The paper presents an analysis of elementary grade mathematics teaching in India focusing on mathematical reasoning. Mathematical reasoning is an important tool to make sense of mathematical ideas, which in turn makes mathematics more accessible to learners and promotes social equality. The paper analyzes 112 lessons from Grades 1 to 8 by 21 teachers in 5 schools in a big city in India. Synthesizing the literature, the paper identifies three main functions of mathematical reasoning (reasoning for sense-making, reasoning for inquiry, reasoning for justification) and concomitant reasoning actions. Working from these three functions of reasoning, a scheme that was suitable for categorizing the reasoning observed in the highly teacher-led instruction was developed and applied to identify the nature and prevalence of reasoning across grade levels and topics. No "reasoning for inquiry" was found in the analyzed lessons. Explanatory Reasoning, a limited form of "reasoning for sense-making" with little student input, was observed, usually in extremely short episodes, in about a quarter of lessons. Modelled Reasoning, a limited form of "reasoning for justification" where step-by-step deductive problem solutions were demonstrated, was more common, dominating lessons in some topics, especially in higher grades. In most lessons, the teacher stated rules and procedures without reason; sometimes providing non-mathematical justifications for procedures in lower grades (e.g., the need to follow arrows or use a mnemonic). The observed rarity of Explanatory Reasoning highlights an urgent need for teacher education programs in India to enhance the sense-making mathematical experiences offered to teachers so that they can, in turn, promote sense-making in their students.