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TODAY IN GEOMETRY… Warm up: Review concepts covered on Ch. 1 test STATs for Ch.1 test Learning Goal: 2.1 You will use patterns and describe inductive reasoning Independent Practice – NO A.T. Return Ch. 1 test

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75 ° b c a

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A B C WARM UP (2 of 4)

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WARM UP (3 of 4)

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WARM UP (4 of 4)

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HOW DID YOU “SHAPE” UP?? Results for ALL of my Geometry classes: GRADE NUMBER OF STUDENTS WHO TOOK THE CH.7 TEST MONDAY 3 RD PERIOD4 TH PERIOD5 TH PERIODTOTAL A/A-65415 B+/B/B-58316 C+/C/C-33713 D+/D45716 F115 27

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INDUCTIVE REASONING: A process that includes looking for patterns and making conjectures. Example: 1, 4, 7, 10, 13… We use inductive reasoning to say that the pattern is adding 3 to get the next term.

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Find the next number in the pattern. 12, 8, 4, 0, -4, ___, ___ -4 **TIPS: Find the patterns between numbers and see if this pattern is continuous. Check if a constant is multiplied, divided, added or subtracted. If you don’t initially find a pattern, then check patterns in second differences. Continue subtracting 4 to find the missing values. -8 -12

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Find the next number in the pattern. 20, 10, 5, 2.5, 1.25,___,___ Continue dividing by 2 to find the missing values. 0.625 0.3125

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Find the next number in the pattern. 8, 24, 72, 216, 648, ___, ___ Continue multiplying by 3 to find the missing values. 1944 5832

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Find the next number in the pattern. 1, -2, 3, -4, 5, ___, ___ next number & alternating signs Continue on the next consecutive number and alternating signs to find the missing values. next number & alternating signs next number & alternating signs next number & alternating signs next number & alternating signs -6 next number & alternating signs 7

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Test your knowledge: Use inductive reasoning to find the pattern: 1, -3, 5, -7, 9, _____, _____ 12, 6, 3, 1.5, 0.75, _____, _____ 4, 9, 16, 25, 36, _____, _____ 1, 1, 2, 3, 5, 8, _____, _____ -1113 49 64 1321 0.375 0.1875 PATTERN: consecutive odd numbers and alternating signs PATTERN: divide by 2 PATTERN: consecutive perfect squares PATTERN: the sum of the previous two terms is the next term

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Test your knowledge: Use inductive reasoning to find the pattern: PATTERN: add diagonal to create two more pieces

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CONJECTURE: An unproven statement that is based on observations. Example: Conjecture: All prime numbers are odd.

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Numbers such as 3, 4 and 5 are called consecutive integers. Make and test a conjecture about the sum of any three consecutive integers.

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A student in 1 st period made the following conjecture: the sum of any two even numbers is always even. Test this conjecture with many cases. This conjecture is TRUE for all cases.

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COUNTEREXAMPLE: A specific case that shows a conjecture is false. Example: Conjecture: All prime numbers are odd. Counterexample: 2 is a prime number and it is not odd.

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A student in 3 rd period made the following conjecture: the sum of two numbers is always greater than the largest number. Test this conjecture with many cases. This conjecture is NOT TRUE for all cases. The last four cases are counterexamples.

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HOMEWORK #1: Pg. 75: 3-17, 23-28, 31

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CHAPTER 1 SECTION 2. MAKING A CONJECTURE: A conjecture is an unproven statement that is based on a pattern or observation. Much of the reasoning in geometry.

CHAPTER 1 SECTION 2. MAKING A CONJECTURE: A conjecture is an unproven statement that is based on a pattern or observation. Much of the reasoning in geometry.

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