2022 2-A-2-1

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2.A.2.1

2.A.2.1 Use objects and number lines to represent number sentences.

In a Nutshell

This objective expands students’ work from first grade where students used physical objects to represent addition and subtraction number sentences by using number lines to represent addition (including repeated addition) and subtraction number sentences. When using objects to concretely model these number sentences, students will also begin arranging them into arrays to show the patterns created through repeated addition. This skill will help to lay the foundation of multiplication.

Student Actions	Teacher Actions
Develop a productive mathematical disposition, describing connections between addition and subtraction in a variety of contexts, e.g., number grids, number lines, counters, ten frames, numerals, connecting cubes, etc. Communicate mathematical ideas to one another through examples, demonstrations, models, drawing, symbols, and logical arguments. Students know how and when to use tools such as blocks, number lines, and objects. Develop mathematical reasoning by justifying their thinking and explaining different strategies for problem-solving. Develop the ability to model number sentences using concrete representations through objects and number lines.	Use and connect mathematical representations by highlighting the connections between addition and subtraction. Implement tasks that promote reasoning and problem-solving by inviting exploration of addition and subtraction with objects and number lines. Pose purposeful questions that help students construct a conceptual understanding of using physical representations of number sentences.
Key Understandings	Misconceptions
Number lines represent a student’s thinking when combining/separating numbers in addition and subtraction. Open number lines can be used to solve problems. Numbers on open number lines are evenly spaced. Number lines can be used to represent a number sentence and to find a solution. Objects can be used to model addition and subtraction problems, including repeated addition. Objects can be arranged in arrays to represent repeated addition number sentences.	Every number line starts with zero. Numbers decrease to the right or up and increase to the left or down on horizontal and vertical number lines respectively.
Knowledge Connections
Prior Knowledge	Leads to
Count forward, without objects (1.N.1.5) Locate a given whole number up to 20 on an open number line (1.N.1.8). Represent and solve problems using addition and subtraction with sums and minuends of up to 10. (1.N.2.1)	Represent whole numbers up to 100,000 on a number line (3.N.1.1). Represent multiplication facts by modeling a variety of approaches. (3.N.2.1)