Students will demonstrate the concepts and skills related to linear patterns and negative integers that they have developed through this contextual learning experience.

The purpose of this assessment is for students to demonstrate their understanding of the following big ideas.

• Patterns can be extended because they are repetitive by nature.
• Pattern rules are generalizations about a pattern, and they can be described in words.
• One common use of linear patterns is predicting future events.
• A pattern can be extended to make a prediction. 
• For far predictions, calculations are required for efficiency. 
• In a growing pattern, the values increase and the rate is positive. 
• In a shrinking pattern, the values decrease and the rate is negative. 
• In a linear pattern, the values increase at the same rate.
• The rate can be determined by finding the difference between the value of two terms through subtraction.
• The order in which integers are written in a subtraction statement matters because the commutative property does not hold true.
• Constant difference refers to the idea that the difference between two numbers does not change after adding or subtracting the same quantity to both numbers. 
• The initial value in a linear pattern is the constant.
• When the initial value is not zero, the relationship between the two variables is not proportional. 
• Graphical representations of linear growing patterns appear as straight lines.
• The initial value in a linear pattern is the constant.
• When the initial value is not zero, the relationship between the two variables is not proportional.

The independent assessment will allow students to demonstrate concepts and skills related to the following learning goals: 

• I will make predictions about linear patterns.
• I will determine the rate and the initial value. 
• I will extend linear patterns.
• I will represent linear patterns.
• I will describe pattern rules in words. 
• I will describe contexts involving a negative rate and/or initial value. 
• I will determine the general term and apply it.
• I will subtract negative integers. 

Students might write and/or model their answers independently. Students can also be interviewed by their teacher. 

An alternative assessment opportunity should be offered if this tool will not successfully capture what the student knows, understands or can do.

In today’s math talk, present the following graphical representations of patterns one at a time. For each pattern, ask students to create a context, describe the pattern rule in words, extend the pattern to 6 terms, and predict the value of the 15th term. Students are encouraged to turn and talk before sharing their responses with the larger group. When asked to determine the value of the 15th term, students should justify their answer. 

Pattern 1: (0,30), (1,28), (2,26), (3,24), (4,22), (5,20)

Show students the following visual math talk prompt and be prepared to pause the video where indicated:

Students will be prompted with:

A snail is climbing down a wall starting at a point 30 feet above ground level. It moves at a rate of -2 feet per hour.
What height will it reach after 6 hours?
…15 hours?

In this first visual number talk prompt, we are providing students with a positive initial value and a negative rate of change.

Allow students to leverage any models they feel most comfortable with to determine the height of the snail after 6 hours and 15 hours.

At this point, we are encouraging students to leverage tables, graphs and equations where possible. If a student is only leveraging one of the models, encourage them to represent using another model to add that tool to their repertoire.

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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