Wednesday ab
Download
1 / 63

Wednesday – AB - PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on

Wednesday – AB. Morning (Part 1) Developing the Concept of a Definite Integral Area Model Riemann Sums and Trapezoidal Method Numerical Integration Break Morning (Part 2) Applications of Integration Solids with Known Cross Sectional Area Discovering the Average Value of a Function

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Wednesday – AB' - lyle


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Wednesday ab
Wednesday – AB

  • Morning (Part 1)

    • Developing the Concept of a Definite Integral

    • Area Model

    • Riemann Sums and Trapezoidal Method

    • Numerical Integration

  • Break

  • Morning (Part 2)

    • Applications of Integration

    • Solids with Known Cross Sectional Area

    • Discovering the Average Value of a Function

    • Free-Response Problem (2013 AB 5)

  • Lunch

  • Afternoon (Part 1)

    • Share an Activity

    • Dan Meyer

    • Discussion of Homework Problems

  • Break

  • Afternoon (Part 2)

    • Curriculum Module: Motion (w/Smartboard)

    • Mean Value Theorem


Wednesday ab bc
Wednesday – AB/BC

  • Morning (Part 1)

    • Developing the Concept of a Definite Integral

    • Area Model

    • Riemann Sums and Trapezoidal Method

    • Numerical Integration

  • Break

  • Morning (Part 2)

  • AB:

    • Applications of Integration

    • Solids with Known Cross Sectional Area

    • Discovering the Average Value of a Function

    • Free-Response Problem (2013 AB 5)

  • BC:

    • Polar

  • Lunch

  • Afternoon (Part 1)

    • Share an Activity

    • Discussion of Homework Problems

  • Break

  • Afternoon (Part 2)

  • AB:

    • Curriculum Module: Motion (w/Smartboard)

    • Mean Value Theorem

  • BC:

    • Parametric & Vectors


Wednesday assignment ab
Wednesday Assignment - AB

  • Multiple Choice Questions on the 2013 test: 25, 26, 27, 77, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92

  • Free Response:

  • 2014: AB4/BC4, AB5

  • 2013: AB4


Wednesday assignment ab bc
Wednesday Assignment – AB/BC

  • Multiple Choice Questions on the 2013 test: 25, 26, 27, 77, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92

  • Free Response for AB Track:

  • 2014: AB4/BC4, AB5

  • 2013: AB4

  • Free Response for BC Track:

  • 2014: AB4/BC4, BC5

  • 2013: BC4


Wednesday files
Wednesday Files

  • Introducing the Definite Integral Through the Area Model

  • Investigation How to Find Area Using Riemann Sums and Trapezoids

  • Developing Understanding for a Definite Integral

  • Fun Finding Volume

  • Numerical Integration

  • Solids with Known Cross-Sections

  • Building Understanding for the Average Value of a Function

  • Share an Activity

  • Dan Meyer

  • Tuesday Assignment

  • Motion

  • Mean Value Theorem

  • Parametric & Vectors


Key ideas to cover on integration
Key Ideas to Cover on Integration

  • A definite integral is the limit of a Riemann sum

  • The definite integral is the net accumulation of a rate of change

    or


All the important concepts related to definite integrals can be taught and understood without knowing antiderivatives.


  • Calculus AP should include opportunities for students to understand

    • Area under a graph

      • Riemann Sum – Definition of a Definite Integral

    • Ways to Evaluate a Definite Integral

      • Fundamental Theorem

    • How integrals accumulate area

    • How functions can be by integrals

    • Techniques for finding indefinite integrals

    • Applications of integrals




Figure 1 shows the velocity of an object, v(t), over a 3-minute interval. Determine the distance traveled over the interval

. The area bounded by the graph of v(t) and the t-axis for represents the distance traveled by this object. The distance can be represented by the

definite integral .


The following chart gives the velocity of a particle, v(t), at 0.5 second intervals. Estimate the distance traveled by the particle in the three seconds using three different methods. Each method is an approximation for .


Investigating how to find area using riemann sums and trapezoids
Investigating at 0.5 second intervals. Estimate How to Find Area using Riemann Sums and Trapezoids

Using the NUMINT program or

LMRRAM and TRAPEZOID program on a TI83/84


Things you should have observed
Things You Should have Observed at 0.5 second intervals. Estimate

  • As the number of rectangles increases on monotonically increasing functions, the left hand sums increase, but remain less then the area.


Things you should have observed1
Things You Should have Observed at 0.5 second intervals. Estimate

  • which sums are always greater than the actual area

  • Which sums are always less than the actual area


Things you should have observed2
Things You Should have Observed at 0.5 second intervals. Estimate

  • The limit of the left hand sum equals the limit of the right hand sum and equals the area of the region.

  • area of the region or


Students should be able to
Students should be able to at 0.5 second intervals. Estimate

  • Set up and evaluate left, right and midpoint Riemann sums from analytical data, tabular data, or graphical data.

  • Set up and evaluate a Trapezoidal sum approximation from analytical data, tabular data, or graphical data.


  • Determine Units of Measure: at 0.5 second intervals. Estimate

    • The units of the definite integral are the units of the Riemann Sum

      • The units of the function multiplied by the units of the independent variable.


  • Verbal Explanation at 0.5 second intervals. Estimate

    • Students need to be able to tell what a definite integral represents in the context of the problem and identify the units of measure.

    • Very common AP question on Free Response Questions



Developing an understanding for the definite integral
Developing an Understanding for the Definite Integral at 0.5 second intervals. Estimate

Smartboard File


Fun finding volume
Fun Finding at 0.5 second intervals. Estimate Volume


Solids with known cross sectional area
Solids with Known Cross Sectional at 0.5 second intervals. Estimate Area


Create a table and a sketch for at 0.5 second intervals. Estimate

scale for the grid is 0.5 cm

on the x and y axes


Re-sketch at 0.5 second intervals. Estimate the graph of f (x).

The scale for this grid is 0.25 cm on

both the x and y axes.


Select one of the figures. Cut out the 9 shapes, keeping the tabs on the shape. Fold the trapezoidal trapezoidal tab. Glue the tab on the graph so that the edge of the shape is the f(x) segment. Face all the colored faces in the same direction.



Volume of solids of revolution
Volume of Solids of Revolution with your group members.


Rotating about a line other than the x or y axis
Rotating about a Line Other than the x- or y-axis with your group members.

Pages 2 to 5


Rotating about a line above the region
Rotating about a Line Above the Region with your group members.

Pages 5 to 7


Rotating about a line to the left of the region
Rotating about a Line to the Left of the Region with your group members.

Pages 10 and 11


Rotating about a line to the right of the region
Rotating about a Line to the Right of the Region with your group members.

Pages 8 and 9


Building understanding for the average value of a function
Building Understanding for the Average Value of a Function with your group members.

An Activity for


2013 ab5
2013 AB5 with your group members.


What activity would you like to share

What Activity Would You Like to Share with your group members.


Dan meyer

Dan Meyer with your group members.

All Examples

Taco Stand


Discussion of tuesday homework problems

Discussion of Tuesday Homework Problems with your group members.


Tuesday assignment ab

Multiple Choice Questions on the 2013 test: 3, 6, 8, 10, 11, 13, 17, 20, 21, 23, 28, 76, 78, 82, 84

Free Response:

2014: AB2, AB3/BC3

2013: AB3

Tuesday Assignment - AB


Tuesday assignment ab bc
Tuesday Assignment – AB/BC 13, 17, 20, 21, 23, 28, 76, 78, 82, 84

  • Multiple Choice Questions on the 2013 test: 3, 6, 8, 10, 11, 13, 17, 20, 21, 23, 28, 76, 78, 82, 84

  • Free Response for AB Track

  • 2014: AB2, AB3/BC3

  • 2013: AB3

  • Free Response for BC Track

  • 2014: AB3/BC3, BC2

  • 2013: BC3


2014 ab2
2014 AB2 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric 2014 ab2
Scoring Rubric 2014 AB2 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


2014 ab3 bc3
2014 AB3/BC3 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric 2014 ab3 bc3
Scoring Rubric 2014 AB3/BC3 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


2014 bc2
2014 BC2 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric 2014 bc2
Scoring Rubric 2014 BC2 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


2013 ab3 bc3
2013 AB3/BC3 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric 2013 ab3 bc3
Scoring Rubric 2013 AB3/BC3 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


2013 ab51
2013 AB5 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric ab5
Scoring Rubric AB5 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


2013 bc5
2013 BC5 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric bc5
Scoring Rubric BC5 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


Scoring rubric bc51
Scoring Rubric BC5 13, 17, 20, 21, 23, 28, 76, 78, 82, 84


College Board has developed a Curriculum Module to assist you in teaching how to use Calculus to study motion.

Dixie Ross

Pflugerville High School

Pflugerville, TX

Motion Smartboard File


What you need to know about motion
What You Need to Know about Motion you in teaching how to use Calculus to study motion.

  • Worksheet 1: page 5


Sample practice problems numerical graphical analytical
Sample Practice Problems you in teaching how to use Calculus to study motion. Numerical, Graphical, Analytical

  • Worksheet 2: pages 7-9


Understanding the relationship among velocity speed and acceleration
Understanding the Relationship Among Velocity, Speed and Acceleration

  • Worksheet 3: page 13-15


What you need to know about motion along the x axis
What You Need to Know about Motion Along the x-axis Acceleration

  • Worksheet 4: page 21


Sample practice problems
Sample Practice Problems Acceleration

  • Worksheet 5: page 23-26



The mean value theorem smartboard
The Mean Value Theorem - AccelerationSmartboard

What is guaranteed?

What must be true for the guarantee?

Can parts be true if the conditions are not met?

How does it apply to real data?


Wednesday assignment ab1
Wednesday Assignment - AccelerationAB

  • Multiple Choice Questions on the 2013 test: 25, 26, 27, 77, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92

  • Free Response:

  • 2014: AB4/BC4, AB5

  • 2013: AB4


Wednesday assignment ab bc1
Wednesday Assignment Acceleration–AB/BC

  • Multiple Choice Questions on the 2013 test: 25, 26, 27, 77, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92

  • Free Response for AB Track:

  • 2014: AB4/BC4, AB5

  • 2013: AB4

  • Free Response for BC Track:

  • 2014: AB4/BC4, BC5

  • 2013: BC4


ad