# Mathematics Guides for SS 1 Algebraic Processes – Logical Reasoning and Quadratic Equation

**MATHEMATICS **

**THEME – ALGEBRAIC PROCESSES **

**TOPIC 1 – LOGICAL REASONING **

**INSTRUCTIONAL MATERIALS**

1. Charts showing examples of simple statements, true or false statements, and negation of statements.

2. Charts showing examples of compound statements, conjunctions, disjunction, implications and bi-implications.

3. Truth table chart.

**LEARNING OBJECTIVES **

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

1. Give the meaning of simple statements, with examples.

2. Identify true or false statements.

3. State the negation of a statement.

4. Distinguish between simple and compound statements.

5. Gives examples of conjunction, disjunction, implication and bi-implication.

6. List the five logical operators and their symbols.

7. Write the truth value of a compound statement involving any of the five logical operators.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Simple statements.

2. Meaning of simple statements:

- True or False

- Negation of simple statements
3. Compound statements:

- Meaning

- Conjuctions

- Disjunctions

- Implication

- Bi-implication
4. Logical operators and symbols.

- Negation

- Conjunction

- Disjunction

- Conditional

- Bi-conditional

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Uses examples to explain simple statements or propositions as either true or false, but not both.

2. Leads the students to state the truth value of a statement.

3. Makes simple statements and states their truth values and guides them to write “not” or “it is not true that”.

4. Gives students a collection of simple and compound statements and guides them to distinguish them.

5. Gives students a collection of conjunction, disjunction, implications and bi-implications, and guides them to distinguish them.

6. Leads students to construct the truth table chart for each of the five logical operations, that is:

- Negation (NA)

- Conjunction (A&B)

- Disjunction (AVB)

- Conditional (A = B)

- Bi-conditional (A = B).

STUDENT’S ACTIVITIESStudents,

1. Give examples and non-examples of simple statements.

2. Write the truth value of a given statement.

3. Negate some given simple statements using “not” or “it is not true that”.

4. Write examples of compound statements, conjunction, disjunction, implications and bi-implications.

5. Construct the truth table chart for each of the five logical operations.

**LESSON EVALUATION**

Students to,

1. Give examples and non-examples of simple statements.

2. Write the truth value of a given statement.

3. Negate some given simple statements using “not” or “it is not true that”.

4. Write examples of compound statements, conjuctions, disjunctions, implications and bi-implications.

5. Construct the truth table chart for each of the five logical operations.

**MATHEMATICS **

**THEME – ALGEBRAIC PROCESSES **

**TOPIC 2 – QUADRATIC EQUATIONS**

**INSTRUCTIONAL MATERIALS**

1. Quadratic expression factors chart

2. Quadratic equation box

3. Factor chart

4. Quadratic equation chart

5. Roots of quadratic equation chart

6. Graph board

7. Graph books

8. Broomstick and French curves

9. Relevant computer assisted instruction (CAI)

10. Graph board

11. Graph books

**LEARNING OBJECTIVES **

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

1. Solve problems involving factorization of quadratiexpressions

2. Solve quadratic equations of the form ab = 0, a or b = 0

3. Form quadratic equations with given roots.

4. Draw quadratic equation graphs.

5. Read and obtain roots from a quadratic graph.

6. Solve word problems involving real life situations.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS **

1. Revision of factorization of quadratic expressions.

2. Solution of quadratic equation of the form – ab = 0, a = 0 or b = 0.

3. Formation of quadratic equations with given roots.

4. Drawing quadratic equation graphs.

5. Obtain roots from a quadratic graph.

6. Application of quadratic equations to real life situations.

**LESSON PRESENTATION**

TEACHER’S ACTIVITIESTeacher,

1. Illustrates the factorization of quadratic expressions.

2. Leads the students to factorize the quadratic expressions thoroughly using,

- grouping method

- factor methobr
3. Leads the students to solve quadratic equatioof the form – ab = 0, a = 0 or b = 0

4. Guides the students in further illustration of factorisation using quadratic box and consequently leads them to solve the equation.

5. Gives students two roots and leads them to use the roots to form a quadratic equation.

6. Guides the students to form more quadratic equations with given roots.

7. Displays the roots of quadratic equation chart.

8. Leads students to construct tables of values.

9. Leads students to draw the X and Y axes, choose the scales and graduate the axes.

10. Guides the students to plot the points using a graph board.

11. Leads the students to join the points using a smooth curve.

12. Guides students to observe where the quadratic curve crosses the axis.

13. Guides students to write down the roots of the equation.

14. Leads students to solve problems on quadratic equations such as – Treasure and AyanfeOluwa contribute equal amounts in a cash group. The square of Treasury’s contribution amounts to N15.00. How much has each of them contributed?

STUDENT’S ACTIVITIESStudents,

1. Demonstrate the factorization of a quadratic expression.

2. Factorize quadratic expressions using the grouping methoand factor method

3. Solve quadratic equation using the factor method – ab = 0, then either a = 0 b.

4. Use quadr box to illustrate factorisation and thus solve the equations.

5. Observe the roots of quadratic equation chart.

6. Use the given roots to construct quadratic equations.

7. Construct more quadratic equations with given roots.

8. Construct tables of values.

9. Draw the X and Y axes, choose the scales and graduate the axes.

10. Plot the points using a graph board.

11. Join the points using a smooth curve.

12. Study the graph plotted in the previous class.

13. Locate where the curve crosses the axis.

14. Read the roots of the equation.

15. Solve problems on quadratic equations involving real life situations.

**LESSON EVALUATION**

Students to,

1. Factorize givenquadratic expression.

2. Solve given quadratiequation.

3.Construct quadratic equations with roots.

4. Construct a table of values.

5. Draw the graph of a given quadratic equation.

6. Read and obtain the roots of a quadratic graph.

7. Solve word problems involving real life situations.