This microcredential represents a teacher’s understanding of early number concepts, their ability to plan appropriate learning trajectories, implement effective teaching practices to help students understand and use these concepts, and use/analyze formative assessments to determine where students are in learning trajectories. (Early number concepts include, but are not limited to: non-quantified comparisons, containment, notions of quantity and measurement, one-to-one correspondence, cardinality, meaningful counting, and ordinality, composing, and decomposing whole numbers). This microcredential is the first of five in the Elementary Mathematics Endorsement: Numbers and Operations Stack. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of fluency and their ability to understand and support students in building procedural fluency from conceptual understanding over time. This includes planning and implementing instruction and assessment to support fluency in mathematics based on current fluency related research, as well as using and analyzing formative and summative assessments to determine where students are in building procedural fluency from conceptual understanding. This microcredential is the fifth of five in the Elementary Mathematics Endorsement: Numbers and Operations Stack. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of whole number addition and subtraction. It includes their ability to understand and respond to learning trajectories related to whole number addition and subtraction, including conceptualizations, problem types, properties, strategies, and representations, by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It also involves selecting, using, and adapting mathematics curricula and teaching materials, including the integration of mathematical tools and technology, as well as using and analyzing formative and summative assessments to determine where students are in learning of whole number addition and subtraction. This is the third of five microcredentials in the Elementary Mathematics Endorsement: Numbers and Operations Stack. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of place value concepts, as well as their ability to plan appropriate learning trajectories, to implement effective teaching practices that help students understand and use place-value concepts, and to use and analyze formative assessments to determine where students are in learning trajectories. This microcredential is the second of five in the Elementary Mathematics Endorsement: Numbers and Operations Stack. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of whole number multiplication and division. It includes his/her ability to understand and respond to learning trajectories related to whole number addition and subtraction, including conceptualizations, problem types, properties, strategies, and representations by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It also involves selecting, using, and adapting mathematics curricula and teaching materials, including the integration of mathematical tools and technology, as well as using and analyzing formative and summative assessments to determine where students are in the learning of whole number addition and subtraction. This microcredential is the fourth of five in the Elementary Mathematics Endorsement: Whole Number Multiplication and Division Stack. These microcredentials can be earned in any order.

Graham Fletcher illustrates how a student progresses through understanding early number concepts to counting. The conceptual and representational domains are focused on heavily.

These eight mathematics teaching practices provide a framework for strengthening the teaching and learning of mathematics. This research-informed framework of teaching and learning reflects the current learning principles as well as other knowledge of mathematics teaching that has accumulated over the last two decades. In essence, these teaching practices represent a core set of high-leverage practices and essential teaching skills necessary to promote deep learning of mathematics.

The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

The Utah State Board of Education adopted the K-12 Utah Core Standards for Mathematics in January 2016. Core guides provide a description of the Core Standards, including concepts and skills to master, critical background knowledge and academic vocabulary. The course overview documents show the major work of the grade level and the coherence of content across grade levels.