1. All students understand the relationship among numbers, quantities and place value in whole numbers up to 1000

• count, read, write whole numbers to 1,000 and identify the place value for each digit
  
• use words, models and expanded form to represent numbers (to 1,000)
  
• order and compare whole numbers up to 1,000 using the symbols <, =, >.
  

2. All students estimate, calculate and solve problems involving addition and subtraction of two- and three-digit numbers

• understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions
  
• find the sum or difference of two whole numbers up to three digits long
  
• use mental arithmetic to find the sum or difference of two 2-digit numbers.
  

3. All students model and solve simple problems involving multiplication and division

• use repeated addition, arrays, counting by multiples to do multiplication
  
• use repeated subtraction, equal sharing and forming equal groups to do division with remainders
  
• know the multiplication tables of 2s, 5s and 10s (to "times 10") and commit to memory.
  

4. All students understand that fractions and decimals can refer to parts of a set and parts of a whole

• recognize, name and compare unit fractions up to 1/12
  
• recognize fractions of a whole and parts of a group (e.g., 1/4th of a pie, 2/3rds of 15 balls)
  
• know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.
  

5. All students model and solve problems by representing, adding and subtracting amounts of money

• solve problems using combinations of coins and bills
  
• know and use the decimal notation and the dollar and cents symbols for money.
  

6. All students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds and thousands places

• recognize when an estimate is reasonable in measurements (e.g., closest inch).

1. All students model, represent and interpret number relationships to create and solve problems involving addition and subtraction

• use the commutative and associative rules to simplify mental calculations and check results
  
• relate problem situations and number sentences involving addition and subtraction
  
• solve addition and subtraction problems using data from simple charts, picture graphs and number sentences.

1. All students collect, record, organize, display and interpret numerical data on bar graphs and other representations

• record numerical data in systematic ways, keeping track of what/who has been counted
  
• represent the same data set in more than one way (e.g., charts with tallies, and bar graphs)
  
• identify features of data sets (range and mode)
  
• ask and answer simple questions related to data representations.
  

2. All students demonstrate an understanding of patterns and how they grow, and describe them in general ways.

• recognize, describe, extend and explain how to get the next term in linear patterns (e.g., 4, 8, 12 ...; the number of ears on 1 horse, 2 horses, 3 horses, 4 horses)
  
• solve problems involving simple number patterns.

1. All students make decisions about how to set up a problem.

• decide about the approach, materials and strategies to use
  
• use tools such as manipulatives or sketches to model problems
  

2. All students solve problems and justify their reasoning.

• defend the reasoning used and justify the procedures selected
  
• make precise calculations and check the validity of the results from the context of the problem
  

3. All students note connections between one problem and another.