The Cornerstone School · Number Sense & Elementary Math
The Counting House: Numbers to 120
Counting, tens and ones, comparing, and the first sums — number sense laid down firmly enough to carry all later arithmetic. · QA 113 · ~24 h
Counting gives each object exactly one number word, in the fixed order, and the last word you say names how many there are in all.
fol. 2 Zero: Counting NothingZero is a true number: it answers how many when a group is empty, and it sits just before one.
fol. 3 Counting OnWhen a group grows, hold the count you already trust and count on from there, keeping track of how many more you add.
Every number from one to nine has a partner that completes a ten: 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5.
fol. 5 The Teen Numbers: Ten and Some MoreA teen number is one full ten and some extra ones — thirteen is ten and three — even though the English word hides the ten.
fol. 6 Tens and Ones, Up to 120In a two-digit number, the right digit counts loose ones and the left digit counts bundles of ten — and ten tens make one hundred.
To compare two groups, pair their members one to one: leftovers mean that side has more, and a perfect pairing with none left means the groups are equal — no counting required.
fol. 8 The Tens DecideTo compare two-digit numbers, look at the tens first — a whole ten beats any pile of ones — and the signs >, <, and = write down the verdict.
fol. 9 Counting by Twos, Fives, and TensSkip counting says only the running totals of equal groups — and lands on exactly the numbers a one-by-one count would reach.
Addition joins two counted parts into one whole — and swapping the parts never changes the total.
fol. 11 Taking AwayThe minus sign answers two questions: how many remain after part of a group leaves, and how much more one group has than another.
fol. 12 One Story, Four SentencesOne part-part-whole picture writes four true number sentences, because addition and subtraction undo each other.
fol. 13 Crossing TenTo add past ten, move just enough from one part to fill a ten first — a ten-and-some number is the easiest kind to read.
A length is measured by laying identical units end to end — no gaps, no overlaps — and counting them; a bigger unit always gives a smaller count.
fol. 15 Halves and Fair SharesA share is fair only when every piece is the same size, and a half is one of exactly two matching pieces of a whole.
fol. 16 The Hiding NumberA number sentence with a blank — 5 + ? = 9 — asks you to find the number that hides, and counting on and fact families are the tools that find it.