Lesson Plan - Extrema and Monotony of a Quadratic Function

Author:Math Teachers' Adventure of ICT Integration, Judith , Beatrice Tiron, Voinea-Axinte Costica

Topic:Quadratic Functions

General information

Subject: Mathematics
Grade: 9th grade
Duration: 50 minutes
ICT tools: computer teacher, projector, smartphones (tablets / computers) for students, Internet connection.

Theme

Extreme and Monotony of Quadratic Function

Learning Outcomes

At the end of the lesson, students will be able to:

determine the extreme point and the extreme value of a function of the second degree, specifying if the maximum or minimum;
to identify the coordinates of the peak point and the end parable;
to characterize the function of the monotony of degree II and indicate the intervals of monotonicity;
interpret graphical representation of a function of the second degree (to read graphics).

Operational objectives and assesment

Cognitive objectives:

to write the vertex coordinates of the parabola;
to discuss according to a and graph shape of the quadratic function;
to find the minimum/maximum of a quadratic function;
to read the graph of a quadratic function.

Psychomotor objectives:

to show interest in the lesson;
to write legibly in notebooks and on the blackboard.

Affective objectives:

to participate actively in the lesson;
to develop their interest in maths study using GeoGebra.

Teaching strategies

Didactic methods:

heuristic conversation, exercise, knowledge transfer, problematization, guided observation.

Equipment, software:

PCs, video projector, smartphones, Geogebra, online resources.

Lesson moments I) Organizing moment (2 min.) The class is organized, presence is done, digital tools are presented, workbooks are distributed, where students will also find GeoGebra applications addresses. II) Checking homework and previous knowledge (8 min.) The theme is checked verbally, and if the homework cannot be solved, it is solved at the blackboard. III) Introducing new knowledge (30 min) Using heuristic conversation they will find following conclusions:

Because domain and codomain of quadratic function is we will write function like this: or , where

A quadratic function is known when we know real numbers .

We must observe that condition is essential in the way that if then they obtain a linear function (studied before in 8th grade).

The name of quadratic function comes from quadratic trinom .
Graph of any quadratic function is a parabola.

We introduce extrem points through guided discovery method, facilitated by new technologies integration: students watch the material https://www.geogebra.org/m/D7GWhRbP realizing changes of a, b and c and identifyind the graph changes for

. They will draw following concluzions and will note them in notebooks: o If

, the minimum value of function f in

, and minimum point is

. o If

, the maximum value of function f in

, and maximum point is

. Monotony: students watch the function graph in GeoGebra and they will interpretate different graphs of function

for different values of a, b, c. Then they will note in notebooks: o If

, then:

reach the minimum value in point

;

decrease in

and increase in

; o If

, then:

reach the maximum vakue in point

;

increase in

and decrease in

. IV) Retention and transfer (8 min.) They solve exercices from worksheet and they check with GeoGebra. V) Homework (2 min.) Exercise 8) from worksheet.

Resources

Quadratic function graph : https://www.geogebra.org/m/D7GWhRbP GeoGebra web resources : https://www.geogebra.org/m/bJJb6Vp9 Web resources: https://ro.wikipedia.org/wiki/Func%C8%9Bie_de_gradul_doi https://prowebdelia.wordpress.com/about/matematica-pe-web/algebra/functia-de-gradul-al-ii-lea-aplicatii/

New technologies integration

Plan B (if we cannot use ICT lab): using students smartphones. In absence of Internet connection we will use powerpoint material.