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Teacher's Guide: Part 3: Introduction - "Don't lose your head over this!"

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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

Setting:

Keisha is shocked out of her socks and Max reels with fright! Green, slimy, headless mannequins confront them as they round the bend. Realizing they’re just dummies, the two investigate the scene and observe a light pattern over certain dummies. Each dummy is numbered 1 to 18 and they light up in a sequence 1-3-6-10…, which is repeated. Nearby there is a keypad containing the set of numbers 1 to 18. A quick attempt to solve the sequence is thwarted as Keisha realizes that they’ve been gone a long time. She’s late! “Hurry up, Max, I have to go!” says Keisha – words that will return to haunt her. Back at home, the same picture and light sequence appears on Keisha’s computer. Astounded that the alien found her computer address, the two friends ponder the sequence, and use addition to try a pattern. It does not work. Eventually they discover that the sequence is 1-3-6-10-15.

Standards:

Identify, describe, and extend geometric and numeric patterns into growing and shrinking patterns.

Objectives:

Students use their number sense to identify and extend a pattern.

Students will have an intuitive introduction to a pattern that is referred to in mathematics as triangular numbers.

Materials:

Prepare student copies of the activity sheet, “Don’t Lose Your Head Over This!” (.pdf file) and an overhead transparency, if desired.
Download PDF Activity Sheet | Get Acrobat
A Printable version of this activity sheet is available in PDF format.
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You can find out if you need it by clicking on the PDF link.

Consider supplying manipulatives such as tiles, disks, or paper pieces that can be moved to create a pattern.

Mathematically Speaking:

Students can explore number sequences using manipulatives. Using tiles, have students create the numbers 1 and 3. The numbers 1 and 3 can build an array that is in a triangular form. Students should discover that to make the next triangle in the sequence, they add a row at the bottom that increases by 1. When they form this picture of 1-3-6, they may realize that this is the array used to set up bowling pins. As they add the next row, the total comes to ten. Adding one more row will solve the missing number in the pattern.

What Is A Number Pattern?

Using the problem from the activity sheets, ask the students what the next two numbers are in the following sequence:

2, 4, 6, __ , __

Answers to this question are interesting and help develop the concept of pattern. Some students will say the next two numbers are 8 and 10 and the pattern is the sequence of even counting numbers. Still, others may say the next two numbers should be 10 and 16 because 2+4=6, 4+6=10, and 6+10=16. Yet another group might see the next two numbers as 12 and 24 because 2+4=6, 2+4+6=12, and 2+4+6+12=24.

In order to have a pattern, the numbers must follow a rule. In all four answers there was a rule. The first was the set of even counting numbers ... the second the sum of the two previous numbers … the third the sum of all preceding numbers.

In order for a sequence to be a pattern there must be predictability. Given a sequence, you can describe or write a rule that will determine the next term in the sequence and so on.

Also note that having three numbers in a sequence still allows for a number of correct answers, but adding the fourth number limits the possible correct answers significantly.

Background Information:

Students should have previous experience with number sequences and their variations. They must be familiar with the idea that a value may seem to give the next term in the sequence, but must be tested to be sure it fits the conditions. Sometimes the next term in the sequence can be predicted if students can justify the entry with a rule that works.

Vocabulary:

The XY Encounter, Part 3 lays the groundwork for introducing:

operation terms

sequence triangular numbers

patterns