infinity (∞), √−1 and √−4 ©Praxis Publishing_Focus On Maths
Chapter 2 REAL NUMBERS Focus-on Mathematics Teacher’s Guide Grade 7 41 Go through the examples provided on page 64 with the class to further explain about the use of the symbols. The teacher can provide more similar examples to check students’ understanding. Direct students to Example 29 on page 64 to gain a better understanding of how symbols are used in mathematical sentences. This example will illustrate the application of symbols in representing relationships between quantities. Guide students to explore Example 30 on page 65 to deepen their understanding of the usage of the greater than and less than symbols in mathematics problems. This will help them comprehend how these symbols are used to compare quantities. Prompt the class for answers for each blank before discussing about the answers with them. Explore Example 31 on page 65 to see how mathematical symbols are utilized in daily life applications. This example will provide real-life scenarios where symbols are used to represent relationships and make comparisons. Guide students to scan the QR codes of on page 64 for more online resources. Let students attempt Practice 2.6 (Textbook Grade 7: P65) and discuss about the answers with them. Closing Guide the whole class to conclude the concept of real numbers. Go to page 66, summarise the key points covered in the lessons. Check for students’ understanding by asking questions or having a brief class discussion. Practice 2.6 Answers: 1. (a) 10 < 12 (b) –5 < –4 (c) (–3)2 = 9 (d) 4 5 > 3 4 (e) 2 2 3 < 2.8 (f) √49 > 22 (g) 250¢ < $2.6 (h) –0.2 < 0.1 2. (a) p ≠ –4 (b) The length of a rope ≤ 2.6 m (c) 1 4 > 0.2 (d) < 3 2 (e) Number of students in the class ≥ 25 3. (a) Jonah’s daily pocket money ≥ $500. (b) Time spent on computer games < 2 hours. 4. (a) x = {0, 1, 2, 3, 4, 5, 6, 7} (b) x = {0, 1, 2, 3, …} (c) x = {5, 6, 7, 8, 9, 10, 11, 12} (d) x = {0, 1, 2, 3, 4, 5, 6, 7} ©Praxis Publishing_Focus On Maths
Chapter 2 REAL NUMBERS 42 Focus-on Mathematics Teacher’s Guide Grade 7 Let students attempt Mastery Practice 2 (P66 –67). Then, discuss about the answers with them. Independent Practice Assign students to complete Enrichment Exercises (Workbook Grade 7: Page 55 – 57). Mastery Practice 2 Answers: Section A 1. C 2. A 3. B 4. D 5. B 6. B Section B 1. (a) 5, –10 (b) (i) (ii) 2. (a) (i) +, – (ii) ÷, × (b) (i) +, – (ii) –, + 3. (a) 403 (b) $680 4. (a) Step 2; 22 9 (b) 30.48 5. Mr Foo gained a profit of $50. Mr. Foo bought the shares when the price of shares decreased because the average cost of 1 unit of shares. 6. (a) (b) No, the temperature in the freezer may be above –18oC. 7. (a) –417.5, 8844.43 (b) 8844.43 – (–417.5) = 9261.93 The points are 9261.93 m apart. 8. (a) Hiker A: 26.4 or 132 5 m Hiker B: –37.2 or – 186 5 m Hiker C: –15.7 or – 157 10 m (b) (c) Hiker C ©Praxis (d) Hiker B Publishing_Focus On Maths
Chapter 2 REAL NUMBERS Focus-on Mathematics Teacher’s Guide Grade 7 43 Assessment At the end of this chapter, teacher needs to make sure that students should be able to • recognise and describe real numbers. • recognise rational and irrational numbers. • differentiate between rational and irrational numbers. • giving examples on rational and irrational numbers. • represents rational number on a number line. • represents fractions with diagrams. • writing fractions for given diagrams. • represents fractions as decimals and percentages. • represents positive and negative fractions on number line. • substitute negative and positive fractions and use them in real-life situations. • compare and arrange fractions in order. • perform computations involving combined basic arithmetic operations or other • solve problems involving fractions. • recognise terminating and recurring decimals. • represent positive and negative decimals on number line. • compare and arrange decimals in order. • perform computations involving combined basic arithmetic operations of positive and negative decimals. • solve problems involving decimals. • recognise set of real numbers. • know how to use of the symbol <, >, ≤, ≥, =, ≠. Materials • GeoGebra App • Focus-on Mathematics Textbook Grade 7 • Focus-on Mathematics Workbook Grade 7 • Focus-on Mathematics Grade 7—PowerPoint ©Praxis Publishing_Focus On Maths
STEM ACTVITY: Is It Rational? 44 Focus-on Mathematics Teacher’s Guide Grade 7 Objective To practice identifying and classifying numbers as rational or irrational through hands-on exploration and reasoning. Materials Needed • Small squares of paper or index cards (enough for each student or group) • Markers or pens • Calculator (optional) Instructions 1. Begin by explaining to the students the difference between rational and irrational numbers. Clarify that rational numbers can be expressed as fractions or terminating decimals, while irrational numbers cannot be represented in this way and have non-repeating, non-terminating decimal expansions. 2. Divide the students into pairs or small groups. 3. Distribute the small squares of paper or index cards to each group. 4. Instruct the students to choose any number they want and write it on their paper or index card. Encourage them to be creative and select both whole numbers and decimals. 5. Once the students have chosen their numbers, they should discuss within their groups and decide if the number they selected is rational or irrational. 6. Ask each group to present their chosen number to the class and explain their reasoning for classifying it as rational or irrational. Encourage them to support their arguments using mathematical properties and examples. 7. As a class, discuss the presentations and engage in a discussion about the classification of each number. Encourage students to ask questions and challenge their peers' reasoning if necessary. ©Praxis Publishing_Focus On Maths
STEM ACTVITY: Is It Rational? Focus-on Mathematics Teacher’s Guide Grade 7 45 8. If time permits, the teacher can provide additional numbers for students to analyse and classify, or you can ask students to come up with their own numbers and repeat the process. 9. To extend the activity, the teacher can introduce a calculator and have students calculate the decimal representation of irrational numbers, such as the square root of 2 or pi, to reinforce the concept of non-terminating, non-repeating decimals. Conclusions Wrap up the activity by summarising the main characteristics of rational and irrational numbers, emphasising the importance of reasoning and mathematical properties in their classification. Note: Adapt the activity and difficulty level based on the grade level and mathematical knowledge of the students. The teacher can also modify the activity by introducing real-life examples or exploring famous irrational numbers like e or the golden ratio. ©Praxis Publishing_Focus On Maths