Week 2. Monday: 1.1. Tuesday: 1.2. Wednesday: 1.3. Thursday: Catch up Friday: 1.4 Monday: OFF Tuesday: 1.5. Problem Solving, Patterns, Induction

Size: px

Start display at page:

Download "Week 2. Monday: 1.1. Tuesday: 1.2. Wednesday: 1.3. Thursday: Catch up Friday: 1.4 Monday: OFF Tuesday: 1.5. Problem Solving, Patterns, Induction"

Matthew Sutton
5 years ago
Views:

1 Monday: 1.1 Week 2 Problem Solving, Patterns, Induction Tuesday: 1.2 Geometry Basics Wednesday: 1.3 Segments and Measuring Thursday: Catch up Friday: 1.4 Monday: OFF Tuesday: 1.5 1

2 Mindfulness Training This week, beginner: Body Scan 3 minutes Meditation.mp3 2

3 1.1: Problem Solving (One day) Four-Step Process for Problem Solving 1. Understand the Problem 2. Devise a Plan 3. Carry out the Plan 4. Look Back Eg: Suduko... 3

4 Understand the Problem Is it clear what is to be found? Do you understand the terminology used in the problem? Is there enough information? Is there irrelevant information? Are any restrictions or special conditions to be considered? 4

5 Devise a Plan How should the problem be approached? Does the problem appear similar to any others you have solved? What strategy might you use to solve the problem? 5

6 Carry Out the Plan Apply the strategy or course of action chosen in Step 2 until a solution is found or you decide to try another strategy. 6

7 Look Back Is your solution correct? Do you see another way to solve the problem? Can your results be extended to a more general case? 7

8 Strategy 1: Draw a Picture Clues A physical situation is involved Geometric figures or measurements are involved You want to gain a better understanding of the problem A visual representation of the problem is possible 8

9 Example Using Drawing If the diagonals of a square are drawn in, how many triangles of all sizes are formed? 9

10 Hints Do you know what the diagonal of a square is? Remember that triangles may be of different sizes. Also, some of the triangles may overlap. If needed, make several pictures to help. 10

11 Strategy 2: Guess and Test Clues There is a limited number of possible solutions to test. You want to gain a better understanding of a problem. You have a good idea what the solution is. You can systematically try possible solutions. Your choices have been narrowed down by first using other strategies. There is no obvious strategy to try. 11

12 Guess and Test Six identical coins are arranged in a pyramid with 1 on top, 2 in the next row, and 3 on the bottom. Can you move just two coins so that there are 3 on top, 2 in the next row, and 1 on the bottom? 12

13 Hints Draw both the before and after pictures. Use coins. Play around with it. 13

14 Other Strategies Turn into an equation or find a formula Look for a pattern Make a table Break up into simpler problems 14

15 Monday Work Day Textbook Page 2: Key Vocabulary, Skill Review, Study Strategy Journal Chapter 1, Section 1 Name and Date in upper right hand side Read and write down any definitions, axioms, postulates, formulas, etc. Conjecture, inductive reasoning, counterexample, Problems: 1-11, all 13-25, oddsl 52-66, all Ask questions last minutes of class 15

16 Tuesday: Mindfulness Training (One Day) This week, beginner: Body Scan 3 minutes Meditation.mp3 16

17 Debrief 1.1 Math is about objects and relationships Any questions on odds? Mixed Review, p. 9: 52-66, evens 17

18 Tuesday 1.2: Points, Lines, Planes Goals: Axiomatic System Define Terms Postulates Measuring 18

19 Elements of Axiomatic Systems Undefined Terms -- Describe but cannot be given a precise definition. Point - a dot with no size Line - infinite length but no thickness Plane - like sheet of paper extending forever 19

20 Defined Terms More Elements Space - the set of all points Geometric figure - any collection of points Postulates - statements we assume are true state relationships among undefined and/or defined terms. Theorems - results deduced from terms, definitions, postulates, and / or results that follow from them. 20

21 Line Co-Ness Collinear - Points are collinear if there is a line containing them. Noncollinear -- Points are noncollinear if there is not a line containing them. 21

22 Planer Co-Ness Coplaner - points are coplaner if there is a plane containing all the points. Noncoplaner -- points are not contained on the same plane. 22

23 Line Segments, Measure Line Segment - determined by A and B, is the points A and B and all points on the line whose coordinates are between A and B. Endpoints -- The points, e.g., A and B, that begin and end the line segment. Length of the line segment - AB, the distance from point A to point B. Ray - a "partial line" in that there is an endpoint but the other end extends indefinitely in one direction. 23

24 Journal Work Read and Write down Missing Definitions Check out the examples Work Guided Practice: 1-8, all Practice and Applications: 9-42; 44-51; even; 68-75; Starting 1.3 tomorrow 24

25 Wednesday: Mindfulness Training (Two Day) This week, beginner: Body Scan 3 minutes Meditation.mp minutes debrief 25

26 Debrief 1.2 Math is about objects and relationships Guided Practice 1-8 Any questions on 9-75 odds? Mixed Review, p. 16: 78-96, evens 26

27 1.3: Segments and their measure Segments and Their Measure Distance Formula 2 days Start: 15 Minutes Journal 1.3 Definitions, Postulates, Formulas, etc. Start Guided Practice 1-12 If finish, start odds 27

28 Day 2: Descartes Spider in the room Cartesian Coordinate system Ruler Postulate: p17 two number lines that are perpendicular X-Axis; Y-Axis It's easy to find the length of a line segment on an axis, (Segment Addition Postulate: p17) but what about if it's not vertical or horizontal? 28

29 Distance on The Grid Cartesian Space Plot Points Draw Triangle Solve Triangle with vertices: (0,0), (3,0), (3,4) Line with endpoints: P(3,4), Q(6,8 ) 29

30 Distance Formula If A(x 1,y 1 ) and B(x 2,y 2 ) are two points in the coordinate plane, then: AB = x 2 x (y 2 y 1 ) 2 given these points, plot and find distance A(-7,-3) B(0,3) C(5,0) D(2,-5) 30

31 1.3: Work 1.3, p21: 1-42; 44-49; 54-56; Day 2 Finish above Quiz 1: 1-7 Journal Check? 31

32 Thursday: Mindfulness Training (Day Two of Two) This week, beginner: Body Scan 3 minutes Meditation.mp3 32

33 Finish 1.3, p21: 1.3: Work Together: Guided Practice, 1-12 Work and ask questions: 1-42; 44-49; 54-56; Debrief last 10 minutes of class Quiz 1: 1-7? Journal Check? Tomorrow: 1 day for

34 Friday: Mindfulness Training (1 Day) This week, beginner: Body Scan 3 minutes Meditation.mp3 34

35 Debrief 1.3 Math is about objects and relationships Quiz 1, Page 25:

36 1.4: Angles and Measures Today: Get that protractor ready Angles Naming Measuring Adding 36

37 Angle, Vertex, Sides Angle two line segments or rays meeting at a common endpoint form an angle. Vertex the common endpoint of angles. Sides the segments or rays of the angle. 37

38 A circle has 360 degrees, Divide in half: 180 Divide in half: 90 Divide in half: 45 Divide by 360: Measuring Angles one degree = 1/360 of a complete revolution around a circle We measure degrees with protractors 38

39 The Protractor Postulate If one ray of an angle is placed a 0 o on a protractor and the vertex is placed at the midpoint of the bottom edge, then there is a 1-1 correspondence between all other rays that can serve as the second side of the angle and the real numbers between 0 o and 180 o inclusive, as indicated by a protractor. This is how we measure angles. 39

40 Draw some random angles and measure them. Measure Angles 40

41 Acute Between 0 and 90 degrees Right 90 degrees Obtuse Between 90 and 180 degrees Straight 180 degrees Reflex Between 180 and 360 degrees Special Angles 41

42 Read Work Write down Definitions, Postulates, Formulas, etc. Check out the examples Work Guided Practice: 1-16 Practice and Applications: 17-25, Even Mixed Review: Next Week: Off Monday; 1.5 (2 days), 1.6 (2 days) 42

Chapter 1 Tools of Geometry

Chapter 1 Tools of Geometry Goals: 1) learn to draw conclusions based on patterns 2) learn the building blocks for the structure of geometry 3) learn to measure line segments and angles 4) understand the