In this lesson you will be having your students record the number of steps it took to reach each palindrome on a chart. This creates a chart where students model with mathematics or MP4. It is a continuation from Palindrome Patterns Part 1. This will give your students a visual representation (MP4). There are rarely any problems with this lesson but it brings out another way for students to look at numbers and discover patterns. You will need to have the student completed Palindrome Recording Chart and the Palindrome Recording 100's Chart.
If you are starting this lesson on another day - and not continuing right away from Palindromes Part 1 - you will want to have a question for your students to get them engaged and link to previous day's lesson. I would ask my class something like, "What do you remember from yesterday's Palindrome lesson?" or "Did you notice any palindromes since yesterday's lesson?" Because today's lesson is about discovering patterns in the steps it took to create palindromes I want to have my final question focus on this. You could ask your students to get out their Palindrome Recording Charts and see if they can discover any patterns in the number of steps and finding palindromes. If they don't you can tell them you are going to help them find some by creating a visual model of the number of steps it takes to create a palindrome from each number they used. When you do this with your students you are reinforcing MP8 where "students look for and express regularity in repeated reasoning."
The next part of the lesson can be done in pairs, groups or individually. Because I use this lesson to build collaboration in my classroom I allowed my students to work in groups of 3 or more. I didn't assign groups because I want to see who is included and who is being left out.
Have your students color in the number of steps it took to reach a palindrome for each number on the 100's chart. You can have your groups of students choose the colors (another group collaboration building strategy) or have them use the colors I have on the Palindrome Recording 100's Chart Answers.
Students must reflect on activities to increase comprehension, critical thinking and retention. It is also a place for you, as their teacher, to check for understanding or misunderstandings.
It may have taken many math periods for all students to finish these two lessons. It took my class two days to find the palindromes and then one day to transfer the number of steps to the chart. During this time I also had students reflect on how they were progressing through the lesson. Groups who were progressing quickly shared tips and groups who were working slower looked at why they were having problems - other students responded with helpful tips.
When all students are done I asked them to share how they divided up the work, if they did. I also asked if they changed the way they were working on the problem at some point.
My next question lead students from the group behavior and problem solving to the academics, "How did your group color the one-digit numbers?" There is no wrong answer but I am looking for their process and an appropriate explanation.
Next focus on the academics by asking if students noticed any patterns that emerged on the chart. I would have already had students looking for patterns and writing them down on the back of the sheet as they finished.
A couple of patterns they might see would be if the sum of the digits add up to less than 10, the number is always a one-step palindrome. Another is that all palindromes are multiples of eleven. There are many more!
This lesson sticks with students for a long time. Here is a former 5th grader who is now in high school! He still remembers working on the lesson and the amount of math it took to find 89 and 98.