# Mathematics Guides for SS 1 Number and Numeration – Indices, Logarithm, Modular Arithmetic, Sets and Simple Equations and Variations

Indices, Logarithm, Modular Arithmetic, Sets and Simple Equations and Variations

**MATHEMATICS **

**THEME – NUMBER AND NUMERATION**

**TOPIC 1 – INDICES **

**INSTRUCTIONAL MATERIALS**

Charts of:

1. Standard form

2. Laws of indices.

3. Solution chart on indical equations.

**LEARNING OBJECTIVES **

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

Solve problems on standard form.

2. Represent indices and give examples using standard notations and

3. Identify indices as a shorthand notation.

4. State the laws of indices and solve problems on indices.

5. Solve problems of indicial equations.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Revision of standard form.

2. Introduce indices and examples.

3. Laws of indices

4. Application of indices, simple indical equations.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Guides students to convert numbers to standard form.

2. Guides students to represent numbers in indices.

3. Gives examples of indices.

4. Guides students to relate to indices.

5. Explains the laws of indices.

6. Illustrates with examples to show that the laws hold.

8. Drills students further on calculations involving laws of indices.

9. Shows the solution chart.

10. Drills students on problem solving.

11. Leads students to solve more problems.

STUDENT’S ACTIVITIESStudents,

1. Convert numbers to standard form.

2. Identify indices an give your own examples.

3. Relate indices to standard form.

4. Study the chart.

5. Deduce the relationship between shorthand and longhand notation of indices.

6. Convert longhand to shorthand notation.

7. Study the chart of laws of indices.

8. Study the laws of indices and deduce their meanings, and give your own examples.

9. Do more examples on the laws of indices.

10. State the laws of indices.

11. Study the chart.

12. Study the steps in solving indicial equations.

13. Solve examples on indical equations with the teacher.

**LESSON EVALUATION**

Students to,

1. Convert numbers to standard form.

2. Represent numbers in indices and give more examples of indices.

3. Relate indices to standard form of numbers.

4. Solve problems on indices.

5. Solve problems on indical equations.

**MATHEMATICS **

**THEME – NUMBER AND NUMERATION **

**TOPIC 2 – LOGARITHMS **

**INSTRUCTIONAL MATERIALS**

1. Indices/logarithm chart.

2. Definition chart of logarithm.

3. Graph board with graph of y = 10.

4. Graph book.

5. Logarithm table chart.

6. Antilogarithm table chart.

7. Logarithm table booklet.

8. Newspaper daily stock summary.

**LEARNING OBJECTIVES **

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

1. Explain and deduce the relationship between indices and logarithms.

2. Define logarithm.

3. Use the graph of y = 10x for multiplication and division.

4. Find logarithms and anti – logarithms of numbers greater than one.

5. Use logarithm tables in calculation.

6. Use log tables to solve problems relating to capital market.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Deducing logarithms from indices and standard form.

2. Definition of logarithm.

3. Graph of y = 10x.

4. Reading of logarithm and the antilogarithm tables.

5. Use of logarithm table in calculation, (division, powers and roots).

6. Application of logarithms in capital market and other real life problems.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Shows the indices/logarithm chart.

2. Guides the students to learn logarithm as inverse of indices i.e. if y = 10^x, then x = log10y

3. Gives more examples of logarithms as inverse of indices.

4. Shows the definition chart of logarithm.

5. Guides students to define logarithm.

6. Guides students to find the logarithm of numbers in base 10, e.g. log101000 = 3.

7. Shows the graph of y = 10x on a graph board.

8. Leads the students to prepare the table of values for log10 y.

9. Guides students to plot the graph of y = 10^x.

10. Guides students to read values of x when y values are given.

11. Hangs a base 10 logarithm chart and shows a base 10 logarithm table booklet.

12. Guides students to draw tables (rows and columns) in preparation for calculation.

13. Guides students to find logarithm of a number (characteristics, mantissa differences).

14. Guides students to locate decimal points.

15. Guides students to find the logarithms and anti – logarithms of numbers greater than one.

16. Guides students to review the laws of logarithm.

17. Guides students to read base 10 logarithm and antilogarithm table in calculations involving multiplication, division, powers and roots.

18. Guides students to explain the meaning of capital market.

19. Guides students to solve related problems in secondary market transaction, e.g. 37, 896 shares of T-Bank traded on the floor of the stock exchange in 21 deals at ₦127.56 per share. How much are the deals worth?

STUDENT’S ACTIVITIESStudents,

1. Study the chart.

2. Deduce the relationship between indices and logarithms.

3. Convert indices to logarithms.

4. Study the definition of logarithm.

5. Define logarithm.

6. Find the logarithm of given numbers.

7. Study the graph of y = 10^x.

8. Prepare the table of values for y = 10^x..

9. Plot the graph of y = 10^x.

10. Rea the values of x when y values are given, and vice versa.

11. Study the base 10 logarithm table chart and compare with logarithm table booklet.

12. Draw tables for calculation.

13. Ask questions about characteristics, mantissa and differences. Also identify characteristics and mantissa.

14. Locate decimal points.

15. Find the logarithms and anti – logarithms of numbers greater than one.

16. Study the logarithm table chart and logarithm table booklet.

17. Asks questions about laws of logarithms.

18. Read logarithm and antilogarithm of numbers and solve problems involving multiplication, division, powers and roots.

19. Explain the meaning of capital market.

20. Solve problems relating to the capital market and other real life problems.

**LESSON EVALUATION**

Students to,

1. Indices/logarithm chart.

2. Definition chart of logarithm.

3. Graph board with graph of y = 10.

4. Graph book.

5. Logarithm table chart.

6. Antilogarithm table chart.

7. Logarithm table booklet.

8. Newspaper daily stock summary.

**MATHEMATICS **

**THEME – NUMBER AND NUMERATION **

**TOPIC 3 – MODULAR ARITHMETIC**

**INSTRUCTIONAL MATERIALS**

1. Modular arithmetic chart.

2. Samples of duty shift charts, menstrual charts, etc.

**LEARNING OBJECTIVES **

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

1. Recall and carry out the basic operations of addition, subtraction, multiplication.

2. Carry out the operations in modular arithmetic.

3. Apply modular arithmetic in daily life.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Revision of addition, subtraction, multiplication and division of integers

2. Concept of module arithmetic

3. Addition, subtraction and multiplication operations in module arithmetic

4. Application to daily life

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Guides students to revise addition, subtraction, multiplication and division of integers, and provides exercises on these concepts.

2. Guides students to define modular arithmetic, and uses activities to develop the concept.

3. Guides students to add, subtract, divide, and multiply in modular arithmetic.

4. Guides students to appreciate its application to duty shifts, name of market days, menstrual calculation in real life situations.

STUDENT’S ACTIVITIESStudents,

1. Define modular arithmetic.

2. Perform addition, subtraction, multiplication and division in modular arithmetic.

3. Appreciate and apply modular arithmetic to market days, duty shifts, menstrual calculations, and anniversaries.

**LESSON EVALUATION**

Students to,

1. Solve problems on addition of numbers in modular form.

2. Solve problems on

- subtraction

- multiplication

- division.

**MATHEMATICS **

**THEME – NUMBER NUMERATION **

**TOPIC 4 – NUMBER BASE SYSTEM**

**INSTRUCTIONAL MATERIALS**

1. Charts showing the conversion from one base (except base 2) to another base

2. Diennes blocks

**LEARNING OBJECTIVES **

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

1. Convert numbers from other bases to base 10.

2. Converdecimal fractions from other bases to base 10.

3. Convert from one base to another base.

4. Perform basic operations on number bases (with the exception of base 2).

5. Apply the number base system to

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Conversion from one base to base 10

2. Conversion of decimal fraction in one base to base 10

3. Conversion of numbers from one base to another base

4. Addition, subtraction, multiplication and division of number bases

5. Aplication to computer programming.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Guides students to realize other bases aside binary (base 2) and denary (base 10) such as quinary, cctal, etc.

2. Guides students to convert from:

- One base to base 10.

- Convert decimal fraction from one base to base 10.

- One base to another base (i.e. from base 5 to base 8, etc).
3. Guides students to perform the operations of:

- addition and subtraction

- multiplication and division.

STUDENT’S ACTIVITIESStudents,

1. Mention other bases aside binary (base 2) and denary (basic), such as Quinary (base 5), Octal (base 8), Hexadecimal (base 16), etc.

2. Convert numbers (except base 2) from one base to base 10.

- convert decimal fraction from one base to base 10.

- convert one base to another base.
3. Perform the operations of,

- addition and subtraction

- multiplication and division.

**LESSON EVALUATION**

Students to,

1. Convert numbers from other bases to base 10.

2. Solve problems involving addition, subtraction, division and multiplication of number bases.

**MATHEMATICS **

**THEME – NUMBER AND NUMERATION **

**TOPIC 5 – SETS **

**INSTRUCTIONAL MATERIALS**

1. Objects in the classroom

2. Sets of students

3. Sets of chairs

4. Mathematical sets, instruments, etc.

**LEARNING OBJECTIVES **

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

1. Define sets.

2. Us set notations.

3. Identify the types of sets.

4.Carry out set operations.

5. Draw, interpret and use venn diagrams.

6. Apply the use of venn diagrams in solving real life problems.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Definition of set.

2. Set notation – listing or roster method,

- rule method

- set builder notation.
3. Types of sets:

- empty sets

- finite and infinite sets

- universal sets.
4. Set operations:

- union

- intersection

- complement
5. Venn diagram and its application up to a 3 set problem.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Leads students to use objects in the classroom, around the school and within the home to illustrate sets.

2. Illustrates to the students the different methods of representing sets and their advantages or limitations.

3. Guides students to define empty sets and the methods of notation, finite and infinite sets with examples, and universal sets.

STUDENT’S ACTIVITIESStudent,

1. Study the objects in the classroom, around the school and ask questions about them.

2. Display sets of objects, use alternative methods to represent them.

3. Get sets of objects and use alternative methods to represent them.

**LESSON EVALUATION**

Students to,

1. Define sets.

2. Represent sets using listing or roster method, rule method, set builder notation.

3. Solve real life problems using venn diagrams.

**MATHEMATICS **

**THEME – NUMBER AND NUMERATION **

**TOPIC 6 – SIMPLE EQUATIONS AND VARIATIONS**

**INSTRUCTIONAL MATERIALS**

1. Charts displaying processes involved in the change of subject in a formula.

2. Charts displaying types of variation.

**LEARNING OBJECTIVES **

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

1. Change the subjects of a given equation.

2. Solve problems involving direct, inverse, joint and partial variations.

3. Apply variation to physical laws and real life situations.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Change of subject of formulae – formula involving brackets, roots and powers.

2. Subject of formula and substitution.

3. Types of variations

- direct

- inverse

- joint and partial
4. Application of variation.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Guides students to discover the process involved in changing the subject in a formula.

2. Guides students to carry out substitution in a formula.

3. Treats each type of variation with examples.

4. Solvs problems in variations. The application of variation to physical laws and real life situations.

STUDENT’S ACTIVITIESStudents,

1. Follow the process involved in changing the subject in a formula.

2. Carry out substitution in a formula and practice examples.

3. Solve problems involving all types of variations.

4. Apply variations to real life situations, especially physical laws.

**LESSON EVALUATION**

Students to,

1. Solve problems on the change of subject in a formula.

2. Solve problems involving substitution into a formula.

3. Solve problems on all types of variations.

4. Apply variation to solve problems involving real life situations.