Tuesday, April 3, 2007
Wednesday, March 21, 2007
Location to Our Buried Treasure
We could use this in a math class to teach: distance, area, proportions, scale, and for pirate students...treasure maps.
Tuesday, February 27, 2007
Lessons w/ Technology (Reflection 7)
Geometer’s Sketchpad Wallpaper
Target Audience: An entry geometry class, either honors 8th grade or early high school.
Goal/Idea: To have students understand rotations, reflections and translations. Students will design a geometric “wallpaper” and apply translations to the design.
Resources: Geometer’s Sketchpad software
Standards: G.2.4: Apply transformations to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know images formed by slides, flips, and turns are congruent to original shape.
Linear Equations in slope-intercept form
Target Audience: An Algebra I class, early in the class or semester.
Goal/Idea: To have students understand slope intercept form and how the slope and y-intercept change the look of the line. Students will analyze sets of equations where slopes, or y-intercepts vary. This will allow students to see how graphs change, by holding variables constant.
Resources: Graphing calculators, overhead, and overhead calculator.
Standards: A1.4.1: Graph a Linear Equation
A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line
Frequency of Music Notes
Target Audience: A high school precalculus class
Goal/Idea: Students will understand graphing sine and cosine curves, in relation to the frequency of the music notes from tuning forks. This includes the changing of the period of the graphs.
Resources: Graphing Calculator, Calculator-based Labs (CBL), and tuning forks
Standards: PC.4.5: Define and graph trigonometric coverage
PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trig functions.
PC.4.7: Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.
Target Audience: An entry geometry class, either honors 8th grade or early high school.
Goal/Idea: To have students understand rotations, reflections and translations. Students will design a geometric “wallpaper” and apply translations to the design.
Resources: Geometer’s Sketchpad software
Standards: G.2.4: Apply transformations to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know images formed by slides, flips, and turns are congruent to original shape.
Linear Equations in slope-intercept form
Target Audience: An Algebra I class, early in the class or semester.
Goal/Idea: To have students understand slope intercept form and how the slope and y-intercept change the look of the line. Students will analyze sets of equations where slopes, or y-intercepts vary. This will allow students to see how graphs change, by holding variables constant.
Resources: Graphing calculators, overhead, and overhead calculator.
Standards: A1.4.1: Graph a Linear Equation
A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line
Frequency of Music Notes
Target Audience: A high school precalculus class
Goal/Idea: Students will understand graphing sine and cosine curves, in relation to the frequency of the music notes from tuning forks. This includes the changing of the period of the graphs.
Resources: Graphing Calculator, Calculator-based Labs (CBL), and tuning forks
Standards: PC.4.5: Define and graph trigonometric coverage
PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trig functions.
PC.4.7: Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.
Reflection 7
Target Audience: Geometry students, grade 10-11.
Big Idea: Have students understand what is really needed to prove geometric concepts.
Goal: Have students examine properties of quadrilaterals and start to make informal conjectures and proofs related to those quadrilaterals.
Standards: G.3.1, G.8.3
Possible Resources: Geoboards, Geometers Sketchpad
Target Audience: Grades 7-8
Big Idea: Students further understanding of the coordinate plane.
Goal: To provide practice plotting and naming points on a coordinate grid using Battleship.
Standards: 7.4.1, 7.4.2, 8.3.5
Possible Resources: Battleship Game
Target Audience: Geometry Classroom
Big Idea: Helps students understand how parts of a funtion relate to the whole part.
Goal: To let students distinguish difference in shapes and see patterns in the shapes.
Standards: G.3.1, G.3.3, G.8.7
Possible Resources: Pattern Blocks http://nlvm.usu.edu/en/nav/frames_asid_171_g_4_t_4.html?open=activities
Big Idea: Have students understand what is really needed to prove geometric concepts.
Goal: Have students examine properties of quadrilaterals and start to make informal conjectures and proofs related to those quadrilaterals.
Standards: G.3.1, G.8.3
Possible Resources: Geoboards, Geometers Sketchpad
Target Audience: Grades 7-8
Big Idea: Students further understanding of the coordinate plane.
Goal: To provide practice plotting and naming points on a coordinate grid using Battleship.
Standards: 7.4.1, 7.4.2, 8.3.5
Possible Resources: Battleship Game
Target Audience: Geometry Classroom
Big Idea: Helps students understand how parts of a funtion relate to the whole part.
Goal: To let students distinguish difference in shapes and see patterns in the shapes.
Standards: G.3.1, G.3.3, G.8.7
Possible Resources: Pattern Blocks http://nlvm.usu.edu/en/nav/frames_asid_171_g_4_t_4.html?open=activities
Sunday, February 25, 2007
Reflection 7
Target Audience of the Lesson:
This lesson is targeted for Algebra I students. These students may be in grades 8 – 10.
Overall Goal of the Lesson:
The goal of this lesson is for students to learn how to factor the difference of two squares, perfect square trinomials, and the difference of two cubes.
Student Learning Objectives:
After the lesson students should be able to:
• identify and factor binomials that are the differences of squares
• identify and factor perfect square trinomials
• identify and factor difference of two cubes
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives, a worksheet can be given to each student. This worksheet will have multiple problems for them to complete including differences of squares, perfect square trinomials, and difference of two cubes. Students could also be given a short quiz over the lesson with each type of task described during the next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
A1.6.5 : Divide polynomials by monomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial.
A1.6.7 : Factor the difference of two squares and other quadratics. Resource
Target Audience of the Lesson:
This lesson is designed for an Algebra I class. It is targeted towards students in grades 8 and 9.
Overall Goal of the Lesson:
The overall goal of this lesson is getting students to learn how to multiply polynomials using the FOIL method and Distributive Properties. Another goal is to have students learn how to multiply polynomials in real-life situations.
Student Learning Objectives:
After the lesson students will be able to:
• Classify a polynomial by degree and by number of terms
• Multiply polynomials by using the Distributive Property
• Multiply two polynomials using FOIL
• Apply polynomials to real-life situations
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
In order to demonstrate that the students have met the learning objectives, you can write problems on the chalkboard or overhead projector. Students will have to either solve the problems themselves or give the instructor step by step instructions to solve the problems. Students can be given worksheets to work on in class and turn them in by the end of the period. Lastly, students can be given homework problems out of the book to work on at home and returned by next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
A1.6.1 : Add and subtract polynomials. Resource
A1.6.2 : Multiply and divide monomials. Resource
A1.6.3 : Find powers and roots of monomials (only when the answer has an integer exponent).
A1.6.4 : Multiply polynomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial. Resource
Target Audience of the Lesson:
This lesson is designed for middle school math. It is targeted towards students in grades 6 and 7 learning about fractions.
Overall Goal of the Lesson:
The overall goal of this lesson is to introduce the concept of common denominators. Another goal is to get students involved in interactive activities by using felt board fraction shapes.
Student Learning Objectives:
After the lesson students will be able to:
• Show awareness of the concept of fraction equivalencies and common denominators
• Correctly write addition equations that represent various felt board equations
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives they should write addition equations on their paper that equal the given felt board fractions. Students could pose their own fractions to their peers. Afterwards, students should solve addition equations together in class. Finally, students could be given worksheets with colored fractions and addition equations. They would have to write addition problems or vice versa for their answers and turn them in during the next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
6.1.4 : Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator. Resource
6.1.6 : Use models to represent ratios. Resource
6.1.7 : Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Resource
This lesson is targeted for Algebra I students. These students may be in grades 8 – 10.
Overall Goal of the Lesson:
The goal of this lesson is for students to learn how to factor the difference of two squares, perfect square trinomials, and the difference of two cubes.
Student Learning Objectives:
After the lesson students should be able to:
• identify and factor binomials that are the differences of squares
• identify and factor perfect square trinomials
• identify and factor difference of two cubes
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives, a worksheet can be given to each student. This worksheet will have multiple problems for them to complete including differences of squares, perfect square trinomials, and difference of two cubes. Students could also be given a short quiz over the lesson with each type of task described during the next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
A1.6.5 : Divide polynomials by monomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial.
A1.6.7 : Factor the difference of two squares and other quadratics. Resource
Target Audience of the Lesson:
This lesson is designed for an Algebra I class. It is targeted towards students in grades 8 and 9.
Overall Goal of the Lesson:
The overall goal of this lesson is getting students to learn how to multiply polynomials using the FOIL method and Distributive Properties. Another goal is to have students learn how to multiply polynomials in real-life situations.
Student Learning Objectives:
After the lesson students will be able to:
• Classify a polynomial by degree and by number of terms
• Multiply polynomials by using the Distributive Property
• Multiply two polynomials using FOIL
• Apply polynomials to real-life situations
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
In order to demonstrate that the students have met the learning objectives, you can write problems on the chalkboard or overhead projector. Students will have to either solve the problems themselves or give the instructor step by step instructions to solve the problems. Students can be given worksheets to work on in class and turn them in by the end of the period. Lastly, students can be given homework problems out of the book to work on at home and returned by next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
A1.6.1 : Add and subtract polynomials. Resource
A1.6.2 : Multiply and divide monomials. Resource
A1.6.3 : Find powers and roots of monomials (only when the answer has an integer exponent).
A1.6.4 : Multiply polynomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial. Resource
Target Audience of the Lesson:
This lesson is designed for middle school math. It is targeted towards students in grades 6 and 7 learning about fractions.
Overall Goal of the Lesson:
The overall goal of this lesson is to introduce the concept of common denominators. Another goal is to get students involved in interactive activities by using felt board fraction shapes.
Student Learning Objectives:
After the lesson students will be able to:
• Show awareness of the concept of fraction equivalencies and common denominators
• Correctly write addition equations that represent various felt board equations
Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives they should write addition equations on their paper that equal the given felt board fractions. Students could pose their own fractions to their peers. Afterwards, students should solve addition equations together in class. Finally, students could be given worksheets with colored fractions and addition equations. They would have to write addition problems or vice versa for their answers and turn them in during the next class period.
Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)
6.1.4 : Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator. Resource
6.1.6 : Use models to represent ratios. Resource
6.1.7 : Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Resource
Sunday, February 18, 2007
Reflection 6
There are many connections that can be made between manipulation and the ISTE Technology Standards. Manipulation is used for the students. It is based around students and helps them to better understand different concepts. Not only does it do that, but it also helps students have a better relationship with technology. It allows them to get more acquainted with technology and the concepts their learning. Manipulatives can be used to follow several of the standards. Including communication, creativity, and solving real world problems while using technology. So, therefore, manipulation is used for both the technology sake and to build students' academic skills.
Manipulation Resources
http://www.webgraphing.com/graphing_advanced.jsp
This web site can be used for graphing, analyzing and comparing equations. This program also shows where graphs are increasing and decreasing. This application will allow students to visualize the equation they are working with and provide a geometric perspective to their algebra work. While the program requires membership for the full benefits, it is free to sign up and use for students and teachers.
http://www.emints.org/ethemes/resources/S00000592.shtml
This website has an entire collection of manipulation activities. The activities range for grades 6,7,8. Students will get work with fractions, decimals, graphs, tessalations, and many other things. While this may seem inappropriate for many secondary teachers, the activites can be modified to fit courses of appropriate level. For example, the problem of the spinner can relate directly to work with probability. Also, some of the links provide material on lessons for an entire class period and some lessons encouraged the use of technology like the Smartboard.
http://www.shodor.org/interactivate/activities/
Again, this is a massive list of interactive lessons that can be used by teachers. The subject matter varies and there are multiple activities per subject. In particular, students direct a robot through a mine field laid out the cartesian plane. Its a list of fun activities that allow students to visualize the math they are working with.
All of these are about engagement and keeping the student invloved and focused. These are all great activities that will be useful for all of us.
And for the standards, manipulation can apply to anything and everything. All of these activites are supplements to actual lesson and there is a lesson for everything. The manipulation activities are here for students to reinforce their learning. Their learning comes from the standards, so its hard to inculde working with manipulations in the standards.
This web site can be used for graphing, analyzing and comparing equations. This program also shows where graphs are increasing and decreasing. This application will allow students to visualize the equation they are working with and provide a geometric perspective to their algebra work. While the program requires membership for the full benefits, it is free to sign up and use for students and teachers.
http://www.emints.org/ethemes/resources/S00000592.shtml
This website has an entire collection of manipulation activities. The activities range for grades 6,7,8. Students will get work with fractions, decimals, graphs, tessalations, and many other things. While this may seem inappropriate for many secondary teachers, the activites can be modified to fit courses of appropriate level. For example, the problem of the spinner can relate directly to work with probability. Also, some of the links provide material on lessons for an entire class period and some lessons encouraged the use of technology like the Smartboard.
http://www.shodor.org/interactivate/activities/
Again, this is a massive list of interactive lessons that can be used by teachers. The subject matter varies and there are multiple activities per subject. In particular, students direct a robot through a mine field laid out the cartesian plane. Its a list of fun activities that allow students to visualize the math they are working with.
All of these are about engagement and keeping the student invloved and focused. These are all great activities that will be useful for all of us.
And for the standards, manipulation can apply to anything and everything. All of these activites are supplements to actual lesson and there is a lesson for everything. The manipulation activities are here for students to reinforce their learning. Their learning comes from the standards, so its hard to inculde working with manipulations in the standards.
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