Ring up decimals with estimation armor — then mine numbers down to their prime blocks.
REMEMBER:Estimate FIRST — a rough answer catches a
runaway decimal point before it costs a customer real money. Every whole number is
built from prime blocks: the blocks two numbers share
build their GCF, and the blocks they combine build their LCM. And in
long division, when the divisor doesn't fit, write the zero — it
holds the place.
Part 1 · The Factor Quarry
Every number is a stack of prime blocks. Mine two numbers and
compare their stacks: blocks they share (gold outline) multiply
into the GCF; merging the stacks — shared blocks counted once —
builds the LCM.
Part 2 · The Cash Register — Estimate First!
A customer is waiting. Before touching the register, commit to a rough
estimate — is the answer about this big, ten times smaller, or ten times
bigger? Estimation is the armor that catches a misplaced decimal point.
Customers served correctly: 0
Part 3 · Back Office Machines
Three machines run the back office. Each prints every step of its standard
algorithm — and says why each move works.
The standard algorithm, one digit at a time: divide, multiply, subtract, bring down.
Any of the four operations on decimals (up to 2 decimal places) — estimation first, always.
GCF packs identical gift bags with nothing left over; LCM predicts when two repeating events land on the same day.
Part 4 · Store Manager Quiz
Question 1 of 10Score: 0
📗 Word Box
Prime number
A whole number greater than 1 whose only factors are 1 and itself — the un-splittable blocks of the quarry.
Prime factorization
A number written as a product of primes: 36 = 2 × 2 × 3 × 3. Every number has exactly one such stack.
Factor
A number that divides another with nothing left over. 4 is a factor of 36 because 36 ÷ 4 = 9 exactly.
Multiple
A number in another number's skip-count: multiples of 6 are 6, 12, 18, 24, ...
Greatest common factor (GCF)
The largest number that divides BOTH — built from all the prime blocks the two stacks share.
Least common multiple (LCM)
The smallest number both divide into — built by merging the stacks, counting shared blocks once.
Distributive property
Pulling a shared factor out front: 36 + 8 = 4(9 + 2). The parentheses hold what's left of each stack.
Quotient & remainder
Division's answer and its leftover: 3655 ÷ 6 = 609 remainder 1, because 6 × 609 + 1 = 3655.