Student Actions

Teacher Actions

• Develop the ability to make conjectures, model, and generalize as students solve real-world problems, not just practicing a collection of isolated skills. Some real-world problems would include using models for adding and subtracting items easily found in the classroom.

• Develop a productive mathematical disposition by communicating their mathematical ideas when adding and subtracting to 10 to one another through examples, models, and drawings.Students will be actively engaged in number talks and will share strategies without hesitation in a risk taking classroom.  

• Develop mathematical reasoning as students begin to explore adding and subtracting to 10 with and without objects justifying their thinking. Students should be able to explain different strategies used in order to find a solution.

• Develop accurate and appropriate procedural fluency as they add and subtract objects through hands on activities with manipulatives in a variety of contexts and settings over time.

• Implement tasks that promote reasoning and problem solving, as teachers choose real-world problems that invite exploration of addition and subtraction up to 10. Provide multiple opportunities in a variety of settings for students to apply addition and subtraction strategies to become more efficient, be able to make sense of the problem, represent the situation, and plan a solution.

• Posing purposeful questions to help students recall prior knowledge and justify their thinking such as Does that make sense? Can you explain how you solved the problem? Can anyone explain a different way to solve the problem? How do you know that is the solution?

• Facilitate meaningful mathematical discourse by challenging students to think deeply about problems and encouraging a variety of approaches to a solution. Teachers will model multiple approaches for students allowing them to respond using appropriate vocabulary on adding this discourse to anchor charts to refer back to as needed.

• Build procedural fluency from conceptual understanding by connecting student-generated strategies to more efficient procedures as appropriate. Teachers will encourage students to use appropriate vocabulary such as how many more, add, plus, all together, subtract, in all, take away, lost, etc. in a variety of settings and contexts over time.

• By having students explain their strategies for solving problems, teacher elicit and use evidence of student thinking for understanding during a variety of settings over time by .  This might include both formative and summative assessments from small group, whole group, and one-on-one situations.

• Build procedural fluency from conceptual understanding as students solve problems by constructing strategies that become more efficient. When given the problem, “Lucy has 3 cookies and Dan has 8 cookies, how many more cookies does Dan have?” Students may begin with direct modeling using materials to solve. As children's counting strategies become more efficient, they will be able to make sense of the problem, represent the situation, and plan a solution. (Contextual problems are connected closely as possible to children’s lives. Van de Walle, 2016) 

Key Understandings

Misconceptions

• Make connections between counting and the operations of addition and subtraction in relationship to the properties of addition.

• Relate addition and subtraction as inverse operations

• Should encounter the equal sign on BOTH sides of an equation. 8+2= ____  or ____= 8+2

• The commutative property applies to subtraction.

• That the equal sign, =, means to give an answer instead understanding equivalence and it is always on the the right side of an equation.