# Crossing

Crossing encourages students to consider one to one correspondence at each turn. Students will count the number of dots on a die, for example, and then need to count that same number of spaces for each path. To be successful, students must compare the number they have rolled to each of their paths and determine which will be most beneficial.

This provides an opportunity for students to begin thinking critically about their options. The Crossing game board also has the number 1-10 written in each space, this allows students to begin a conversation about addition, even without formal instruction.

A student who has a game piece on the number 5, and then rolls a 3, can move their piece by counting each space, but may see that they are now on space number 8 and be able to draw the conclusion that 5+3=8. This reasoning is not essential to success, but may be an opening for discussion and exploration.

Materials: Crossing game board; 3 markers for each player (9 total markers, in 3 different colors); one standard die

Math Skills: One to one correspondence

Recommended # of players: 3

### 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)

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.

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.

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.

• 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 = _.