PBS Teachers™

XY Encounter

Funded by the US Department of Education

Teacher's Guide: Part 3: Pause Point 2

Watch Video Clips @ XY Encounter Streaming Video Page

Map of Teacher's Guide	Part 1	Part 2	Part 3	Part 4
	Introduction	Introduction	Introduction	Introduction
	Pause Point 1	Pause Point 1	Pause Point 1	Pause Point 1
	Pause Point 2	Conclusion	Pause Point 2	Conclusion
	Pause Point 3		Conclusion
	Conclusion

Key Phrase:

At the computer, Keisha explains to Max, “It’s a sequence. The
numbers are forming some kind of pattern. The alien wants us to
find the next number in the sequence.” [End of clip 2.]

Encourage students to use manipulatives to determine what might be the next term in the pattern 1-3-6-10. Have students share their solutions. Attempt to have students discover the triangular shape.

Have students look at part 6 of activity sheet “Don’t Lose Your Head Over This!” (.pdf file)
Download PDF Activity Sheet | Get Acrobat
A Printable version of this activity sheet is available in PDF format.
This requires a free plug-in, Adobe Acrobat Reader.
You can find out if you need it by clicking on the PDF link.

This section will only have numbers on it, giving room for the student to explore with manipulatives, then sketch a diagram of their solutions as shown in Figure 6.

Lead the students to “test” the sequence by comparing the first term to the second and asking, “How did I get from 1 to 3?” [Add 2] “How did I get from 3 to 6? [Add 3] “How did I get from 6 to 10?” [Add 4] “What should I do next to continue the pattern?” [Add 5. Note that this sequence of numbers can be represented in triangular form. We call them triangular numbers.] Triangular numbers can also be generated by the formula n(n+1), where n is the number of the term in the sequence.

Figure 6