*Contiguous* requires students to go beyond solving equations; they must create them. This higher level of thinking helps solidify the relationships between operations. Students are also being asked to solve a problem using multiple steps, paving the way for algebraic thinking. Initially, students may be able to use number relationships they are familiar with, but as the board fills up and choices are few, students will need to search for new ways to reach a solution. In *Contiguous,* students are also limited in their play options because they must cover a square next to a previously played square. Often, the equation will not be obvious, and students will need to explore multiple options.

When introducing this game, it may be beneficial for the teacher to model his or her own thinking when considering their play options. It is also helpful to have students talk about their thinking with their peers during game play, and to justify their chip placement. This keeps other players involved and engaged throughout the game.

##### Click the below icons to print out game board, rules and notes.

Contiguous: Game board | Contiguous: Rules | Contiguous: Notes |

**Common Core Standards**

*Click on the category title (ex: "Counting and Cardinality") to view the entire standards of the Common Core.

**Kindergarten**

Know number names and the count sequence.

- K.CC.1. Count to 100 by ones and by tens.
- K.CC.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1)

*Operations and Algebraic Thinking*

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

- K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
- K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
- K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
- K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
- K.OA.5. Fluently add and subtract within 5.

*Number and Operations in Base Ten*

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

- K.NBT.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 Grade**

*Operations and Algebraic Thinking*

Represent and solve problems involving addition and subtraction.

- 1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
- 1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction.

- 1.OA.3. Apply properties of operations as strategies to add and subtract.
*Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)* - 1.OA.4.Understand subtraction as an unknown-addend problem.
*For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20.*

Add and subtract within 20.

- 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
- 1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.

- 1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
- 1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
*For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.*

*Number and Operations in Base Ten*

Understand place value.

- 1.NBT.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- 10 can be thought of as a bundle of ten ones called a ten.
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

**Second Grade**

*Operations and Algebraic Thinking*

Add and subtract within 20.

- 2.OA.2. Fluently add and subtract within 20 using mental strategies.By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication.

- 2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
- 2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.