Expanding on the first-grade math curriculum using insights from the newly uploaded document, we can refine and add some specific instructional strategies and standards to address more mathematical concepts. Below are the additional components for the first-grade curriculum:

6. Understanding Addition and Subtraction Properties

• Objective: Students will explore the properties of operations, specifically focusing on the commutative, associative, and identity properties of addition.

• Activities: Engage students in hands-on activities using blocks or other manipulatives to demonstrate that the order of addition does not affect the sum (commutative property), how grouping affects addition (associative property), and adding zero (identity property).

• Standard: This addresses specific properties of operations as outlined in the document .

7. Using Mathematical Practices in Problem Solving

• Objective: Encourage students to use different mathematical practices to enhance problem-solving skills.

• Activities: Activities that encourage students to make sense of problems, reason abstractly, and communicate their reasoning. This could include simple word problems where students need to choose the best operation and explain their choice.

• Standard: Emphasizes the use of SMP1, SMP2, SMP3, and SMP6 as described in the document for engaging students in mathematical thinking .

8. Developing Number Sense Through Play

• Objective: Develop number sense and understanding through interactive play and exploration.

• Activities: Use games like "dot talks" where students quickly see and count dots to encourage subitizing, and ten-frame activities to develop quick recognition of number patterns and relationships.

• Standard: Supports developing a strong number sense foundation as students engage with numbers in meaningful contexts, relevant for first grade as outlined in the document .

9. Engaging with Numbers Up to 120

• Objective: Expand students' ability to count, understand, and operate with numbers up to 120.

• Activities: Counting collections where students practice counting various items up to 120, use number lines, and participate in skip counting activities.

• Standard: Aligned with 1.NBT.1, focusing on counting and understanding numbers to 120 as mentioned in the document .