Learning About the World

Mathematics


Number Relationships and Operations -- Numbers and Operations in Base Ten

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 Through Older Toddlers

Infants

(0-12 Months)

  1. No standards in this age group for this Element.

Young Toddlers

(9-18 Months)

  1. No standards in this age group for this Element.

Older Toddlers

(18-36 Months)

  1. No standards in this age group for this Element.
Younger Preschoolers Through Kindergartners

Younger Preschoolers

(36-48 months)

  1. No standards in this age group for this Element.

Older Preschoolers

(48-60 months)

  1. No standards in this age group for this Element.

Kindergartners

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

  1. 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 Through Third Graders

First Graders

Extend the counting sequence.

  1. 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.

  1. Understand that the two digits of a two-digit number represent amounts of tens and ones.
  2. 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.

  1. 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
  2. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain reasoning used.
  3. 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.

  1. 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.
  2. Count within 1000; skip-count by 5s, 10s, and 100s.
  3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
  4. 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.

  1. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  2. Add up to four two-digit numbers using strategies based on place value and properties of operations.
  3. 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.
  4. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
  5. 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.

  1. Use place value understanding to round whole numbers to the nearest 10 or 100
  2. 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.
  3. 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.

Vermont Agency of Education
Secretary Daniel M. French
219 North Main Street, Suite 402
Barre, VT 05641

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