Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding as students solve equations using manipulatives in a variety of situations and settings.  As students demonstrate understanding of addition and subtraction families they will explore the mathematical relationship between numbers in addition and subtraction sentences known as the commutative property. Students will be introduced to the concept of turn around facts and related subtraction.

• Develop strategies for problem solving as students are actively engaged in a variety of activities during whole and small group instruction such as games including dominoes, dice, fact triangles, number bonds, and number cards to create meaningful relationships using numbers in related addition and subtraction.

• Develop the ability to communicate mathematically as students use specific language to communicate procedures they are using such as add, subtract, take away, put together, compare, equation, equals, and commutative property.

• Developing the ability to make conjectures, model and generalize what it means to “take apart”, “put together’, and “compare solutions.”

• Builds procedural fluency and conceptual understanding by allowing students to discover and apply the commutative property for addition. Ask them to investigate whether this property works for subtraction. Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction. First graders might have informally encountered negative numbers in their lives, so they think they can take away more than the number of items in a given set, resulting in a negative number below zero.

• Implement tasks that promote reasoning and problem solving as the teacher provide many problems situations where students take away all objects from a set, e.g. 19 - 19 = 0 and focus on the meaning of 0 objects and 0 as a number. The teacher will also facilitate meaningful math discourse as they ask students to discuss whether they can take away more objects than what they have.

• Pose purposeful questions while actively questioning students and circulating among groups. Some examples are: How do you know ___+___=___? What is the turn around fact? Can you tell a related subtraction fact? How are these numbers related? How can you prove they are related?

• Supporting productive struggle as teachers support students’ exploration as they discover how to use the numbers from an addition number sentence to make a related subtraction number sentence.

Key Understandings

Misconceptions

• Understand the relationship between addition and subtraction and that they are not independent of each other.

• Choose flexibly between strategies to solve addition and related subtraction facts up to 10 fluently.

• Use symbols such as +, -, and = to develop understanding and procedural fluency of addition and related subtraction facts up to 10.

• They know the number names and/or guess.

• They can count an item or count it twice.

• That a number doesn’t name a quantity.

• That a number sentence will result in a negative number and not understand what a negative number is

• That there is no difference between addition and subtraction.

• They will not be able understand the symbols and order in a number sentence