Acquisition Lesson Planning Form - Ciclt.net

More documents

Recommendations

Info

$Math III, Unit 4, Lesson 1 - Ciclt.net$

$Math III, Unit 1 Lesson 4 PowerPoint - Ciclt.net$


$Math III Unit 6, Lesson 2 - Ciclt.net$


$Math III, Unit 2 Assessment - Ciclt.net$

2c. Create another table of values for the general quadratic function y = ax + bx + c . Thistime start with an x-value other than 0 and choose x-values with a constant differenceother than 1.2x y = ax + bx + c First differences Seconddifferencesd. What happens with the second differences in the table from part c?From our calculations for Items 4 and 5, we have seen that, when we start with equally spacedx-values (that is, x-values that have a constant difference), linear functions have constant firstdifferences and quadratic functions have constant second differences. We have explored howthe constant slope of a line gives the constant first differences for linear functions. We cancalculate values of the general quadratic function for inputs of x, x + k, and x + 2k to prove that2the constant second difference for a general quadratic is always 2k a, where k is the constantdifference in the x-values. These results are part of a pattern for polynomial functions. Similarcalculations for general polynomials of higher degree show that, when we start with x-valuesthat have a constant difference, cubic functions have constant third differences, fourth degreepolynomials have constant fourth differences, and so forth for higher degree polynomials..2y = ax + bx + cFirst differences SeconddifferenceLeast squares regression techniques can be applied to functions and relationships that are notfunctions. Calculating first differences, second difference, third differences, and so forth todetermine whether a polynomial model fits a set of data points applies only to relationships thatdefine functions. When we have a set of data that defines a function, we can apply the methodof finite differences to determine whether the data fit a polynomial model.6. Consider the table of values below.Math 2 Unit 5 <strong>Lesson</strong> 3 Linear and Quadratic Regression Page 36
x y– 7 – 6– 5 – 5– 3 3– 1 221 563 1095 185a. Explain why it is possible to calculate finite differences for the data points in the table.b. Determine whether a linear, quadratic, cubic, or other polynomial model fits the data.Diameter of viewingcircle in centimetersArea of viewingcircle in sq. cms3 6. 10.5625 π ≈ 334 9.0 20.25 π ≈ 645 11.5 33.0625 π ≈ 1046 14.0 49 π ≈ 1547 16.5 68.0625 π ≈ 2148 19.0 90.25 π ≈ 284c. Use the method finite differences to determine if the data points for expressing thediameter of the viewing circles as a function of the distance from the wall fits apolynomial model, and if so, which model.d. Use the method finite differences to determine if the data points for expressing the areaof the viewing circles as a function of the distance from the wall fits a polynomial model,and if so, which model.e. When the teacher saw this student data, the teacher suspected that the students hadjust calculated two values and then made up the rest of the data. Why might theteacher have thought this?Math 2 Unit 5 <strong>Lesson</strong> 3 Linear and Quadratic Regression Page 37
Page 1 and 2: Acquisition Lesson Planning FormKey
Page 3 and 4: GO #1: How do we eyeball a line bes
Page 5 and 6: GO #3: How do we find the median-me
Page 7 and 8: Now that you have found the median-
Page 9 and 10: 5. Plot the following points on the
Page 11 and 12: Traveling on the Turnpike Learning
Page 13 and 14: Exit # Toll Predicted toll fromthe
Page 15 and 16: Traveling on the Turnpike Learning
Page 17 and 18: function. We’ll name this approxi
Page 19 and 20: a. Use an algebraic method to answe
Page 21 and 22: Orbital Debris Learning TaskWheneve
Page 23 and 24: elationship between the variables;
Page 25 and 26: c. How well does the parabola appea
Page 27 and 28: 6.1990 101995 192000 282005 40a. Ba
Page 29 and 30: hypotheses are tested in a study th
Page 31 and 32: View Tube Learning TaskThis learnin
Page 33 and 34: 3. Consider the basic linear equati
Page 35: 1511c. Assume you have a table of v
Page 39: f. Compare your results with other

Acquisition Lesson Planning Form - Ciclt.net

Create successful ePaper yourself

Delete template?

Save as template?