### ACTIVITY 1: What do consecutive numbers have in common?

**Grades:**4–6

**Purpose:**To use consecutive numbers to learn to make generalizations.

**Materials:**pencil and paper

**Time Needed:**20 minutes

- I divided the class into groups of four and wrote the following sets on the board:
- Set 1: 1 2 3 4
- Set 2: 8 9 10 11
- Set 3: 42 43 44 45
- Set 4: 19 20 21 22
- Set 5: 77 78 79 80

- I went on to say, "When I examine these sets, I notice that when I subtract the first number from the last, I always get 3." Then I asked groups to check to see if this was true for all the sequences. While students talked this over, I wrote the generalization on the board: "The difference between the first and last numbers in a sequence of four consecutive numbers is always 3." Students agreed that this statement was correct.
- I then gave these instructions to groups: "See what else you can say about all sets of four consecutive numbers. Write sentences to describe your generalizations."
- After students worked for about 15 minutes, I asked each group to choose one person to read one of the group's generalizations. I added: "I'll go around the room. Each group will report just one conclusion on a turn. Listen carefully because I want you to read one that hasn't been reported."
- After each group read a statement, I asked the other groups to check to see if it matched one they had written and to talk about whether they agreed with it.

### EXTENSION ACTIVITIES

Ask students to try these explorations in which they'll practice making generalizations.- What can you say about any 2-by-2 array of numbers on a 0-99 chart? What about a 3-by-3 array?
- What can you say about any three diagonally adjacent numbers on a 0-99 chart?
- Try problems 1 and 2 using numbers on a calendar instead. Do your generalizations still hold? Why or why not?

### YOUR RESOURCES

*by Marilyn Burns, distributed by Cuisenaire. For more ideas on consecutive sums, try the extended activity "The Consecutive Sums Problem" that appears in this book.*

**A Collection of Math Lessons from Grades 3 Through 6**