Grade 2: Place value

Principles:

  1. You group in tens for convenience so that you need only ten digits (0-9) to represent all numbers.
  2. Patterns are inherent in our numeration system because each place value is ten times the value of the place to the right.
  3. A number has many different forms. Foe example, 123 is 1 hundred, 2 tens, 3 ones and also 12 tens, 3 ones.
  4. A place value system requires a symbol for a place holder. For example, the 0 in 304 is a place holder; it pushes the digit 3 over to show that it represents 300 instead of 30.
  5. Numbers can be compared when written in standard, or symbolic, form.

Outcomes:

Grade 1 / Grade 2 / Grade 3
Demonstrate an understanding of base 10 groupings to hundreds. (2A6,2A7)
Recognize, extend and create simple place- value patterns, focusing on numbers to 100. (2A9),(2C4) / Demonstrate an understanding of base 10 groupings to thousands. (3A4)
Record, model, and interpret numbers up to and including the thousands. (3A5,3A6,)
Recognize the pattern implicit in the place value system. (3C1)

Concepts/Skills:

!,D,M / Represent 2 digit numbers in various groupings (e.g. 46 is 4 tens, 6 ones or 46 ones or 3 tens, 16 ones)
I,D / Represent 3 digit numbers in various groupings. (e.g.324 is 3 hundreds, 2 tens, 4 ones or 32 tens, 4 ones)
I,D / Represent numbers to 3 places:
  • Concretely (ten frames, cube a links ,base ten blocks, bundles of straws)
  • Pictorially (place value chart, hundred chart, pictures)
  • Symbolically ( numbers in the place value chart, numerals)
  • Verbally (different ways of saying it , written )
  • Contextually (story problems)

Extend a given number pattern based on place value relationships
Create a given number pattern based on place value relationships

Grade 3: Place value

Principles:

  1. You group in tens for convenience so that you need only ten digits (0-9) to represent all numbers.
  2. Patterns are inherent in our numeration system because each place value is ten times the value of the place to the right.
  3. A number has many different forms. Foe example, 123 is 1 hundred, 2 tens, 3 ones and also 12 tens, 3 ones.
  4. A place value system requires a symbol for a place holder. For example, the 0 in 304 is a place holder; it pushes the digit 3 over to show that it represents 300 instead of 30.
  5. Numbers can be compared when written in standard, or symbolic, form.

Outcomes:

Grade 2 / Grade 3 / Grade 4
Demonstrate an understanding of base 10 groupings to hundreds. (2A6,2A7)
Recognize, extend and create simple place- value patterns, focusing on numbers to 100. (2A9),(2C4) / Demonstrate an understanding of base 10 groupings to thousands. (3A4)
Record, model, and interpret numbers up to and including the thousands. (3A5,3A6,)
Recognize the pattern implicit in the place value system. (3C1) / Model, read, and record numbers to ten thousands. (3A4,4A3)

Concepts/Skills:

!,D,M / Represent 3 digit numbers in various groupings (e.g. 246 is 2 hundreds, 4 tens, 6 ones or 2 4 tens, 6 ones).
I,D / Represent 4 digit numbers in various groupings. (e.g.5324 is 5 thousands,3 hundreds, 2 tens, 4 ones or 53 hundreds,2 tens, 4 ones)
I,D / Represent numbers to 4 places:
  • Concretely (base ten blocks)
  • Pictorially (place value chart, hundred chart, pictures)
  • Symbolically ( numbers in the place value chart, numerals)
  • Verbally (different ways of saying it , written )
  • Contextually (story problems)

I,D,M / Understand the positional structure of the place value system. (hundreds is to the immediate left of tens, H,T,O)
Understand the multiplicative pattern in the place value system. ( 10 ones make 1 ten)

Grade 4: Place value

Principles:

  1. You group in tens for convenience so that you need only ten digits (0-9) to represent all numbers.
  2. Patterns are inherent in our numeration system because each place value is ten times the value of the place to the right.
  3. A number has many different forms. Foe example, 123 is 1 hundred, 2 tens, 3 ones and also 12 tens, 3 ones.
  4. A place value system requires a symbol for a place holder. For example, the 0 in 304 is a place holder; it pushes the digit 3 over to show that it represents 300 instead of 30.
  5. Numbers can be compared when written in standard, or symbolic, form.

Outcomes:

Grade 3 / Grade 4 / Grade 5
Demonstrate an understanding of base 10 groupings to thousands. (3A4)
Record, model, and interpret numbers up to and including the thousands. (3A5,3A6,)
Recognize the pattern implicit in the place value system. (3C1) / Model, read, and record numbers to ten thousands. (3A4,4A3) / Model, read, and record numbers to hundred thousands. (5A6)

Concepts/Skills:

!,D,M / Represent 4 digit numbers in various groupings (e.g. 3 246 is 3 thousands,2 hundreds, 4 tens, 6 ones or 32 hundreds, 4 tens, 6 ones).
I,D / Represent 5 digit numbers in various groupings. (e.g.65 324 is 6 ten thousands,5 thousands,3 hundreds, 2 tens, 4 ones or 65 thousands, 3 hundreds,2 tens, 4 ones)
I,D / Represent numbers to 5 places:
  • Concretely (base ten blocks)
  • Pictorially (place value chart, hundred chart, pictures)
  • Symbolically ( numbers in the place value chart, numerals)
  • Verbally (different ways of saying it , written )
  • Contextually (story problems)

I,D,M / Understand the positional structure of the place value system. (hundreds is to the immediate left of tens, H,T,O )
I,D / Understand the multiplicative pattern in the place value system. ( 10 ones make 1 ten)

Grade 5: Place value

Principles:

  1. You group in tens for convenience so that you need only ten digits (0-9) to represent all numbers.
  2. Patterns are inherent in our numeration system because each place value is ten times the value of the place to the right.
  3. A number has many different forms. Foe example, 123 is 1 hundred, 2 tens, 3 ones and also 12 tens, 3 ones.
  4. A place value system requires a symbol for a place holder. For example, the 0 in 304 is a place holder; it pushes the digit 3 over to show that it represents 300 instead of 30.
  5. Numbers can be compared when written in standard, or symbolic, form.

Outcomes:

Grade 4 / Grade 5 / Grade 6
Model, read, and record numbers to ten thousands. (3A4,4A3) / Model, read, record and extend numbers to hundred thousands. (4A3, 5A6, 5C1) / Model, read, and record numbers to millions. (5A6)
Demonstrate an understanding of the place value system. (6A8)

Concepts/Skills:

!,D,M / Represent 4 digit numbers in various groupings (e.g. 3 246 is 3 thousands,2 hundreds, 4 tens, 6 ones or 32 hundreds, 4 tens, 6 ones).
I,D / Represent 5 digit numbers in various groupings. (e.g.65 324 is 6 ten thousands,5 thousands,3 hundreds, 2 tens, 4 ones or 65 thousands, 3 hundreds,2 tens, 4 ones)
I,D / Represent numbers to 5 places:
  • Concretely (base ten blocks)
  • Pictorially (place value chart, hundred chart, pictures)
  • Symbolically ( numbers in the place value chart, numerals)
  • Verbally (different ways of saying it , written )
  • Contextually (story problems)

I,D,M / Understand the positional structure of the place value system. (hundreds is to the immediate left of tens, H,T,O )
I,D / Understand the multiplicative pattern in the place value system. ( 10 ones make 1 ten)

Grade 6: Place value

Principles:

  1. You group in tens for convenience so that you need only ten digits (0-9) to represent all numbers.
  2. Patterns are inherent in our numeration system because each place value is ten times the value of the place to the right.
  3. A number has many different forms. Foe example, 123 is 1 hundred, 2 tens, 3 ones and also 12 tens, 3 ones
  4. A place value system requires a symbol for a place holder. For example, the 0 in 304 is a place holder; it pushes the digit 3 over to show that it represents 300 instead of 30.
  5. Numbers can be compared when written in standard, or symbolic, form.

Outcomes:

Grade 5 / Grade 6 / Grade 7
Model, read, and record numbers to hundred thousands. (5A6, 5C1) / Model, read, and record numbers to millions. (5A6)
Demonstrate an understanding of the place value system . (6A8)

Concepts/Skills:

I,D,M / Represent 6 digit numbers in various groupings (e.g. 753 246 is 7 hundred thousands, 5 ten thousands, 3 thousands, 2 hundreds, 4 tens, 6 ones or 753 thousands, 24 hundreds, 6 ones).
I,D / Represent numbers to 7 places:
  • Concretely (base ten blocks)
  • Pictorially (place value chart, hundred chart, pictures)
  • Symbolically ( numbers in the place value chart, numerals)
  • Verbally (different ways of saying it , written )
  • Contextually (story problems)

I,D,M / Understand the positional structure and the multiplicative pattern of the place value system. (each position represents ten times as much as the position to it’s right, each position represents one tenth as much as the position to it’s left, positions are grouped in threes for purposes of reading them.)