This case shows a teacher helping her students understand hexagon trains and students engaged in learning how to recognize patterns and represent the linear growth as their trains grow.

In this case the teacher is working with students to help them determine how to find the formula of a circle and students are manipulating a paper circle, cutting it into pieces, folding it or writing on it, brainstorming with each other to figure out the formula of the area of a circle using prior knowledge of the area of other shapes.

This case shows a teacher working with individual groups of students on how to determine the fat content of foods and students trying to work out the area of fat soaked into grid paper as a percentage.

In this case the teacher is discussing with the students the various meanings of the minus sign and how they are applied in algebraic and variable expressions and students are discussing examples and learning how to use minus signs appropriately when evaluating the value of a variable.

In this case the teacher is facilitating students in developing a concrete understanding of non-perfect square roots and students are using manipulatives to see differences between perfect and non-perfect squares and then determining the fractional/decimal value of the non-perfect square.

This case shows a teacher working with students on an intertidal zone marine habitat activity and students using their prior and new knowledge to place organisms in the correct tidal zone and graph the tide zone patterns.

This case shows a teacher working with groups of students while they observe and sort leaves they collected on a school trip.

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.

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 extending the knowledge of students with regards to Venn Diagrams and students are building their thinking and reasoning skills of 3-Circle Venn Diagrams in a whole class discussion, interpreting the diagrams to make connections and formulate the set notation statement.