In this case the teacher is facilitating a jigsaw activity on ratio word problems and small groups of students are solving problems using bar models and are responsible for knowing their unique solutions so they can teach their problem to a new group of students.

In this case the teacher is facilitating students calculating ratios and unit rate based on beads in bracelets and the students are creating models to become familiar with the differences between rate and unit rate.

In this case the teacher is helping students develop a wall dictionary to build academic vocabulary about proportional relationships and students are defining and describing the relationships among graphs, tables, and equations, sharing their understanding with their peers in order to create ownership of the terms.

In this case the teacher is helping to bridge students' previous knowledge regarding ratios to new understanding incorporating proportional reasoning and students are working on a student response sheet in groups, discussing various strategies for creating tables using the given ratios and tiles.

In this case the teacher is helping students understand linear equations that model sets of data points and students are engaged in a hands-on activity where they are listening to each other, referring to their charts and scatter plots, and reasoning through the problem in order to understand their data.

This case shows a teacher meeting with groups to discuss their design for water filtration systems and students discussing various options for their designs.

In this case the teacher is guiding students in comparing and discussing various representations about confidence levels and students are analyzing strengths and weaknesses and formulating conjectures about three work samples they are studying.

In this case the teacher demonstrates a pressure experiment to engage students in the inquiry process and students then design their own investigation to explain pressure and volume relationships, creating hypotheses, testing them, modifying their designs, analyzing data, and finally communicating their findings to their peers.

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.

In this case the teacher is engaging students in an investigation that focuses on the money raised from a walk-a-thon and students are creating tables that represent linear relationships between distance and money, writing representative equations, determining rates of change, and answering questions about their analyses.

In this case the teacher is facilitating mathematical discourse amongst her students who have just explored a real-life, multi-step ratio problem with multiple solutions and students are discussing their strategies, comparing and contrasting them with their classmates.

In this case the teacher is facilitating discussion amongst student groups as the students do an activity and simulation investigating probabilities between 0 and 1, engaging in mathematical discourse, and learning correct vocabulary to describe what they see.

In this case the teacher is facilitating group work to help students understand how ratio and rate are related and students are working together to discover how ratio and rate can be determined from a grocery sales ad, justifying their work with each other.

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.

In this case the teacher is facilitating students in discovering how to find equivalent ratios and students are sharing their conjectures with the whole class, using evidence, justifying their thinking, and critiquing the reasoning of others.

In this case the teacher is focusing on proportionality and reasoning about relationships among shapes and students are engaged in an activity using several similar squares, creating cups and origami hats using linear dimensions of the squares to further explore volume and size relationships.

In this case the teacher is assisting students in learning how to use ratio reasoning to solve real-world problems and students are engaged collaboratively, making connections and using logical thinking in the activity they are working on while also bringing to light a misconception they all shared about the topic.

In this case the teacher is engaging students in a cooperative learning strategy that encourages cooperation and competition and students are playing a game about equivalent ratios and rates, competing with other groups, strategizing and solving real-life problems.

In this case the teacher is introducing students to assumptions, applications, and vocabulary of the divider-chooser method of division and students are exploring this idea, sharing and explaining their choices and representations with their peers.

In this case the teacher is assisting groups in an activity to understand and visualize ratio relationships and students are using manipulatives to compare ratio lengths, constructing viable arguments and critiquing the reasoning of others.