Mathematics Scheme of work for SS 1 Federal

Education Research Centre (ERC), Federal Generation Mathematics Scheme of Work for SS 1. Set notation, Approximation – Schemeofwork.com

Table of Contents

GENERAL MATHEMATICS SS ONE FIRST TERM SCHEME GENERAL MATHEMATICS SS ONE SECOND TERM SCHEME GENERAL MATHEMATICS SS ONE THIRD TERM SCHEME

GENERAL MATHEMATICS SS ONE FIRST TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	NUMBER BASES (I) i. Decimal base (Base 10) and other bases e.g. base 2(binary) base 7 (days of the week) etc. ii. Conversion from Base 10 to other bases, conversion from other bases to base 10.	Teacher: i. Guides students to realize other bases other than binary (base 2) and denary (base 10) ii. Guides students to convert the following: one base to the other, are numbers with decimal fraction to base 10. Students: Mention other base such as 4, base 5(quandary), base 8(octal) base 16 (Hexadecimal). Convert decimal fractions to base 10 and one base to another base. Instructional Resources: Charts showing the conversion from one base (except base 2) to another base.
2	NUMBER BASES (II) i. Problem solving, addition, subtraction, multiplication and division of number in the various bases. ii. Conversion of decimal fraction in one base to base 10. iii. Apply number base system to computer programming.	Teacher: Guides students to perform mathematical operations of: addition, subtraction, multiplication and division. Students: Perform the mathematical operations. Instructional Resources: As in week one above.
3	MODULAR ARITHMETIC i. Revision of addition, division, multiplication and subtraction of integers. ii. Concept of modular arithmetic iii. Addition, subtraction and multiplication operations in modular arithmetic. iv. Application to real life situations.	Teacher: Guides students to revise the mathematical operations of integers -to define modular arithmetic and uses activities to develop the concept. – To add, subtract, divide and multiply in modular arithmetic. – To appreciate its application to shift duty, menstrual chart, name of market days. Students: -Define modular arithmetic -Perform the mathematical operations in modular arithmetic -Appreciate the concept of modular arithmetic and apply in daily life. Instructional Resources: Modular arithmetic charts, samples of shift duty chart, menstrual chart.
4	INDICES i. Laws of indices and their applications e.g. a. a^x x a^y = a^x+y b. a^x/a^y = a^x-y c. (a^x)^y = a^xy ii. Application of indices, simple indicial/exponential equations.	Teacher: Guides students to represent numbers in indices and gives examples. Explains laws of indices with examples, drill students on problem solving. Students: -Study the laws of indices and solve related problems. -Study the steps in indicial equation and solve exercises.
5	STANDARD FORM (AX10ⁿ) i. Writing numbers in index form ii. Adding two numbers and writing the results in standard form. iii. Subtracting one number from the other in standard form. iv. Multiplying numbers in standard form v. Dividing numbers in standard form including square root of such numbers.	Teacher: Guides students to convert numbers to standard form with emphasis on the values of ‘A’ and ‘n’. Students: -Convert numbers to standard form -Convert long hand to short hand notation. (i.e. ordinary form to standard form and standard form to ordinary form) Instructional Resources: Charts of standard form and indices.
6	LOGARITHMS (I) i. Deducing logarithm from indices and standard form i.e. if y=10^x, then x=log_y10 ii. Definition of logarithm e.g. log₁₀1000=3 iii. Graph of y=10^x using x=0.1, 0.2,………..	Teacher: Guides students to learn logarithm as inverse of indices with examples. -Define logarithm and find the various values of expressions like log_aN -plot the graph of y=10^x and read the required values. -to find logarithm of a number (characteristics, mantissa, differences and locate decimal points) and the antilogarithm. Students: Deduce the relationship between indices and logarithms. Define logarithm and find the various values of expressions like log_aN numbers plot the graph of y=10^x. Find the logarithm and antilogarithm of numbers greater than 1. Instructional Resources: Indices/logarithms chart, definition chart of logarithm, graph board with graph of y=10^x, graph book etc.
7	LOGARITHM (II) Calculations involving multiplication and division.	Teacher: Guides students to read logarithm and antilogarithm table in calculation involving multiplication and division. Students: Read the tables and solve problems involving multiplication and division. Instructional Resources: Logarithm table chart and Antilogarithm table chart made of flex banner logarithm table booklet.
8	LOGARITHM (III) i. Calculations involving power and roots using the logarithm tables. ii. Solving practical problems using logarithm tables relating to capital market. iii. Explain the concept of capital market operation iv. Use logarithm tables in multiplying the large numbers involved in capital market operation.	Teacher: -Guides students to read logarithm and antilogarithm tables in calculations involving powers and roots. -Explain meaning of capital market. -Solve related problems and other real life problems. Students: Read the tables and solve problems involving multiplication and division, and solve problems related to real life problems. Instructional Resources: Logarithm tables chart, logarithm table booklet etc.
9	DEFINITION OF SETS i. Set notation – listing or roster method, rule method, set builder notation ii. Types of sets: e.g. universal set, empty set, finite set and infinite set, subset, disjoint set, power set etc.	Teacher: Guides students to: -define set -define types of sets -write down set notations -use the objects in the classroom, around the school and within home to illustrate sets. Students: Define set, use set notations Identify types of sets. Instructional Resources: Objects in the classroom, sets of students, set of chairs, mathematical sets, other instrument etc.
10	SET OPERATIONS i. Union of sets and intersection of sets complement of sets. ii. Venn diagram iii. Venn diagram and application up to 3 set, problems	Teacher: Guides students to explain and carry out set operations: -explains Venn diagram, draws, interprets and uses diagram. -applies Venn diagram to real life problems. Students: Carry out set operations, draw, interpret and use Venn diagrams. Instructional Resources: As in week nine above.
11	SIMPLE EQUATIONS i. Change of subject of formulae ii. Formula involving brackets, roots and powers. iii. Subject of formula and substitution.	Teacher: Guides students in the process involved in changing the subject in a formula and carries out substitution. Students: Follow the process involved in changing subject in a formula and substitute in the formula. Instructional Resources: Charts displaying processes involved in change of subject in a formula. Charts displaying the various types.
12	SIMPLE EQUATION AND VARIATIONS i. Revision of simultaneous linear equation in two (2) unknown ii. Types and application of variations.	Teacher: Revises solution of simultaneous equations in two unknowns. Treats each type of variation with examples and solve problems in variation. Students: Solve problems involving all types of variations. Instructional Resource s: As in week 11 above.
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14	Examinations

Education Research Centre (ERC), Federal Generation Mathematics Scheme of Work for SS 1. Definition o – Schemeofwork.com

GENERAL MATHEMATICS SS ONE SECOND TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	FACTORISATION OF QUADRATIC EXPRESSION OF THE FORM ax²+bx+c where a, b, c are constants i. Factorising quadratic expression of the form ax²+bx+c ii. Factorising quadratic expression of the form ax²-bx+c iii. Factorising quadratic expressions of the form ax²+bx-c iv. Factorising quadratic expressions of the form ax²-bx-c v. Solving quadratic equation of the form ax²+bx+c = 0 using factorization method.	Teacher: i. Illustrates the factorization of quadratic expressions using: (a) Grouping (b). factor methods ii. Teacher leads students to factorize quadratic expressions written in the different forms. Students: -Factorize quadratic expressions using the methods. -Factorize the different forms given. Instructional Resources: Quadratic expressions and factors chart. Sharing at least six expressions each of the form ax²+bx+c, ax²-bx+c, ax²+bx-c and ax²-bx-c (could be in flex banners).
2	APPROXIMATION i. Rounding up and rounding down of numbers to significant figures, decimal places and nearest whole numbers. ii. Application of approximation to everyday life iii. Percentage error.	Teacher: Gives students two roots and leads them to form a quadratic equation. Students: Use the roots given to construct quadratic equation. Instructional Resources: Given values, in integer and fractions incomplete table showing various numbers and approximation to various significant figures, decimal places etc. to be completed in class as illustration
3	QUADRATIC EQUATIONS(III) i. Plotting graph in which one is quadratic function and one is a linear function. ii. Using an already plotted curve to find the solution of the various equations. iii. Finding the gradient of a curve, the maximum value of y, and minimum value of y and the corresponding values of x. iv. Solving a comprehensive quadratic and linear equation graphically. v. Word problem leading to quadratic equations.	Teacher: – Leads students to construct tables of values, draws the x and y axis, chooses scale, graduates the axis and plot the points. – Leads students to observe where the quadratic curve crosses the axis and write down the roots of the equation. – Identifies the maximum and minimum values. Students: – Follow the teacher lead in plotting the graph – Follow the teacher leads and read the roots. – Read the minimum and maximum values. Instructional Resources: Graph boards, graph books are mandatory.
4	LOGICAL REASONING (I) i. Meaning of simple statement – open and close statements, true or false. ii. Negation of simple statements iii. Compound statements – conjunctions, disconjunctions, implication, bi-implication with examples.	Teacher: Uses examples to explain simple statements.State the true value of a statementStates simple statements and writes not or “it is not true that” a negation of simple statements.Guides students to write examples of compound statements and distinguishes them from simple statements. Students: i. Gives examples of the non examples of simple statements writes the true value of a given statements. ii. Negates some simple statement using ‘not’ or ‘it is not true that’. iii. Write examples of compound statements. Instructional Resources: Charts showing examples of simple statement, true and false statements, negation of statements.
5	LOGICAL REASONING (II) i. Logical operations and symbols – Truth value table – compound statement, Negation (NA), conditional statement, bin-conditional statement.	Teacher: Leads students to list the five logical operations and their symbols. -Leads students to construct truth value for each operation. Students: List the five logical operations with symbols and construct truth value chart for each. Instructional Resources: Truth table chart etc.
6	MENSURATION OF SOLID SHAPES (I) i. Length of arc of a circle with practical demonstration, using formula ii. Revision of plane shapes – perimeter of sector and segment iii. Area of sector and segment.	Teacher: Guides students to find the length of arcs of circle using cut card board practically, deduces the formula and apply it in solving problems. -cuts out sectors and segment, solve exercises. -guides students to cut a circle into sectors and measure the angles. -cut out triangle from a sector. Students: Practice the practical demonstration. Participate in deducing the formula and apply it to solve problems carry out teacher activities. Follow the teacher instruction to carry out the activities. Instructional Resources: Cardboard paper, rope, string, scissors, drawings on cardboard showing various arcs (minor and major arcs in a circle).
7	MENSURATION OF SOLID SHAPES (II) i. Relationship between the sector of a circle and the surface area of a cone. ii. Surface area of solids – cube, cuboids, cylinder, cone, prism, pyramids.	Teacher: -Guides students to cut out a sector and folding sector into a cone. -Leads students to determine the relationship between the sector of a circle and the surface area of a cone. -Revise the areas of the plane shapes that formed the listed solids and lead students to find their surface areas. Students: -Follow the teacher in carrying out the activities and observe the relationships -Participate in the revision of the areas of the solids. Instructional Resources: Cut out papers, (sectors and segments) etc.
8	MENSURATION OF SOLID SHAPES (III) i. Volume of solids – cube, cuboids, cylinder, cone, prism, pyramids, frustum of cone and pyramids. ii. Surface area and volume of compound shapes.	Teacher: -Revise the area of the listed solids and lead students to find their volumes. – show model of fraction of cones pyramids and solve problems. -Lead students to solve problems on surface area and volume of compound shapes. Students: Participate in the revision of the areas and volume of the solids. -Solve problems on compound shapes. Instructional Resources: Shapes of cube, cuboids, cylinder, cone, prism, pyramids, lampshade and buckets as frustum as cone etc.
9	CONSTRUCTION (I) i. Lines, line segments, bisection of a line segment e.g. horizontal, vertical, inclined lines etc. ii. Construction and bisection of angles e.g. 180^o, 90^o, 45^o, 22^o, 60^o, 30^o, 150^o, 75^o, 135^o, 105^o, 165⁰ etc. iii. Construction of triangles iv. Construction of quadrilaterals.	Teacher: -Lists out steps for drawing a line segment and how to bisect line segment. -Leads students to construct special angles with the steps involved in bisection of angles. Inspect them. Students: List out triangle, draw a line and bisect, construct the given angles and bisect them. Instructional Resources Whiteboard, mathematical set, students mathematical set. Teacher’s construction instruments mandatory.
10	LOCUS OF MOVING POINTS i. Equidistant from 2 intersecting straight lines ii. Equidistant from 2 points iii. Equidistant from a fixed point etc. iv. Construction of locus equidistant from a given straight line.	Teacher: Guides students to list and explain the steps involved in constructing locus of moving points equidistance from: Two intersecting straight lines Two given points One pointA given straight line on the chalkboard using chalkboard mathematical set . Inspects students constructing. Students: -Attempts to list and explain the steps involved, write down the steps listed and explained by the teacher and ask questions. – Follow teacher’s demonstration on the chalkboard by carrying out similar activities in their exercise book with their mathematical sets. – Participate in the teacher’s re-demonstration and take special notes of the salient steps. Instructional materials: As shown in week 9
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12	Examinations	Examinations

Education Research Centre (ERC), Federal Generation Mathematics Scheme of Work for SS 1 – Schemeofwork.com

GENERAL MATHEMATICS SS ONE THIRD TERM SCHEME

WEEK	TOPIC / CONTENT	ACTIVITIES
1	DEDUCTIVE PROOFS (I) i. Types and properties of triangles ii. Proofs of sum of angles in a triangle is 180^o, the exterior angles is equal to the sum of its two interior opposite angles.	Teacher: – Leads students to explain the format for carrying out proofs in geometry, by explaining the concepts of: given, required to prove, construction, proof, conclusion. – Guides the students to prove the two theorems on the board with necessary diagrams. – Assists students to carryout practical demonstrations, and to solve examples and give students some task to solve and inspect them. Students: Participate in discussing the format for proving geometrical theorem, take special note of the format, then write them down and ask questions. -Solve the task given. Instructional Resources: Cardboard paper, cutout of triangles, protractor to verify and establish the truth about the theorem.
2	DEDUCTIVE PROOFS (II) i. Similar and congruent triangles ii. Isosceles and equilateral triangles.	Teacher: Demonstrates on the chalkboard how to prove the followings: Angles of parallel lines, angles in a polygon, congruent triangles, properties of parallelogram, deductive reasoning and axioms using relevant models of plane shapes. Students: Participate in the teacher’s demonstrations by contributing in making some deductions and write down essential points agreed upon, on angles of a polygon, congruent triangles. etc. Instructional Resources: Parallel lines, congruent triangles, polygons, cut out paper, protractors.
3	DEDUCTIVE PROOFS (III) i. Properties of parallelogram and related quadrilaterals. ii. Intercept theorem iii. Parallelogram of the same base and between the same parallel lines are equal in area.	Teacher: – Leads students to demonstrate the properties of the riders using paper cutouts, protractors, models of parallelogram, polygon, congruent triangle etc. – Guides students to solve problems and help them to reproduce arguments based on the reasons (theorem or axioms). Students: Carry out practical demonstration of the properties of the rides along with the teacher using paper cutouts, construct models of plane shapes. Apply deductive reasoning to solve the given practical problems. Instructional Resources: As in week 2
4	POLYGON – TYPES i. Sum of interior angles of any n-sided polygon. ii. Sum of exterior angles of any polygon iii. Problem solving on polygon.	Teacher: As in week 2 and 3 above. Students: As in week 2 and 3 above Instructional Resources: As in week 2 and 3 above.
5	TRIGONOMETRY (I) i. Basic trigonometric ratios, sine, cosine and tangent with respect to right-angled triangles. ii. Trigonometric ratio of special angles 30^o, 45^o, 60^o. iii. Deriving trigonometric ratios of 30^o, 45^o, 60^o.	Teacher: – Shows students a chart of right angled-triangle with a clearly marked angle. – Guides students to identify ratios forming sine, cosine and tangent of the marked angles. (verify the position of the marked angles) – Lead students to construct right angled-triangles of 30^o, 45^o, 60^o. – Guides students to use the above shapes to derive trigonometric ratios of 30^o, 45^o, 60^o. Students: Study the chart; identify ratios forming cosine and tangent of marked angle on the chart. Draw right-angled triangles and use it to solve problem involving calculation of lengths, construct right-angled triangles of 30^o, 45^o and 60^o. Derive trigonometric ratios of 30^o, 45^o and 60^o under teacher’s supervision. Instructional Resources: Charts showing trigonometric ratios of a right angled triangle, pencil and ruler, protractor, cutout shapes of right angled triangles showing angles 45^o, 30^o and 60^o respectively.
6	TRIGONOMETRY (II) i. Solving problems involving use of sine, cosine and tangent at right-angled triangles. ii. Application of trigonometric ratios of 45^o, 30^o and 60^o to solving problem without the use of calculating aids.	Teacher: i. Guides students to use sine, cosine and tangents to solve problems involving calculation of length, angles, angles of elevation and depression etc. ii. Leads students to draw right-angled triangle of side 1 unit on the equal sides. iii. Guides students on how to derive trigonometric of ratio. iv. Leads students to measure the two other angles in the right angled triangle. v. Lead students to obtain sine and cosines of various angles using measured lengths. Students: Solve problems on practical application of trigonometric ratios under guidance of teacher. Obtain sine and cosine of various angles. Identify the relationship between the trigonometric ratios and the measured values. Instructional Resources: Chart showing unit circle etc.
7	TRIGONOMETRY (III) Trigonometric ratios related to the unit circle i. Draw graphs of sine from 0^o ≤ ө ≤ 360^o ii. Draw graphs of cosine from 0^o≤ ө ≤ 360^o	Teacher: Guides them to see the relationship between calculated sine and cosine of trigonometric ratios and the angles measured with protractor in the unit circles. Constructs table of values for 0^o ≤ ө ≤ 360^o fie both sine and cosine, plots the points on the graph board and draw the graphs. Guides them on the activities to obtain accurate values. Leads them to obtain solution from graph drawn. Students: Participates in the construction of table of value for y and plotting of the points and drawing of the graph. Instructional Resources: Graph board, graph book, pencils, and mathematical sets. Mandatory.
8	STATISTICS i. Revision on collection, tabulation and presentation of data. ii. Construction of frequency tables iii. Bar charts and histogram differentiate between bar chat and histogram.	Teacher: Guides students to: -information on their age, number of children in the families and other areas of life. -tabulates data collected -lists various forms of presentation of data e.g. bar chart, pie chart. -leads students to construct table from given data; draw bar chart and histogram. Students: Submit objects like corks brought to class. Tabulate into specific categories, list various of presentation of dates, table from given data. Draw bar chart and histogram. Instructional Resources: Ages of students recorded on cardboard, prices of goods, objects of different kinds. Corks of soft drinks, posters containing real life data. Graph board, graph book.
9	STATISTICS (II) i. Calculating the sectoral component of pie chart. ii. Drawing pie chart correctly. iii. Interpreting the pie chart and bar chart.	Teacher: Leads students to calculate the angular equivalent of the different frequency in a given distribution using the idea of ratio and proportion. Guides students to draw pie chart using their compass, and protractor. Interpret the pie chart in terms of sectoral angles. Students: Calculate sectoral angles, draw pie charts, correctly to interpret data using the pie chart. Instructional Resources: Graph board, graph papers, a pair of compass and protractor etc.
10	STATISTICS (III) GROUPED DATA i. Drawing histogram ii. Estimation of mode from histogram.	Teacher: Guides students to use frequency table to draw histogram. Leads students to construct table from given data, construct group frequency table. Guides students to use class boundaries to draw histogram and how to read or estimate mode from the histogram. Students: Participate in the activities with the teacher, perform the instructions given by the teacher. Draw histogram and estimate mode from the histogram. Construct frequency table of a grouped data. Instructional Resources: Graph board, graph papers etc.
11	STATISTICS (III) Construction of frequency polygon of a given distribution.	Teacher: Guide the students to construct frequency polygon of a given distribution. Students: Construct frequency polygon from a grouped data. Instructional Resources: Graph board, graph papers etc.
12	Revision	Revision
13	Examinations	Examinations