23 Feb 2018

Geometry

Continue with yesterday's lesson.

Finish and check worksheets.




Calculus

C.D.AD.C.15 Model rates of change, including related rates problems. In each case, include a discussion of units.

Related Rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Because problems involve several variables, differentiation with respect to time or one of the other variables requires application of the chain rule.


p.144  Related Rates (Continued)

p.144 - 148

---Day One---

Related Rates 01

Related Rates 02

Work (1,2,15,16)

---Day Two---





Verbal to Mathematical Statements p146

Work thru Examples 3, 4, 5 p.146/147 as time allows.

Related Rates 03

Related Rates 04

Working (24) p.149  and  (35) p.151  include diagrams and all side equations.

Students check answers for correctness against one another or in solution manual.

Students turn in a related rate problems at end of class to be evaluated for correctness.

Ref:  Paul's Math Notes - Related Rates

Geometry

see above




Geometry



Bridge

22 Feb 2018

Geometry

 G.MG.A.2 

Apply geometric methods to solve real-world problems.

Geometric methods may include but are not limited to using geometric shapes, the probability of a shaded region, density, and design problems.

Video:
Density Practice Problems

Find the Area of the Shaded Region

Area of Shaded Region Concentric Circles

Worked Practice Problems:
Finding Areas of Shaded Regions between Polygons & Circles


Practice:
Shaded areas (practice) | Area | Khan Academy

Worksheets:
Area of shaded Region
Concentric Circles Problems
Density Problems




Calculus


Continue to work problems from yesterday.

Short Chain Rule Quiz involving Trig.





Bridge

Continue last lesson.

21 Feb 2018

Geometry

G.SRT.A.1 

Verify informally the properties of dilations given by a center and a scale factor. 

Properties include but are not limited to: a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center of the dilation unchanged; the dilation of a line segment is longer or shorter in the ratio given by the scale factor.


Video:
How Do I Dilate a Figure? | Common Core Geometry Transformations

Video 6 Dilations Not Centered at the Origin 

Text; p.579- 581

Work (4-20) p.582

Worksheet 01  Work R or F as HW.


Calculus

p.144  Related Rates

p.144 - 148

Related Rates 01

Related Rates 02

Related Rates 03

Related Rates 04

Work (1,2; 15-20) p.149

Geometry

see above



Bridge

Section 33  p.447

Notes and Examples p. 447 - 452

Work (1- 46) p.453

20 Feb 2018

Day 21


Geometry


G.SRT.A.2 

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Introduction to Similar Polygons and Similar Triangles

Missing Measurements for Similar Triangles

Problems:
Similar Figures - Missing Sides, etc.

Similar Triangles


Text, p. 603 - 605

Work (5-16) p.606




Calculus

Implicit Differentiation  p.138

p.138 - 141





Stillwater Calculus:  Implicit Diff.







p.142  Work (1-16; 21-25)

Geometry

see above



Bridge


Finish last section

16 Feb 2018

Day 20


Geometry


Construct Perpendicular Bisector of Line Segment  (watch vid, work out on paper and turn in.  Bisect a 3, 4 and 5 inch segment)




Construct Angle Bisector  (watch vid, work out on paper and turn in.  Bisect a 20, 45 and 120 degree angle)


"Yo, yo, yo..."  Lol!



Lesson Performance Tasks

4.4

4.3

4.2

Calculus

Notes p. 132
Examples 9-12
Work p.133(33,34; 47-60)
Check


Geometry

see above



Bridge

Section 32  Exp. Log., and Quadratic Functions

Notes & Examples p. 431 - 441

Work (1-40) p.442

15 Feb 2018

Day 19


Geometry

7.3 Triangle Inequalities   p. 341

Theorem p. 342







Work through p. 342 to p. 344


Note p. 345 side length - angle relationship

Work through p. 346

Work (1 - 17) p. 348




Calculus

Quiz



Geometry

see above





Bridge

All class gone on Gear Up Trip

Geometry Standards

MrStanislow - All Circle Videos

01) G.C.A.2

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.



Videos:

Central Angles

Inscribed Angles

Circles - Secant - Secant Angles

Circles - Tangent - Secant Segments

Circles - Tangent - Tangent Angles

Circles - Tangent - Secant Angles

Circles - Tangent - Chord Angles





Notes 


Item 01

Item 02

Item 03



02) G.C.B.4 

Know the formula and find the area of a sector of a circle in a real-world context. 

Videos:

Circles - Sector Area

Circles - Sector Area 2


Practice:

Area of a sector (practice) | Sectors | Khan Academy

IXL - Area of sectors (Geometry practice)




Quiz & Worksheet - Practice Finding the Area of a Sector | Study.com

Extra:
Area of a Sector in a Circle Worksheet | Problems & Solutions



03) G.CO.C.11 

Prove theorems about parallelograms.

Proving includes, but is not limited to, completing partial proofs; constructing two-column or paragraph proofs; using transformations to prove theorems; analyzing proofs; and critiquing completed proofs. 

Theorems include but are not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.


Parallelogram Theorems Overview

Proving a Quadrilateral is a Parallelogram: Examples

Parallelograms 4 Theorems




04) G.GMD.A.1 

Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.

Video:
Introduction to Circles - radius, diameter, circumference and area of a circle

Multiple Practice PDFs:
Circumference and Area of Circle Worksheets

Circumference and Area Practice Problems


Videos:
Volume & Surface Area of a Cylinder

Volume and Surface Area of Prisms

Volume and Surface Area of Cones

Multiple Generated Worksheets
Geometry Worksheets | Surface Area & Volume Worksheets

Surface Area and Volume - Prisms, Cyl, Pyramids

Surface Area and Vol Pyramids and Cones











05)  G.GPE.A.1

Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

Equation for a circle using the Pythagorean Theorem | Circles | Geometry | Khan Academy


Practice:
Features of a circle from its standard equation | Analytic geometry (practice) | Khan Academy

Circle Equation Practice - MathBitsNotebook(Geo - CCSS Math)



Problems:
Graphing with Center/Radius Form

Graphing and Properties of Circles

Center/Radius Quiz




06)  G.MG.A.2 

Apply geometric methods to solve real-world problems.

Geometric methods may include but are not limited to using geometric shapes, the probability of a shaded region, density, and design problems.

Video:
Density Practice Problems

Find the Area of the Shaded Region

Area of Shaded Region Concentric Circles

Worked Practice Problems:
Finding Areas of Shaded Regions between Polygons & Circles


Practice:
Shaded areas (practice) | Area | Khan Academy

Worksheets:
Area of shaded Region



07)  G.CO.A.5 

Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another.

Rotations  1A

Work Problems from page 1 together, finish page 2 in your groups.


Reflections 1A

Work Problems from page 1 together, finish page 2 in your groups.


Translations 1A

Work Problems from page 1 together, finish page 2 in your groups.





G.C.O.A.5 Resource.







       G.CO.B.6 

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to determine informally if they are congruent.

Properties of Transformations 1

Work problems with students and then they finish in groups.



 Properties of Transformations 2

Work problems with students and then they finish in groups.




Geometry Resources





08)  G.SRT.B.4 

Prove theorems about similar triangles.

Proving includes, but is not limited to, completing partial proofs; constructing two-column or paragraph proofs; using transformations to prove theorems; analyzing proofs; and critiquing completed proofs. 

Theorems include but are not limited to: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 


      G.SRT.B.5 

Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.




09)  G.SRT.A.1 

Verify informally the properties of dilations given by a center and a scale factor.

Properties include but are not limited to: a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center of the dilation unchanged; the dilation of a line segment is longer or shorter in the ratio given by the scale factor.


Video:
How Do I Dilate a Figure? | Common Core Geometry Transformations

Video 6 Dilations Not Centered at the Origin 

Text; p.579- 581

Work (4-13) p.582



      G.SRT.A.2 

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.



Introduction to Similar Polygons and Similar Triangles

Missing Measurements for Similar Triangles

Problems:
Similar Figures - Missing Sides, etc.

Similar Triangles


Text, p. 603 - 605

Work (5-16) p.606