The Challenge of Directions
Lesson 11 of 13
Objective: SWBAT use patterns to determine a rule or expression to find the nth step and create a graph to match the expression.
Students participate in a math museum (a/k/a gallery walk) activity to share their homework assignments. For homework the prior night, students determined the rule of 3 patterns and then graphed each to make comparisons. During the gallery walk students focus on their class mates graphs and rules.
• Do you notice any graphs that look different from yours?
• If you do, what could be the reason?
Since I have been pulling from many resources to target this standard, the directions are always a little different, the tables that are used are arranged differently, and the questions are phrased differently. I like this because it requires the students to think about the question before determining and entry point.
On the board, I project different pattern problems that are represented in tables. Each has similar directions, worded differently and therefore are looking for different outcomes.
At the top of the board I write "Compare and contrast these three organizational tools. There is no need to solve."
After 5 minutes we discuss these tables and talk about table and set of directions, using the prompt, "What exactly am I supposed to do here?"
I let the students know that they will continue to work with patterns today during their choice time. It is their mission to also focus on the directions to make sure they solve the problem exactly the way they are expected to.
Now You Try
There is no whole class guided practice today, because the students have been working with patterns, graphs, and expressions for an extended amount of time. The purpose of today's lesson is to allow them time to apply these skills to many different problems that are pulled from many resources.
While students work on their choice time activities, I pull small groups of students to the side table to work on using models and manipulates to solve problems. The goal of this guided practice is to help students make connections between modeling a problem, writing and expression, and solving it.
With the small group of students (grouped by ability/color group) ask the students to take turns reading a story problem out loud. Guide the students through the process of:
1. Making a bar diagram (part- part- whole model) to match the story.
2. Just one variable. Coach the students to use just one variable when a relationship between two unknowns is provided. For example, if the problem states that there are 11 red hats, and 3 more white than green, encourage the students to use w and w - 2 or g and g + 2 for the unknown parts.
3. Use tiles to "act out" the situation and determine the value of the variable.
4. Complete the bar diagram by using the expressions and value of variables.
During choice time, students have the freedom to move from station to station at their own pace. They are encouraged to attempt to solve the problems independently first, then ask a friend at the same station for help if needed. Before moving on, I ask them to compare answers and have a discussion if their answers vary.
Choices (the majority of these resources are pulled from our text book, I use them as a review at the end of the topic to help students reinforce skills).
• What is this question asking me? Students answer a variety of questions about patterns. They unpack the directions before solving to make sure they are not making assumptions about the question.
• Writing and interpreting expressions: students translate words into algebraic expressions and vis.versa.
• "Number Game" Open response question: Answers only! Students work on solving the number game open response question (this question uses a table to represent a pattern). Students answer the questions first, focus on writing is saved for another day. (This choice is a must do, because students need extensive practice in responding to an open-ended question.)
• Create your own patterns: Students create their own patterns, ask a question about it, and then solve it on the back of a page. These patterns will be used later in the year as review for finding patterns and following the directions asked.
Students complete a checklist to show the choices they have made today, this check list helps the students organize their work from today's choice time.
It is important that I check in on student progress from class today before they move on to the choice time again tomorrow.