6.6

Math6th Grade

Knowledge and Skills Statement (Standard Cluster)

The student applies mathematical process standards to use multiple representations to describe algebraic relationships

Texas Essential Knowledge and Skills for Mathematics

Cluster contents

6.6 is a knowledge and skills statement. These are the student expectations under it.

Teacher's field guide

What Students Need to Do: Students decide which quantity is controlled and which quantity changes because of it. They connect a situation, table, graph, equation, and verbal rule. They write equations for constant-rate patterns and patterns with a starting value.
What Mastery Looks Like: Students correctly label inputs as independent and outputs as dependent. They use a table to write an equation and graph ordered pairs accurately. They can explain how the equation, table, graph, and situation show the same relationship.
Common Misconceptions: Students may switch the independent and dependent quantities or place them on the wrong axes. They may confuse the rate k with the starting value b. Some assume every table is proportional, even when the output has a nonzero starting value.
How to Assess It: Give students the pairs (0, 3), (1, 4), and (2, 5). Ask them to label each quantity, write the equation, and sketch the graph.

Lesson moves

Have students stack linking cubes, recording stack number and total cubes, then create a table, graph, equation, and verbal rule.
Ask students to explain in writing how changing the independent quantity affects the dependent quantity in a given table.
Play a matching game with cards showing situations, tables, graphs, and equations that represent the same relationship.
Use a taxi fare or hourly pay example to compare a constant rate relationship with one that includes a starting fee.

Keep exploring

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