The Cornerstone School · grades K–5
Number Sense & Elementary Math
Counting, place value, the four operations, and fractions — arithmetic built to be understood before it is memorized.
Counting, tens and ones, comparing, and the first sums — number sense laid down firmly enough to carry all later arithmetic.
Why 4,306 means what it means — base ten from bundling sticks to reading large numbers in the news.
Syllabus · 3 units · ~12 hours
Unit I — The Base-Ten Idea
Ten of these makes one of those · Hundreds, thousands, and beyond · Expanded form: 4,306 as 4000 + 300 + 6
Unit II — Comparing and Rounding
Comparing multi-digit numbers place by place · Rounding to the nearest ten and hundred · When rounding helps and when it misleads
Unit III — Place Value at Work
Adding and subtracting with regrouping, explained · Multiplying by ten and what really moves · Reading large numbers in the newspaper
Equal groups, arrays, and the facts derived rather than drilled — then division as the question multiplication answers.
Syllabus · 4 units · ~20 hours
Unit I — What Multiplication Is
Equal groups and repeated addition · Arrays: rows and columns · The order does not matter: 3 × 4 and 4 × 3
Unit II — The Tables, with Reasons
Twos, fives, and tens from skip counting · Doubling: from twos to fours to eights · Nines and their patterns · The handful left over: 6 × 7 and 7 × 8
Unit III — Division
Sharing equally and making groups · Division as the question multiplication answers · Remainders and what to do with them
Unit IV — Bigger Numbers
Multiplying by tens and by hundreds · One digit times two digits, by area · Choosing multiplication or division in a story problem
A fraction is a number, not a picture of pie — equal parts, equivalence, and comparison, placed on the line.
Syllabus · 3 units · ~18 hours
Unit I — What a Fraction Names
Equal parts of a whole · The top counts, the bottom names · Fractions of a set, not just of a shape
Unit II — Fractions on the Number Line
Placing halves, thirds, and fourths · Equivalent fractions: same point, different name · Comparing fractions with the same bottom or the same top
Unit III — Working with Fractions
Adding and subtracting with like denominators · Whole numbers written as fractions · Mixed numbers and improper fractions
Rulers, clocks, coins, and honest bar graphs — measuring the world and writing down what you find.
Syllabus · 3 units · ~14 hours
Unit I — Length, Weight, and Volume
Units you invent and units everyone shares · Rulers, scales, and measuring cups · Estimating before you measure
Unit II — Time and Money
Reading a clock to the minute · Elapsed time: from then to now · Counting change and making amounts
Unit III — Collecting and Showing Data
Tally charts and pictographs · Bar graphs that tell the truth · Asking a question your data can answer