In this case the teacher is helping students recognize and understand the importance of variables, constants, and coefficients and students are doing an activity involving pattern blocks, visualizing actual changes, and formulating a rule as an equation for unknown terms based on the patterns they observe.

In this case the teacher is striving to increase algebraic awareness with his students and students are involved in an activity using manipulatives and writing expressions and equations to a real-life problem.

This case shows a teacher supporting small groups of students as they conduct science experiments and analyze real-world data, and students exploring slope-intercept, standard, and point-slope forms.

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 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 leading a class discussion on fractions, decimals, and percentages using a concept splash, and students providing real-life examples that explore the relationship among the concepts.

In this case the teacher is assisting students in exploring and solving systems of equations on a worksheet and students are working through the problems in small groups, identifying systems that have no solution or infinitely many solutions using different strategies.

This case shows a teacher supporting student investigations of Sierpinski's Triangle, and students using measurement tools to create precise drawings, explore number patterns, and develop an understanding of the relationship between geometry and algebra.

This case shows a teacher asking questions and guiding small groups of students in exploring systems of linear equations, and students collecting and plotting data, drawing a line of best fit, and analyzing the information.

In this case the teacher is facilitating a discussion about a "Garden Border Problem" and is helping students analyze several different methods of finding how many square units make up a border and students are reasoning abstractly and quantitatively, engaging in discourse and reasoning with peers.

In this case the teacher is challenging students to write and solve word problems using equation manipulatives and students are practicing how to solve real-life problems by assessing and writing algebraic equations.

In this case the teacher is facilitating small groups of students to help them make decisions about which operations they need to conduct and students are using their reasoning skills to solve word problems on percentages, verifying their solutions with each other, and monitoring their own work in light of the ideas of their group members.

This case shows a teacher working very effectively with lower ability students on linear equations and students engaged in using manipulatives and math discourse to understand the new concepts.