In this case the teacher is using post-its with positive and negative rational numbers and students are working together to place each one on a number line, converting the numbers to different forms, and then using sentence stems to explain their decisions.

This case shows a teacher leading a class discussion and supporting students in seeing patterns involved in combining positive and negative values, and students creating or defining a rule in their own words.

This case shows a teacher supporting the conceptual understanding of real numbers, and students extending their thinking by answering and asking questions, and hearing other students' approaches to problem solving.

This case shows a teacher role-playing as a leader from another planet to engage students in a discussion about the use of manipulatives for counting and re-grouping simple problems in order to understand how to count in base six.

In this case the teacher is engaging students in an activity using manipulatives to help them distinguish between rational and irrational numbers and students are working together to place equivalent rational and irrational numbers on their number lines, sharing their placements with others to learn about common misconceptions and errors.

This case shows a teacher supporting the development of higher-order thinking skills through class discussion on finding percentages, and students engaging in mathematical reasoning and problem-solving.

This case shows a teacher leading a discussion to support mathematical understanding, thinking, and reasoning, by engaging students to think deeply, make sense of information, and communicate effectively about fractional equivalents and the multiplication of fractions.

This case shows a teacher using a stock market simulation to engage her students in fraction and decimal concepts and students using problem solving skills and higher order thinking to make connections between fractions and decimals, using discourse and academic conversation.