Students will demonstrate the concepts and skills related to growing linear patterns 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.
• 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. 
• 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. 

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, we will be presenting the following numerical patterns, one at a time. For each pattern, we will be asking students what number comes next, extend the pattern to 10 terms and how can you determine any number in the list?

Students are encouraged to turn and talk before sharing their responses with the larger group and justifying how they know.

This number talk can be facilitated in a no tech fashion by simply writing the list of values on the board or by leveraging the visual number talk prompt videos and sharing with a projector.

If you plan on using the visual number talk prompt videos to make this process as visual as possible, begin playing the video and be prepared to pause where indicated.

Students will first be prompted to think about:

What number comes next?

Although it doesn’t say this in the video, you should be asking students to turn and talk to justify why they think so.

At this point, students will see that we are identifying the first 5 values in the list as the first 5 terms in the relationship.

Then, be ready to pause when students are prompted with:

What is the 10th number in the list?

Ask students to think independently first – without the use of a calculator – and to craft a written argument on their whiteboard or on a piece of paper.

Give students the opportunity to turn and talk to share with their elbow partners or group members while monitoring the different strategies students are using.

Which students skip counted by 4 to get to the 10th term and extended the list or table?
Which students noted that they can craft a linear pattern rule to help them arrive at the answer?

Note that just because a student uses an additive thinking strategy such as repeated addition or skip counting to reveal the value for the 10th term, this does not necessarily mean they are limited to this strategy.

After revealing that the 10th term is 55, students will be prompted with:

How can you determine any number in the list?

As the facilitator, you should be aware that this is simply another way of asking students:

What is the pattern rule?

At this point in our patterning and linear relationships learning journey, some students may stick to a verbal description of the pattern rule while others may resort to developing an algebraic equation.

Facilitator note:

This is the point in the visual number talk where we can discuss the important of the term numbers in our relationship. You may (or may not) have noticed that we explicitly identified the term and term number in the relationship in order to avoid confusion when determining an initial value. Since these patterns are shared without context, deciding which term is the initial value is in the hands of the mathematician. You may or may not want to give students this pattern without the terms identified to see the variety of equations they come up with to note that any term can be thought of as the initial value and an equation can be crafted to suit.

In this case, if we are noting that the first value in the list is “Term 1”, then students will need to reveal what comes before Term 1 to identify the initial value.

Students who share a pattern rule in words might say:

The pattern begins at 15 and increases by 4 each term.

While students who craft an equation might come up with:

V = 15 + 4t

Consider asking different groups of students to make predictions for different terms and different term numbers to provide an opportunity to substitute into the equation and solve for the unknown variable.

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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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