Explorer

Every studio, from easiest to hardest.

Number and place value

counting and comparing to 10Match apples one to one, count them and compare. Then meet the signs <, > and =.
Numbers to 20: a ten and some onesRead and build the numbers 10 to 20 with two ten-frames. One more, the number between, and first, second, third.
Number lines, counting in steps, odd and evenFind numbers on a number line, count in 2s, 5s and 10s, and discover odd and even numbers.
Tens and ones: numbers to 100Bundle ten ones into a ten. Build and read numbers to 100 with tens and ones.
Hundreds and thousands: place value and expanded formBuild, read and write numbers to 10 000 with base-ten blocks, write them in expanded form, compare them from the highest place, and meet Roman numerals.
Large numbers, rounding and estimatingRead and build numbers in the millions in groups of three digits, round to the nearest 10, 100 or 1000 by looking at the next place, and estimate a sum before you work it out.
Estimating and rounding to tens and hundredsRound numbers to the nearest ten or hundred and estimate sums and differences without an exact calculation.
Negative numbers and integersCarry the number line on to the left of zero. Show temperatures below zero and depths below sea level, then add and subtract with jumps.
Rounding decimalsZoom in between a number's two neighbours and see which is nearer: to the nearest whole number, to 1 and 2 decimal places, and to significant figures. Then find every number that rounds to the same value.
Factors, multiples and primesArrange counters into rectangles to find a number's factors. See why some numbers make only one rectangle.
Divisibility, HCF, LCM and powersShade multiples on a hundred square to discover divisibility rules. Then common multiples and factors, square numbers and powers.
Multiplying and dividing integers; absolute valueMultiply and divide negative numbers with hops on the number line, find the pattern behind the signs, and measure distance from zero.
Rational numbers: ordering and the four operationsPut negative fractions and decimals on one number line, compare them, then add and multiply them as moves and as scalings.
The sieve for prime numbersWrite the numbers 1 to 50 and cross out multiples until only the primes are left, then find out where to stop.
Subtracting a negative numberRewrite every subtraction as an addition, see subtracting a negative on the line, and work two-digit sums in tens and ones.
Powers of negative numbers and doubling growthFollow the order of operations with powers, understand the difference between (−3)² and −3², and see why repeated doubling gets large so fast.
Prime factors, HCF × LCM, and exact rootsSplit two numbers into primes with factor trees. Build the HCF and LCM from the primes, and find square and cube roots by pairing and grouping the primes in threes.
Laws of indices, zero and negative powersWrite powers out as factors on a fraction bar: multiply by putting the factors together, divide by cancelling equal factors above and below, and see why a⁰ = 1 and why a negative index means a fraction.
Dividing rational numbersFind the reciprocal of a rational number and turn divisions of signed numbers into multiplications. See why dividing by zero makes no sense.
nth roots and rational powersLearn nth roots through powers: even and odd roots, multiplying roots, then fractional powers like 27¹³ and 8²³.
Standard form (scientific notation)Slide the digits with ÷10 and ×10 until one non-zero digit is left of the decimal point, and watch the power of ten count the slides.
Estimating square roots; irrational numbers on the lineTrap a square root between whole numbers, zoom in to tenths and hundredths by squaring, and sort rational from irrational numbers on the real line.
Surds and simplifying themSplit the number under a root into factors and take each pair out: √12 = 2√3. Multiply roots, add like surds, and rationalise a denominator.
Euclid's method for the highest common factor (HCF)Find the highest common factor (HCF) of two numbers with a chain of divisions, without listing any factors.
Absolute value of real numbers and approximate calculationSee absolute value as distance from the origin, meet the three cases, compare |a + b| with |a| + |b|, and calculate with approximate roots.
Root properties, rational powers and irrational equationsFind the root of a quotient and the root of a root, compare roots of different degrees, and solve an irrational equation by squaring, checking the condition and substituting. Section: Grade 10, nth roots, rational powers, irrational equations; the Grade 8 square root is in another studio.
Numbers in words: ten thousands, hundred thousands and billionsBuild and read big numbers: five-digit numbers, a hundred thousand, and numbers past the million.
Roots: square and cube roots and their signsCount the numbers that square to a positive number, see why a negative has no real square root but does have a cube root, and why the root of a square is the absolute value.
Rounding on the number lineFind the number on the number line and see which ten, hundred or thousand it is nearest to. A number exactly halfway rounds up.
Numbers in wordsBuild two- and three-digit numbers from tens and ones, and read and write them in words.
Divisibility in the integersThe division algorithm, properties of divisibility, and the gcd written as a combination of the two numbers.
Number table and skip countingSkip count in 3s, 4s, 6s and 7s on a number table, and see repeated addition with rods.
Congruence in the integersNumbers with the same remainder on division by m are congruent. See how to calculate with them.
Place value in decimalsWrite and read decimals in a place-value table with ones, tenths and hundredths columns, build them in expanded form and compare them.
Approximation: rounding and truncatingApproximate a number to the nearest 10, 100, 1 or 0.1 with two methods, rounding and truncating, tell which one is rounded, approximate a fraction and estimate a product.
Approximate values and errorFind the absolute and relative error, compare the accuracy of measurements and bound the error of a sum.
Composition of 6–10 and zeroSplit the numbers 6, 7, 8, 9 into two parts with counters. Then find out what happens when all, or nothing, is taken away.
Composition card and stripsWrite the two parts that make 6, and build a strip of 7 cells.
Properties of the arithmetic square rootFind roots of squares, products, quotients and powers with the properties of the arithmetic square root, as in the Grade 8 Ukrainian book. Section: Grade 8, arithmetic square root; nth roots are in the Grade 10 studio.
The natural series and the coordinate rayFind the number before a given one, find out why there is no largest natural number, mark K(5) on a coordinate ray and read a scale.
Division with remainder, divisibility by 9 and 3Find out why the remainder is smaller than the divisor, build the dividend with a = bq + r and test divisibility by 9 and 3 by the digit sum.
Nested roots: √(a ± 2√b)Get rid of a root under a root: write the expression as the square of a sum or a difference and find the numbers from their sum and product.
Comparing and ordering big numbersCompare numbers up to a million place by place, put them in order and add whole thousands.
Binary numbers and Roman numeralsRead and write binary numbers with the place values 1, 2, 4, 8, 16 and compare Roman numerals with our place value system.
Distance between points and equations with a modulusFind the distance between two points of the number line as |a - b| and solve equations |x - a| = b by marking points.
Divisibility of sums, differences and products; tests for 4, 8, 6 and 11Decide whether a sum, difference or product is divisible without calculating it, and use the tests for 4, 8, 6 and 11.
Heron's method and irrational numbersApproximate a square root with the Heron method (a rectangle that becomes a square), then see why √2 is not a fraction.

Calculation

Fractions

Ratio and proportion

Money

Measurement

Shape and geometry

Position and direction

Patterns and sequences

Algebra

Coordinate geometry

Functions and graphs

Vectors

Trigonometry

Statistics

Probability

Sets and logic

Complex numbers

Matrices

Calculus

Numerical methods

Solving equations numericallyTrap a root of an equation with no formula by a change of sign, close in on it by repeating a rule, and go faster with the Newton–Raphson method.

Problem solving