During the author's everyday math discussions with her class, young children talk about mathematical ideas, theories, and concepts within a predictable structure. These discussions include many concepts from--and beyond--the first-grade math curriculum, and their depth and complexity build throughout the school year. Concepts and skills include exploring number patterns on a cumulative number line, place value, graphing the weather and temperature, reading the calendar, making arrays, using a tally, and learning about odd and even numbers. Students engage with ideas and participate in lively discussions about mathematics. Many opportunities arise for differentiation. This article presents how first graders can learn to routinely theorize and explain their thinking about odd and even numbers, factors, multiplication, and skip counting. A bibliography is included.