In this lesson, I want my students to examine sets of numbers and try to guess the relationship among the numbers. It is my hopes that students use open-discussion to determine the repeated pattern. (MP1) In a long term sense I want my students to develop fluency with operations. To create an opportunity for students to explore this concept, I demonstrate how to build on to an array. I begin by inviting students to sit on the carpet. I ask them to spread out in an open-circle, and I take a seat in the center of the circle. I then ask students to skip count by two’s starting at 2. I carefully tell students to stop counting once they make it to 20. I repeat this by using arrays. I start by taking two figures out of the jar and placing them on the floor. I ask students how many do I need to pull out next, if I was counting by 2’s. Some students say two, but some are still having a hard time seeing it from a visual stand point, so I begin to count by two’s softly to help them make the connection. After that, I continued pull out two figures at a time until I made it two twenty.
I repeat this same concept however, I write the numbers on the board for visual learners; 2,4,6,8.… and so on. After we count to 12, we stop. I ask students to start again, but this time we will start with 1 and continue until we get to 12. (1,2,3,4,5,6,7,8,9,10,11,12). I write +1 over each number that was skipped during our counting. To check for understanding, I ask.. Does anyone know why I wrote in between each number? (If we add 1 to the number before it, it will be the next number). Great! So, if I add 1 to the number, who can predict the next number? (14).
I explain to students that we will work on finding the rule for given patterns and we will be creating our own patterns for our classmates to find the rule. The pattern that is written on the board is very easy; however, I want you to show me how difficult of a pattern you can make for your classmates to find the rule.
In this lesson we will be focusing on the following Mathematical Practices:
MP.2. Reason abstractly and quantitatively.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.6. Attend to precision.
MP.7. Look for and make use of structure.
MP. 8. Look for and express regularity in repeated reasoning.
Material: Pattern Rule.docx
In this portion of the lesson, I want to check and make sure that students understand that a pattern is an ordered set of numbers or objects. The order is what helps you predict what will come next. The rule has to be followed in order for the next number to be correct. I also explain that if the number predicted is incorrect, then the entire pattern is correct; therefore, it is essential that the rule is followed.
I write the numbers 3, 8, 13, and 18 on the board. I ask students to silently observe the numbers and try to guess the rule for the set of numbers. (Students immediately answer 5). I clear up the myth that they have to say more than five. You have to be specific with the rule. You can add/subtract/multiply/divide 5. Now let’s look again. What is the rule? Add 5. Awesome! Can someone predict the next number? 23. Great! Now, I want to check to see if you guys understand what I am asking. You will work in groups to create a similar pattern, using the rule add 5. The catch is; you have to use different numbers.
My goal is to have students investigate different patterns to find rules, identify features in the patterns, and to justify the reason for those features by composing a written explanation. As students are working, I circle the room to make sure students thinking is focused on the intended purpose of this activity.
In this portion of the lesson I want students to give it a go on their own. I ask them to move back into their assigned seats, so that they can create their own patterns, choosing numbers 1-100. I carefully explain to stick with smaller numbers if they are having trouble detecting the pattern rule. As students are working, I ask them what the number pattern is. How do you know? What number is being added? Can you illustrate this concept? Explain?
I encourage struggling students to use a number line. I give them a blank number line and ask them to select any number that they want. We then proceed to write that selected number on the number line. I ask them to put five indentations after that number to write the next number. For example,( 19)I explain that they should begin 19, continue counting the indentations and write the number that comes after the last indentation, which is 23. I continue to monitor, and I am amazed at how students are progressing on making their own pattern. After all students correctly make a rule for add 5; I explain that they will create more difficult patterns in their independent practice. However, manipulative and number lines will be provided for those that will need additional assistance.
Materials: Blank Number Lines.docx
The students are given a worksheet that contains two blank number lines. Each student is given a set of counters. The students are given a rule for a number pattern and asked to illustrate the rule on the number line. The first rule is add 7 and the second rule is subtract 3. Each student is given a different starting number. The students are asked to continue until their number line is completed. The bottom portion of the worksheet will be used to determine is students can determine the rule for a given set of numbers and determine what comes next in the pattern. The students performed exceptionally well on the assignment.
I encourage students who finish early to use the additional line on the paper to create other pattern. However, I want them to take time and explain the concept in their math journals. I use their response to determine if a high- level of understanding has been reached, or if they need additional practice on this objective.