In this activity, students encounter a diagram representing a context that has been described verbally. They then organize information from the diagram in a table and discuss how the table can help them see the pattern.

Students reason abstractly and quantitatively to extend the pattern (MP2). As students work, look for students who draw a picture, those who describe a picture, and those who rely on numerical (rather than visual) reasoning, especially for the fifth step. Invite them to share their strategies during the synthesis of this activity.

The purpose of this discussion is to highlight how organizing numbers in a table can help with recognizing patterns. Focus the discussion on how the table helped with describing the pattern. Here are some questions for discussion:

• “What is the purpose of a table?” (Tables help us organize data in order to interpret what has been observed and to recognize patterns.)
• “What are some advantages of using a table?” (Tables typically show data in columns and rows that are labeled. With tables, we can focus on a couple of numbers at a time. Tables communicate information using exact values, including decimals and fractions.)
• “What are some disadvantages of tables?” (It can be difficult to understand all the data in a table, because they can include a lot of detail. Tables don’t visually show trends in data over time.)

In this activity, students are presented with an equation that represents a relationship. They then create a table and a graph of the relationship. Finally, they consider which representation is the most helpful to answer questions about the relationship.

This activity prepares students to compare two verbal descriptions of contexts and create a table of values to use to answer questions about the contexts in the associated Algebra 1 lesson. This activity is also useful for when students analyze or create the graph of a relationship from a table in upcoming lessons.

When students explain correspondences between equations, verbal descriptions, tables, and graphs, they are reasoning abstractly and quantitatively (MP2).

In this partner activity, students take turns matching different representations of the same situations. If desired, they can also identify and create any missing representations (this would require removing some cards from the sets distributed). The practice will be helpful when students make connections between verbal and tabular representations in the associated Algebra 1 lesson. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).