Contiguous

Contiguous is a game that promotes flexible usage of operations including addition, subtraction, multiplication, and division. = Continuing the Investigation = As you play **Contiguous**, reflect on the following:

Mathematics Involved:
1.) What is the mathematical reasoning that is possible as the game is being played? 2.) What standards are being addressed? 3.) What are some strategies or mathematical models I can promote through thinking aloud?

Pedagogical Issues:
1.) What are effective ways to introduce the game? 2.) Who could benefit from playing this game? 3.) How can I facilitate student autonomy in playing the game? 4.) How can I get students to share their thinking with their peers while playing the game?

Ways to Improve the game:
1.) Appearance 2.) Wording of rules 3.) Changing of rules

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• count with understanding and recognize "how many" in sets of objects; • use multiple models to develop initial understandings of place value and the base-ten number system; • develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections; • develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; • connect number words and numerals to the quantities they represent, using various physical models and representations;

Grades 3–5 Expectations: In grades 3–5 all students should–
• recognize equivalent representations for the same number and generate them by decomposing and composing numbers;

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations; • understand the effects of adding and subtracting whole numbers; • understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

Grades 3–5 Expectations: In grades 3–5 all students should–
• understand various meanings of multiplication and division; • understand the effects of multiplying and dividing whole numbers; • identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; • understand and use properties of operations, such as the distributivity of multiplication over addition.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• develop and use strategies for whole-number computations, with a focus on addition and subtraction; • develop fluency with basic number combinations for addition and subtraction; • use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Grades 3–5 Expectations: In grades 3–5 all students should–
• develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50; • develop fluency in adding, subtracting, multiplying, and dividing whole numbers; • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results; • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• sort, classify, and order objects by size, number, and other properties; • recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; • analyze how both repeating and growing patterns are generated.

Grades 3–5 Expectations: In grades 3–5 all students should–
• describe, extend, and make generalizations about geometric and numeric patterns; • represent and analyze patterns and functions, using words, tables, and graphs.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• illustrate general principles and properties of operations, such as commutativity, using specific numbers; • use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

Grades 3–5 Expectations: In grades 3–5 all students should–
• identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers; • represent the idea of a variable as an unknown quantity using a letter or a symbol; • express mathematical relationships using equations.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

Grades 3–5 Expectations: In grades 3–5 all students should–
• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–
• describe qualitative change, such as a student's growing taller; • describe quantitative change, such as a student's growing two inches in one year.

Grades 3–5 Expectations: In grades 3–5 all students should–
• investigate how a change in one variable relates to a change in a second variable; • identify and describe situations with constant or varying rates of change and compare them.