In this case the teacher is facilitating discussion about the rules, meanings, and correct mathematical vocabulary behind adding mixed numbers and students are creating and defending their arguments concerning what two mixed numbers could be added to arrive at a sum of 10 7/8.

This case shows a teacher effectively helping students understand how to represent fractions with unlike denominators and students fully engaged in an activity using fraction cubes and mathematical reasoning as they communicate their thinking to each other.

This case shows a teacher working with students on scale factors of models and students engaged in an activity where they explain their reasoning for specific scale factors using fraction skills.

In this case the teacher is facilitating a lesson involving undefined slopes and fractions and students are developing a conceptual understanding of these by trying to figure out what a 4/0 pizza would look like, sharing and discussing their ideas and solutions.

In this case the teacher is facilitating small groups using computer software to learn more about fractions and students are thinking and reasoning abstractly while trying to develop multiple strategies to solve a real-world problem on area, ultimately developing a formal algorithm for adding and subtracting fractions.

This case shows a teacher working with students engaged in a pattern block activity and students modeling relationships between parts and whole pattern blocks and communicating their methods.

This case shows a teacher using M & M's as manipulatives to teach about fractions and students engaged in modeling different strategies to multiply fractions and determine specific patterns.

In this case the teacher is helping students apply operations with fractions to real-life problems and students are using manipulatives to solve problems involving parts of a part and parts of a whole, presenting solutions to the class, and developing their mathematical thinking.

In this case the teacher is working with small cooperative groups to deepen their understanding of division of fractions and students are using manipulatives as concrete visuals to fold, cut, shade, and compare fractions.

In this case a math specialist is guiding students in the use of pattern blocks to discover the ratio identity of fractions and students are using abstract and concrete modeling to build understanding of the relationship between whole numbers and fractions.

In this case the teacher is working with groups of students studying fractions and students are using prior knowledge about fractional parts of a whole, modeling problems with manipulatives, applying their knowledge to solve problems and constructing viable arguments supporting their answers.

In this case a teacher reviews and discusses standards of good listening, viewing, and speaking skills and students practice these skills in a "Fraction Art Gallery Walk."

This case shows a teacher demonstrating effective questioning skills with student groups in his class while they are engaged in a fraction activity and students effectively using number lines and fraction tiles to compare and order fractions on a number line.

This cases shows a teacher adeptly facilitating mathematical discourse to teach about fractions and students using visual representations to figure out how to share pizza slices equitably.