Palindromes

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Objective

SWBAT determine if a sum created from adding two numbers together creates a plaindrome to find a pattern on a 100 chart.

Big Idea

Students use addition skills and knowledge of properties to find sums that result in a palindrome when two numbers are added together.

Introduction To Palindromes

10 minutes

To introduce students to palindromes (words, symbols, numbers, phrases things that are the same going forward or backward), I first provide students with a list of words to look for patterns including April, May, mom, pencil, radar. 

I ask the students which words are palindromes? After some discussion and reasoning, many students are still unable to explain a palindrome. Many of the explanations I hear include information about proper nouns and capital letters.  I remind the students that palindromes have patterns, and I ask them to think about consonants and vowels in these words.

This results in one of my students saying a palindrome must be like the math property for adding in any order. This is when the students are able to identify the palindrome words mom and radar, recognizing they are the same when they are read forward and backward.

I present this lesson during the middle of April when the dates create palindromes, such as   4-18-14.  I want the students to see these patterns in real world examples.

Mini Lesson

10 minutes

I explain to the students they will be finding palindromes on the hundred chart by repeatedly adding the palindrome of a given number until the resulting sum is a palindrome.  

To begin, I have the students look for numbers on the chart that are already palindromes. For example, the number 1 is a palindrome because it is the same forward and backward. Other examples include 33, 44, and all other doubles.  I have the students color these numbers yellow. 

Next, I have the students look at the number 12.  Since it is not a palindrome, I explain to the students to add the numbers in reverse to 12.  Students add 12 + 21 = 33.  Thirty three is a palindrome, but it took one additional step to create a palindrome.  Twelve is colored orange. Other numbers with single step palindromes are 32, 14, and 45.   

Then I have the students analyze the number 57.  It is not a palindrome, so we add 75 to 57.  57 + 75 = 132.  132 is not a palindrome so we add 231.  132 + 231 = 363.  There are two addition steps, so this is two-step palindrome. This one is colored pink.  

Finally the students are given the directions to look and solve each number on the 100 chart.  They will need to decide if it is already an palindrome, or begin adding to determine how many additional steps are needed to create a palindrome.  

Below is the color chart I used for this lesson.  The colors can be varied to fit your own preferences. 

Yellow - already a palindrome

Orange - one addition step to create a palindrome sum

Pink -  two addition steps to create a palindrome sum

Green - three addition steps to create a palindrome sum

Blue - four addition steps to create a palindrome sum

Purple - five addition steps to create a palindrome sum

Red - six addition steps to create a palindrome sum

Working On Palindromes

30 minutes

This is a multi-day activity, or it can be completed as needed when another lesson is complete and you are waiting for other students to finish. 

The students use whiteboards for adding, or they can use scratch paper.  Some students will be quickly realize two-step palindromes do not involve regrouping.  A reminder to the students to be deliberate in considering how to determine how many addition steps are required before they start (count the addition signs). Some students in my class want to color columns and modify the activity to be odd and even patterns.  

Examples of completed charts are available online as well as lists of how many steps needed to create a palindrome..  Number 89 and 98 are the most complex palindromes consisting of 24 steps to create a palindrome.  In this lesson the students are only looking for palindrome of more than 6 steps. It may be an opportunity to challenge students to determine how many steps are required for these two numbers.