Reading, Writing, and Comparing Numbers to Billions

Understand the base-ten place value system from ones through billions and explain how multiplying or dividing by ten shifts digit values.

Read, write in standard, word, and expanded forms, compare, and order multi-digit whole numbers through billions.

Round multi-digit whole numbers to any place and use compatible numbers to estimate and check reasonableness in everyday financial scenarios.

Fluently add and subtract multi-digit whole numbers using column algorithms, mental strategies, regrouping across zeros, and digital verification.

Multiply multi-digit numbers using area models, arrays, the distributive property, perfect squares up to 15 × 15, and mental calculation shortcuts.

Execute the standard multiplication algorithm fluently for up to 4-digit by 1-digit and 2-digit by 2-digit numbers and solve complex word problems.

Divide multi-digit dividends by one- and two-digit divisors using area models, arrays, partial quotients, and Euclidean division.

Fluently perform long division with up to four-digit dividends and two-digit divisors, and interpret remainders in real-world contexts.

Read, write, and convert Roman numerals up to 3,000, and explore the historical emergence of zero, place value, and unified measurement systems.