Noticethat we havenotprovedArtur’s conjecture.Manyexampleshave(almost)convincedus that it is
true.
LessonSummary
In this lessonyou workedwith visualand numberpatterns.You extendedpatternsto beyondthe givenitems
and usedrulesfor patterns.You also learnedto makeconjecturesand to test themby lookingfor counterex-
amples,whichis how inductivereasoningworks.
Pointsto Consider
Inductivereasoningaboutpatternsis a naturalway to studynew material.But we saw that thereis a serious
limitationto inductivereasoning:No matterhow manyexampleswe have,examplesalonedo not prove
anything.Toproverelationships,we will learnto usedeductivereasoning,also knownas logic.
LessonExercises
How manydots wouldtherebe in the fourthpatternof eachfigurebelow?
1.
2.
3.
- Whatis the next numberin the followingnumberpattern?
- Whatis the tenthnumberin this numberpattern?
The tablebelowshowsa numberpattern.
- Whatis the valueof when?