23 mathematics experiments from grade 5 to grade 9: Numbers and calculation, Expressions, equations and inequalities, Functions and graphs, Plane geometry…
Sections
Numbers and calculation
Natural numbers, fractions, percentages, powers, methods of calculation
Prime numbers, HCF and LCM — Grade 7. Two buses leave at 12 and 18 minutes — when will they leave together again? What size of tile?
The number line: from −7 to √2 — Grade 7. −7 °C at night, +4 °C by day — what is the difference? Why can’t √2 be written exactly?
Powers: from folding to a formula — Grade 7. How thick is a sheet of paper folded 10 times? How many bacteria will there be by morning?
Roots: from squares to powers — Grade 8. What is the side of a square room with an area of 50 m²? Squares on a grid will not give it
Expressions, equations and inequalities
Expressions with letters, equations, inequalities, systems
Expressions: from numbers to letters — Grade 7. A taxi: 5 000 soum plus 2 000 soum per km. What is the fare for x km? How are brackets expanded?
Monomials and polynomials — Grade 7. The vegetable plot was extended by 5 m: which pieces make up the area (x + 3)(x + 5)?
Special products (algebraic identities) — Grade 7. A carpet has been widened by b on every side — what are the pieces of (a + b)²? Work out 55² in your head
Algebraic fractions — Grade 7. One pipe fills a pool in 4 hours, another in 12 hours. How long if both are open?
The linear equation: the balance — Grade 7. The pans are equal: 3 sacks + 4 kg = 2 sacks + 13 kg. How many kilograms is one sack?
Systems of equations — Grade 7. 2 kg of apples and 3 kg of pears — 29 000; 1 kg and 1 kg — 12 000 soum. The prices?
Point, segment, angle — Grade 7. When two streets cross, why are opposite angles always equal?
Congruent triangles — Grade 7. Why is a bridge truss made of triangles? How much information fixes a triangle?
Parallel lines — Grade 7. The street crossing the rails makes eight angles — why are four of them equal?
Angles of a triangle — Grade 7. If you tear off the three angles and put them side by side, why do you always get a straight angle?
Compass and straightedge — Grade 7. With an unmarked straightedge and a compass, how do you halve an angle or bisect a segment?
Pythagoras’ theorem — Grade 8. How high up the wall does the ladder reach? Does the rod fit in the box?
Combinatorics, probability and statistics
Sets, counting, probability, data and charts
Combinatorics: counting rules — Grade 7. 3 shirts and 2 pairs of trousers — how many different outfits? In how many orders can 6 people stand in a line?
Statistics: mean, median, σ — Grade 8. What is the “typical” height of a class? By how much does one very tall student shift the average?
Probability: coin, die, Venn — Grade 9. If we toss a coin 1000 times, how many heads will we get? What is the probability that two dice differ by 1?