![Page 1: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/1.jpg)
Entry task• 1) What can be concluded from the following pattern?
• 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5• 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5• 3 + 4 + 5 + 6 + 7 = 25 = 5 × 5• 4 + 5 + 6 + 7 + 8 = 30 = 6 × 5• 5 + 6 + 7 + 8 + 9 = 35 = 7 × 5
• 6 + 7 + 8 + 9 + 10 = 40 = 8 × 5
• 2) Can you find the pattern? J,F,M,A,…
![Page 2: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/2.jpg)
Using Patterns and Inductive
Reasoning
Learning Target:I can observe patterns and
reach a conclusion based on those patterns
![Page 3: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/3.jpg)
Definitions
• Inductive Reasoning – type of reasoning that allows you to reach
conclusions based on a pattern of specific examples
• Conjecture – conclusion reached by using inductive
reasoning
• Counterexample– An example that shows a conjecture is incorrect
![Page 4: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/4.jpg)
• We can all see the pattern here, but what is important is the ideas we can take away from this to help us see other patterns.
![Page 5: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/5.jpg)
![Page 6: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/6.jpg)
![Page 7: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/7.jpg)
![Page 8: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/8.jpg)
Extra credit
• Find the sum of all numbers from 1 to 100– Hint : Look for a pattern– (you will not get credit if you simply use a
calculator, you must find the pattern)
![Page 9: Entry task 1) What can be concluded from the following pattern? 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5 3 + 4 + 5 + 6 + 7 = 25 =](https://reader035.vdocument.in/reader035/viewer/2022062511/55155d55550346a1418b4967/html5/thumbnails/9.jpg)
Homework
• Homework: p. 85 #7,12,13,14,21,23,33,35,37,39,41,46,53,55
• Challenge - 56