A number is a structure, not a label. The same digit is worth seven, seventy or seven hundredths depending on where it sits, and every whole number above 1 is built from primes in exactly one way. This unit takes that structure apart: place value and decimals, powers and roots, factors and primes, prime factorization, common factors and multiples, the agreed order of operations, and rounding and estimating to check an answer.
Every idea is something you can move: slide a digit through the places, grow a factor tree, sort two numbers' primes into a Venn diagram, step through an expression. Only lesson 7 uses a scientific calculator, once, to check an estimate.
The lessons, in order
- Lesson 1 · Place value and decimals The value of a digit in whole numbers and decimals, zero as a placeholder, comparing and ordering decimals. Slide one digit along the places and see its value grow or shrink by ten at every step. No calculator
- Lesson 2 · Powers, squares and roots Powers as repeated multiplication, squares and cubes, perfect squares, and square and cube roots. Build a power one factor at a time, then find the side of a square or cube from its size. No calculator
- Lesson 3 · Factors, multiples and primes Factors, multiples, prime and composite numbers, why 1 is not prime, and divisibility tests. Build every rectangle a number can fill, then see exactly what each divisibility rule tests. No calculator
- Lesson 4 · Prime factorization Writing a number as a product of primes with a factor tree, index form, and why the result does not depend on the tree. Grow a factor tree one split at a time, then choose a different first split and watch the primes match. No calculator
- Lesson 5 · Common factors and multiples The greatest common factor and lowest common multiple, from prime factors, and deciding which one a problem needs. Sort two numbers' primes into a Venn diagram, then watch two repeating events line up on a timeline. No calculator
- Lesson 6 · Order of operations The order of operations: brackets, powers, then multiplication and division, then addition and subtraction, left to right. Step through an expression and see which operation each rule picks, against what left to right would give. No calculator
- Lesson 7 · Rounding and estimating Rounding to a place or to decimal places, and estimating a calculation to check an answer. Zoom in on the two nearest friendly numbers to see which way a number rounds, then estimate and check. Scientific calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.