Maths curriculum in Polish lower-secondary school Comenius Why Maths?

1. Maths curriculum in Polish
lower-secondary school
GIMNAZJUM IM. ANNY WAZÓWNY, GOLUB-DOBRZYŃ

2. Class 1 ( 13-14 years old) Class 2 ( 14-15 years old) Class 3 ( 15-16 years old)
Arithmetic Arithmetic Arithmetic
1. Rational numbers - repetition from the 1. Indices and roots 1. Real numbers - operations and their
primary school a) positive, negative and zero indices properties - repetition
a) natural numbers (multiples, factors, and the index laws for multiplication 2. Operations on real numbers - repetition
common factors, highest common and division of positive integer
factors, lowest common multiples powers,
and primes) b) laws of indices
b) integers a) standard index form,
c) fraction and decimals 2. Roots
d) rounding off a) square and cube roots
2. Percentages b) simplifying roots, adding and
a) expressing percentage as a fraction or subtracting square roots, multiplying
decimal roots, dividing by square/cube roots,
b) expressing one quantity as a c) basic rule of radicals: roots/surds -
percentage of another irrational numbers
c) increasing/decreasing a quantity by a d) rationalisation of denominators ( type
given percentage reverse percentages a a d
d) problems involving percentages of ,
b c b c
quantities and percentage increases
or decreases;
e) problems involving, e.g., mobile
phone tariffs, currency transactions,
shopping, VAT, discount, simple
interest
Algebra Algebra Algebra
1. Algebraic expressions 1. Algebraic expressions 1. Functions
a) monomials, binomials and a) expanding the product of two linear a) the intuitive concepts of functions,
polynomials expressions including squaring a domains and co-domains, range,
b) translation of simple real-world linear expression independent and dependent variables
situations into algebraic expressions b) multiply expressions of the form e.g.: b) the notation of functions and use
c) collecting like terms, simplifying (ax + b)(cx + d) tabular, algebraic and graphical
expressions, substituting, (ax + b)( cx2+ dx + e) methods to represent functions

3. d) simplifying polynomial expressions c) multiplication of polynomials a) simple linear functions and plot the
by adding, subtracting, and d) use of special products: corresponding graphs arising from
multiplying (a ± b)2 = a2 ± 2ab + b2 real-life problems;
e) multiplying a single term over a a2 − b2 = (a + b)(a − b) b) zeros of functions,
bracket, f) rationalisation of denominators c) determine y-intercept and x-intercept
f) taking out single term common
( types a a b c d) plot graphs of simple quadratic
factors, , )
b c d  e functions y = ax2 + b, y = a
g) rearrange formulae 2. Linear simultaneous equations - x
2. Linear equations and inequalities algebraic methods 2. Linear functions
a) linear equations in one unknown, a) the substitution method a) Linear simultaneous equations -
with integer or fractional coefficients b) the elimination method. graphical method
b) formulate a linear equation in one c) find the exact solution of two b) interpreting and finding the equation
unknown to solve problems simultaneous equations in two of a straight line graph in the form
c) solve simple linear inequalities in unknowns by eliminating a variable, y = mx + c
one variable, and represent the and interpret the equations as lines c) condition for two lines to be
solution set on a number line and their common solution as the parallel or perpendicuar
d) types of intervals point of intersection d) finding the gradient of a straight
3. Direct and inverse proportion d) formulate a pair of linear equations in line given the coordinates of two
two unknowns to solve problems points on it
e) determine the equation of a line,
given its graph, the zero and y-
intercept, or two points on
the line.
3. Finding the exact solution of two
simultaneous equations in two
unknowns using determinants
4. System of three linear equations in
three variables
5. Absolute value and distance
Statistics and Probability
1. Finding, collecting and organising data
2. Representing data graphically and

4. numerically
3. Analysing, interpreting and drawing
conclusions from data
4. Mean, median, mode
5. Outcomes of simple random processes
a) Finding the probability of equally
likely outcomes - examples using
coins, dice, urns with different
coloured objects, playing cards,
Geometry Geometry Geometry
1. Basic figures - plane geometry 1. Circle 1. Similar figures
a) segments and lines a) centre, radius, chord, diameter, 2. Similarity of triangles
b) properties of angles at a point, angles circumference, tangent, arc, sector 3. Properties of similar polygons
on a straight line (including right and segment, tangent  corresponding angles are equal
angles), perpendicular lines, and b) circumferences of circles and areas  corresponding sides are proportional
opposite angles at a vertex - vertically enclosed by circles 4. Ratio of areas of similar plane figures
opposite angles c) arc length and sector area 5. Make and use scale drawings and
c) alternate angles and corresponding d) area of a segment interpret maps
angles e) symmetry properties of circles 6. Ratio of volumes of similar solids
2. Properties of triangles  the perpendicular bisector of a 7. Map scales (distance and area)
a) types of triangles chord passes through the centre 8. Theorem of Thales
b) segments in triangles (altitudes and  tangents from an external point 9. Pyramids
medians) are equal in length a) surface area of pyramids
c) angle properties of equilateral,  the line joining an external point b) draw simple nets of solids e.g. regular
isosceles and right-angled triangles to the centre of the circle bisects tetrahedron, square based pyramid,
d) the interior angles and exterior angle the angle between the tangents ect.
of a triangle f) angle properties of circles 10. Cylinder, cone and sphere
e) similarity of triangles (SSS, SAS, 2. Right triangles a) volume and surface area of cylinder,
ASA)and of other plane figures a) Theorem of Pythagoras cone and sphere
b) determining whether a triangle is 11. Trigonometric functions in right
3. Quadrilaterals right-angled given the lengths of triangles
a) properties of special types of three sides a) use of trigonometric ratios (sine,
quadrilateral, including square, a) equilateral triangle and its properties cosine and tangent) of acute

5. rectangle, parallelogram, trapezium (the formulas of the height and the angles to calculate unknown sides
and rhombus; area of an equilateral triangle) and angles in right-angled
b) classification of quadrilaterals by c) special right triangles - properties of triangles
their geometric properties sides in right triangles of 30°, 60°, 90° b) simple trigonometrical problems
4. Areas of triangles and quadrilaterals and of 45°, 45°, 90° in two and three dimensions
5. Angle sum of interior and exterior angles 3. Polygons and circles including angle between a line and
of any convex polygon b) use a straight edge and compasses to a plane
6. Cartesian coordinates in two dimensions construct: – the midpoint and
a) finding the length of a line segment perpendicular bisector of a line
given the coordinates of its end segment – the bisector of an angle
points c) properties of perpendicular bisectors
b) midpoint of line segment of line segments and angle bisectors
c) finding the area of simple rectilinear d) constructions: inscribed and
figure given its vertices circumscribed circles of a triangle,
7. Central symmetry and axial symmetry of and a tangent line to a circle from a
plane figures point outside a circle
8. Properties of perpendicular bisectors of e) inscribed and circumscribed circles of
line segments and angle bisectors a triangle
9. Construction of simple geometrical f) the radius of the inscribed circle and
figures from given data using compasses, circumscribed circle in an equilateral
ruler, set squares and protractors, where triangle/a right triangle
appropriate g) inscribed and circumscribed
quadrilaterals
h) inscribed and circumscribed
polygons
i) regular polygons
j) calculating the interior or exterior
angle of any regular polygon
k) inscribed and circumscribed
regular polygons
4. Polyhedra - prisms
a) surface area of cuboids and
(rigth)prisms

6. b) volumes cuboids and (rigth)prisms
c) draw simple nets of solids, e.g.
cuboid, triangular prism etc.
The topics in red are out of the curriculum but I am usually able to introduce these topics to my students because I prepare them to
different Maths contests.