Workshop: Addition

Est. Class Sessions: 2–3

Developing the Lesson

Part 1. Palindromes and Addition

Find Palindromes. This activity provides a fun context for practice with addition as students explore palindromes. A palindrome is a number, word, or phrase that reads the same forward and backward—22, 121, 8448, and 32123 are examples of number palindromes. Refer students to the Workshop: Addition pages in the Student Guide. Discuss the examples of palindromes that Professor Peabody gives and ask students to give several of their own examples of palindromes in Question 1.

In Question 2, students are asked to find all the palindromes in the chart on the Palindrome Recording Chart page in the Student Activity Book. Students will select a color for the key and color in the palindromes accordingly.

Once students have identified all the palindromes, display the Palindrome Recording Chart page. Have the class look at and describe the chart.

Ask:

Where does the chart start? (0)
Where does it end? (99)
Do you notice any patterns? (Multiples of 10 are on the left. When you move from row to row you move ten. The palindromes are on a diagonal starting at zero.)

Display the 200 Chart page from the Student Guide Reference section.

Ask:

How is the palindrome chart different from a 200 Chart? (The chart starts and ends at a different number; multiples of ten are on the other side of the chart.)
How is the chart similar to the 200 Chart? (When you move from row to row you move ten. The numbers are in order with the smallest at the top and largest at the bottom.)

Find Multistep Palindromes. As described in the Student Guide after Question 2, the number 134 is not a palindrome. However, by doing some addition, a palindrome can be created from 134. Use the two examples in the vignette to describe how to find multistep palindromes. Once students understand the process, tell them to identify the different kinds of multistep palindromes on the Palindrome Recording Chart.

All the numbers 1–100 are palindromes in 6 or fewer steps except for 89 and 98. It takes 24 steps to convert 89 and 98 into palindromes! The resulting palindrome is 8,813,200,023,188. You may want to tell your students to skip those two numbers or make it a challenge problem. You also may want to make calculators available for this problem.

Since a major goal of this activity is to develop fluency with addition, students should solve the problems without a calculator. You can call this a “dead battery day.” Students can refer to the strategies on the Addition Strategies Menu page in the Student Activity Book as they are working.

This activity creates an opportunity for students to work at their own pace and get as far as they can through an activity. Expect students who are more confident with addition to identify all or most of the palindromes from 1–99. Students who need more practice with addition should be encouraged to find addition strategies that work for them and to get as far as they can in their search for palindromes. To encourage further practice, students could be given several days to complete the chart.

Students who are having trouble with multidigit addition should use strategies that are conceptual: base-ten pieces, expanded form, or mental-math strategies. See the Workshop Menu in the Using Different Methods section of the Student Activity Book.

As students begin filling in the Palindrome Recording Chart, they will see patterns and may use the patterns to find various shortcuts for filling in the chart. Encourage them to make predictions based upon the patterns.

Once students have gotten as far as they can on the Palindrome Recording Chart, ask students to describe the patterns they see in the chart using the following discussion prompts:

Describe the patterns on your palindrome chart.
What do you notice about the diagonals on the chart? (Every number on a diagonal is the same type of palindrome unless the number is a palindrome. See Figure 2.)
Why do you think that pattern is there? (The number and the number written backwards are on the same diagonal. For example, 19 and 91 are on the same diagonal and therefore would take the same number of steps to make it into a palindrome.)
Did you use the patterns to help you complete the chart? If so, how?