Numbers and Algebra

Real Numbers - Odd and even numbers

By the end of the lesson, the learner should be able to:

- Define odd and even numbers
- Classify whole numbers as odd or even by examining the ones place value
- Use classification of odd and even numbers to solve everyday sharing and grouping problems

- Discuss with peers the meaning of odd and even numbers
- Classify given numbers by examining the digit in the ones place value
- Sort numbers from real-life contexts such as workshop inventories into odd and even categories

How do we determine whether a whole number is odd or even?

- Master Core Mathematics Grade 10 pg. 1
- Number cards
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Prime numbers
Real Numbers - Composite numbers

By the end of the lesson, the learner should be able to:

- Define a prime number
- Identify prime numbers by determining factors of given numbers
- Use prime numbers to solve puzzles and form passwords in everyday contexts

- Discuss the meaning of prime numbers
- List the factors of given numbers and identify those with only two factors
- List all prime numbers within given ranges

What makes a number prime?

- Master Core Mathematics Grade 10 pg. 3
- Number cards
- Charts
- Master Core Mathematics Grade 10 pg. 5

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Rational and irrational numbers

By the end of the lesson, the learner should be able to:

- Define rational and irrational numbers
- Classify real numbers as rational or irrational by expressing them as decimals
- Relate rational and irrational numbers to real-life measurements such as lengths and areas

- Use digital devices or other resources to find the meaning of rational and irrational numbers
- Express given numbers as decimals and classify them as terminating, recurring, or non-terminating
- Categorise numbers as rational or irrational

How do we distinguish rational numbers from irrational numbers?

- Master Core Mathematics Grade 10 pg. 6
- Calculators
- Digital devices

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Reciprocal of real numbers by division

By the end of the lesson, the learner should be able to:

- Define the reciprocal of a number
- Determine the reciprocal of integers, fractions, and decimals by dividing 1 by the number
- Use reciprocals to solve everyday proportional problems such as recipes and sharing tasks

- Discuss how to get the reciprocal of whole numbers and fractions
- Work out reciprocals of given integers, decimals, and fractions by division
- Verify that the product of a number and its reciprocal equals 1

How do we find the reciprocal of a number using division?

- Master Core Mathematics Grade 10 pg. 8
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Reciprocal of real numbers using tables

By the end of the lesson, the learner should be able to:

- Read reciprocals of numbers from mathematical tables
- Determine reciprocals of numbers in standard form using tables
- Use reciprocal tables to solve problems involving fuel consumption and wave frequency

- Discuss the features and columns of the table of reciprocals
- Read reciprocals of numbers between 1 and 10 directly from tables
- Express numbers less than 1 or greater than 10 in standard form and determine their reciprocals using tables

How do we use mathematical tables to find reciprocals?

- Master Core Mathematics Grade 10 pg. 9
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Reciprocal of real numbers using calculators
Real Numbers - Application of reciprocals in computations

By the end of the lesson, the learner should be able to:

- Identify the reciprocal button on a scientific calculator
- Determine reciprocals of real numbers using a calculator
- Use calculators to solve real-life problems involving reciprocals such as subdividing land and cutting materials

- Identify the reciprocal button (x⁻¹ or 1/x) on the calculator
- Key in numbers and use the reciprocal function to determine their reciprocals
- Compare calculator results with those obtained from tables

Why is a calculator useful in finding reciprocals of numbers?

- Master Core Mathematics Grade 10 pg. 12
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 13
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Numbers in index form

By the end of the lesson, the learner should be able to:

- Identify the base and index of a number in index form
- Express numbers as products of prime factors and write them in index form
- Relate index form to real-life contexts such as expressing large populations and tree planting records

- Discuss how to express numbers in index form
- Express given numbers as products of prime factors and write in power form
- Identify the base and index in given expressions

Why do we write numbers in index form?

- Master Core Mathematics Grade 10 pg. 15
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication law of indices

By the end of the lesson, the learner should be able to:

- State the multiplication law of indices
- Simplify expressions by adding indices with the same base during multiplication
- Apply the multiplication law to calculate areas and volumes in real-life contexts such as rooms and swimming pools

- Discuss and derive the multiplication law of indices
- Simplify given expressions using the multiplication law
- Determine areas and volumes of shapes expressed in index form

What happens to the indices when we multiply numbers with the same base?

- Master Core Mathematics Grade 10 pg. 16
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Division law of indices

By the end of the lesson, the learner should be able to:

- State the division law of indices
- Simplify expressions by subtracting indices with the same base during division
- Use the division law to solve real-life problems such as determining the number of tiles needed to cover a floor

- Discuss and derive the division law of indices
- Simplify given expressions using the division law
- Solve problems involving division of numbers in index form

What happens to the indices when we divide numbers with the same base?

- Master Core Mathematics Grade 10 pg. 17
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers, zero index and negative indices
Indices and Logarithms - Fractional indices and application of laws

By the end of the lesson, the learner should be able to:

- Apply the power of indices rule, zero index rule, and negative index rule
- Simplify expressions involving powers of indices, zero index, and negative indices
- Relate zero and negative indices to real-life contexts such as bacteria growth models and financial processing fees

- Discuss and derive the rules for powers of indices, zero index, and negative indices
- Simplify expressions such as (aᵐ)ⁿ, a⁰, and a⁻ⁿ
- Evaluate expressions involving zero and negative indices

How do we simplify expressions with zero or negative indices?

- Master Core Mathematics Grade 10 pg. 19
- Charts
- Calculators
- Master Core Mathematics Grade 10 pg. 22

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers of 10 and common logarithms

By the end of the lesson, the learner should be able to:

- Relate index notation to logarithm notation to base 10
- Convert between index form and logarithm form
- Use logarithm notation to express real-life quantities such as vaccination figures and bacteria counts

- Discuss the relationship between powers of 10 and logarithm notation
- Write numbers in logarithm form and convert from logarithm to index form
- Express given numbers in logarithm notation

How are powers of 10 related to common logarithms?

- Master Core Mathematics Grade 10 pg. 26
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers between 1 and 10

By the end of the lesson, the learner should be able to:

- Read logarithms of numbers between 1 and 10 from mathematical tables
- Determine logarithms using the main columns and mean difference columns
- Express real-life measurements such as mass and density in the form 10ⁿ using tables

- Discuss the features of the logarithm table
- Read logarithms of numbers with 2, 3, and 4 significant figures from tables
- Express given quantities in the form 10ⁿ

How do we read logarithms of numbers from tables?

- Master Core Mathematics Grade 10 pg. 27
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers greater than 10

By the end of the lesson, the learner should be able to:

- Determine logarithms of numbers greater than 10 using standard form and tables
- Identify the characteristic and mantissa of a logarithm
- Express real-life measurements such as diameters and forces in the form 10ⁿ

- Express numbers greater than 10 in standard form (A × 10ⁿ)
- Read the logarithm of A from tables and add the index n
- Identify the characteristic and mantissa parts of logarithms

How do we find logarithms of numbers greater than 10?

- Master Core Mathematics Grade 10 pg. 29
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers less than 1

By the end of the lesson, the learner should be able to:

- Determine logarithms of numbers less than 1 using standard form and tables
- Write the bar notation for negative characteristics
- Express real-life quantities such as pipe diameters and pollutant concentrations in the form 10ⁿ

- Express numbers less than 1 in standard form
- Read the logarithm of the number from tables and identify the negative characteristic
- Write logarithms using bar notation for the characteristic

Why do numbers less than 1 have negative characteristics?

- Master Core Mathematics Grade 10 pg. 30
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Antilogarithms using tables

By the end of the lesson, the learner should be able to:

- Define antilogarithm as the reverse of a logarithm
- Determine antilogarithms of numbers using tables of antilogarithms
- Use antilogarithms to find actual values from logarithmic results in practical calculations

- Discuss antilogarithm as the reverse process of finding a logarithm
- Use tables of antilogarithms to determine numbers whose logarithms are given
- Determine antilogarithms of numbers with positive and negative (bar) characteristics

How do we use antilogarithm tables to find numbers?

- Master Core Mathematics Grade 10 pg. 31
- Mathematical tables
- Antilogarithm tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms and antilogarithms using calculators

By the end of the lesson, the learner should be able to:

- Determine logarithms and antilogarithms of numbers using a calculator
- Use the log and shift-log buttons to find logarithms and antilogarithms
- Compare calculator results with table values to build confidence in using digital tools for computation

- Identify the log button on a scientific calculator
- Determine logarithms and antilogarithms of numbers by keying values into the calculator
- Compare results obtained from calculators with those from tables

How do we use calculators to find logarithms and antilogarithms?

- Master Core Mathematics Grade 10 pg. 33
- Scientific calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms and antilogarithms using calculators

By the end of the lesson, the learner should be able to:

- Determine logarithms and antilogarithms of numbers using a calculator
- Use the log and shift-log buttons to find logarithms and antilogarithms
- Compare calculator results with table values to build confidence in using digital tools for computation

- Identify the log button on a scientific calculator
- Determine logarithms and antilogarithms of numbers by keying values into the calculator
- Compare results obtained from calculators with those from tables

How do we use calculators to find logarithms and antilogarithms?

- Master Core Mathematics Grade 10 pg. 33
- Scientific calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication and division using logarithms

By the end of the lesson, the learner should be able to:

- Use logarithms to multiply and divide numbers
- Apply the steps of finding logarithms, adding or subtracting them, and finding the antilogarithm
- Solve real-life multiplication and division problems efficiently using logarithms

- Determine logarithms of numbers, add them to perform multiplication, and find the antilogarithm of the sum
- Determine logarithms, subtract them to perform division, and find the antilogarithm of the difference
- Arrange solutions in a table format

How do logarithms simplify multiplication and division?

- Master Core Mathematics Grade 10 pg. 35
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication and division using logarithms

By the end of the lesson, the learner should be able to:

- Use logarithms to multiply and divide numbers
- Apply the steps of finding logarithms, adding or subtracting them, and finding the antilogarithm
- Solve real-life multiplication and division problems efficiently using logarithms

- Determine logarithms of numbers, add them to perform multiplication, and find the antilogarithm of the sum
- Determine logarithms, subtract them to perform division, and find the antilogarithm of the difference
- Arrange solutions in a table format

How do logarithms simplify multiplication and division?

- Master Core Mathematics Grade 10 pg. 35
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers and roots using logarithms

By the end of the lesson, the learner should be able to:

- Use logarithms to evaluate powers and roots of numbers
- Multiply or divide logarithms by the index to find powers or roots
- Use logarithms to solve real-life problems involving squares, cubes, and roots

- Determine the logarithm of a number and multiply by the power to evaluate squares and cubes
- Divide the logarithm by the root order to evaluate square and cube roots
- Make the bar characteristic exactly divisible when dividing logarithms with bar notation

How do logarithms help in finding powers and roots of numbers?

- Master Core Mathematics Grade 10 pg. 37
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations using logarithms

By the end of the lesson, the learner should be able to:

- Use logarithms to evaluate expressions involving combined operations of multiplication, division, powers, and roots
- Organise logarithmic computations systematically in a table format
- Apply logarithms to solve complex real-life calculations involving multiple operations

- Add logarithms of the numerator and denominator separately
- Subtract the sum of denominator logarithms from the sum of numerator logarithms
- Find the antilogarithm of the result to obtain the final answer

How do we use logarithms to evaluate complex expressions?

- Master Core Mathematics Grade 10 pg. 38
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations using logarithms

By the end of the lesson, the learner should be able to:

- Use logarithms to evaluate expressions involving combined operations of multiplication, division, powers, and roots
- Organise logarithmic computations systematically in a table format
- Apply logarithms to solve complex real-life calculations involving multiple operations

- Add logarithms of the numerator and denominator separately
- Subtract the sum of denominator logarithms from the sum of numerator logarithms
- Find the antilogarithm of the result to obtain the final answer

How do we use logarithms to evaluate complex expressions?

- Master Core Mathematics Grade 10 pg. 38
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic expressions
Quadratic Expressions and Equations - Quadratic identities (a+b)² and (a−b)²

By the end of the lesson, the learner should be able to:

- Define a quadratic expression and identify its terms
- Expand and simplify products of two binomials to form quadratic expressions
- Relate quadratic expressions to real-life measurements such as areas of desks, tiles, and rooms

- Measure the sides of a desk and express the area in terms of a variable x
- Expand expressions such as (x+3)(x+5) and (2x−1)(x−3) by multiplying each term
- Identify the quadratic term, linear term, and constant term in the expansion

How do we form quadratic expressions from given factors?

- Master Core Mathematics Grade 10 pg. 40
- Rulers
- Master Core Mathematics Grade 10 pg. 43
- Rulers
- Graph papers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Difference of two squares identity and numerical applications

By the end of the lesson, the learner should be able to:

- Derive the identity (a+b)(a−b) = a²−b² using the concept of area of a rectangle
- Apply quadratic identities to evaluate numerical expressions mentally
- Use identities to quickly calculate areas of ranch lands, gardens, and metal plates

- Draw a rectangle with sides (a+b) and (a−b) and derive the difference of two squares
- Use identities to evaluate numerical squares such as 25², 82², and products like 1024 × 976
- Compare results with calculator answers

How do quadratic identities make numerical calculations easier?

- Master Core Mathematics Grade 10 pg. 44
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:

- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation