**Goal 1:** Children develop an understanding of the base-ten system and use place-value notation.

*By the end of each age group or grade level, most children will have met prior age group or grade level standards in this domain.*

## Infants

(0-12 Months)

- No standards in this age group for this Element.

## Young Toddlers

(9-18 Months)

- No standards in this age group for this Element.

## Older Toddlers

(18-36 Months)

- No standards in this age group for this Element.

## Younger Preschoolers

(36-48 months)

- No standards in this age group for this Element.

## Older Preschoolers

(48-60 months)

- No standards in this age group for this Element.

## Kindergartners

Work with numbers 11-19 to gain foundations for place value

- Compose and decompose numbers from 11 to 19 into ten ones and some further ones (e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

## First Graders

Extend the counting sequence.

- Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Understand place value.

- Understand that the two digits of a two-digit number represent amounts of tens and ones.
- Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <

Use place value understanding and properties of operations to add and subtract.

- Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
- Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain reasoning used.
- Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

## Second Graders

Understand place value.

- Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
- Count within 1000; skip-count by 5s, 10s, and 100s.
- Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons

Use place value understanding and properties of operations to add and subtract.

- Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Add up to four two-digit numbers using strategies based on place value and properties of operations.
- Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.
- Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
- Explain why addition and subtraction strategies work, using place value and the properties of operations.

## Third Graders

Use place value understanding and properties of operations to perform multi-digit arithmetic.

- Use place value understanding to round whole numbers to the nearest 10 or 100
- Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.