This microcredential represents a teacher’s ability to understand and respond to progressions related to addition and subtraction with rational numbers, including conceptualizations, properties, strategies, and representations, by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 addition and subtraction with rational numbers. This is the fifth of seven microcredentials in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of comparison and equivalence with rational numbers and their ability to understand and respond to progressions related to comparison and equivalence with rational numbers by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 comparison and equivalence with rational numbers. This microcredential is the fourth of seven in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning Stack. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of decimal and percent concepts and their ability to understand and respond to developmentally appropriate learning trajectories/progressions related to decimal and percent concepts by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 trajectories related to fraction concepts. This is the third of seven microcredentials in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of early fraction concepts and the ability to respond to developmentally appropriate learning progressions related to early fraction concepts by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 trajectories related to early fraction concepts. This is the first of seven microcredentials in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of fraction concepts and their ability to understand and respond to developmentally appropriate learning trajectories/progressions related to fraction concepts by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 trajectories related to fraction concepts. This is the second of seven microcredentials in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning. These microcredentials can be earned in any order.

This microcredential represents a teacher’s understanding of multiplication and division with rational numbers. It includes their ability to understand and respond to progressions related to multiplication and division with rational numbers, including conceptualizations, properties, strategies, and representations, and 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 multiplication and division with rational numbers. This microcredential is the sixth of seven in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning Stack. These Microcredentials can be earned in any order.

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.

This microcredential represents a teacher’s understanding of proportional relationships and their ability to understand and respond to progressions related to proportional relationships by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes 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 proportional relationships. This microcredential is the seventh of seven in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning Stack. These microcredentials can be earned in any order.

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.