Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to
100,000.
Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form.
Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to
record the results of comparisons.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding.
Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value
understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the
algorithm.
Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using
rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or the relationship between
multiplication and division.
Number and Operations – Fractions
Extend understanding of fractions.
Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size
of the parts differ even though the two fractions themselves are the same size.
Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and
100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with
symbols >, =, or <, and justify the conclusions by:
• Reasoning about their size and using area and length models.
• Using benchmark fractions 0, ½, and a whole.
• Comparing common numerator or common denominators.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.