The DreamBox Learning K-2 Math curriculum

NUMBER AND OPERATIONS:
Representing, comparing, and ordering whole numbers and joining and separating sets

Children use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as:

• Counting objects in a set
• Creating a set with a given number of objects
• Comparing and ordering sets or numerals by using cardinal meanings
• Modeling simple joining and separating situations with objects

They choose, combine, and apply effective strategies for answering quantitative questions, including:

• Quickly recognizing the number in a small set
• Counting and producing sets of given sizes
• Counting the number in combined sets
• Counting backward

NUMBER AND OPERATIONS AND ALGEBRA: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts

Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including:

• Discrete objects
• Length-based models
• Number lines

They use these models in order to model:

• “Part-whole”
• “Adding to”
• “Taking away from”
• “Comparing”

Children develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems.

Children understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as “counting on” two).

They use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties to solve addition and subtraction problems involving basic facts.

NUMBER AND OPERATIONS: Developing an understanding of whole number relationships, including grouping in tens and ones

Children compare and order whole numbers (at least to 100) to develop an understanding of and solve problems involving the relative sizes of these numbers.

Children think of whole numbers between 10 and 100 in terms of groups of tens and ones (especially recognizing the numbers 11 to 19 as 1 group of ten and particular numbers of ones).

They understand the sequential order of the counting numbers and their relative magnitudes and represent numbers on a number line.

NUMBER AND OPERATIONS: Developing an understanding of the base-ten numeration system and place-value concepts

Children develop an understanding of the base-ten numeration system and place-value concepts (at least to 1000).

Their understanding of base-ten numeration includes counting in units and multiples of hundreds, tens, and ones

Their understanding of base-ten numeration includes a grasp of number relationships, which they demonstrate in a variety of ways, including:

• Comparing and ordering numbers
• Understanding multidigit numbers in terms of place value

Children use place value and properties of operations to create equivalent representations of given numbers; to write, compare, and order multidigit numbers.

NUMBER AND OPERATIONS AND ALGEBRA: Developing quick recall of addition facts and related subtraction facts and fluency with multidigit addition and subtraction

Children use their understanding of addition to develop quick recall of basic addition facts and related subtraction facts.

They solve arithmetic problems by applying their understanding of:

• Models of addition and subtraction
• Relationships and properties of number
• Properties of addition

Children develop, discuss, and use efficient, accurate, and generalizable methods to add and subtract multidigit whole numbers.

They develop fluency with efficient procedures for adding and subtracting whole numbers, understand why the procedures work, and use them to solve problems.