ALEX Lesson Plans
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Title: From Knotty to Calculating
Description:
In this lesson, students will work within their math and English language arts classes to research the development of mathematical tools and their applications. A research paper will be produced for and graded by the English language arts teacher. A presentation will be made in the math class.
Standard(s): [ELA2013] (10) 29: Draw evidence from literary or informational texts to support analysis, reflection, and research. [W.910.9] [ELA2013] (9) 28: Draw evidence from literary or informational texts to support analysis, reflection, and research. [W.910.9] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama) [ELA2013] (11) 27: Draw evidence from literary or informational texts to support analysis, reflection, and research. [W.1112.9]
Subject: English Language Arts (9  11), or Mathematics (9  12)
Title: From Knotty to Calculating
Description: In this lesson, students will work within their math and English language arts classes to research the development of mathematical tools and their applications. A research paper will be produced for and graded by the English language arts teacher. A presentation will be made in the math class.
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Title: Slide Into the Past
Description:
Students will be introduced to the slide rule through A brief history on its use. They will practice simple calculations (multiplying and finding values of trigonometric, exponential, and logarithmic functions) using a virtual slide rule.
Standard(s): [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics (9  12)
Title: Slide Into the Past
Description: Students will be introduced to the slide rule through A brief history on its use. They will practice simple calculations (multiplying and finding values of trigonometric, exponential, and logarithmic functions) using a virtual slide rule.
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Title: Napier's Bones  A Useful Calculation Tool
Description:
This lesson deals with John Napier's historical contributions to the field of mathematics. Focus is given to Napier's Bones or Rods. Students will create a set or will use an online interactive set to perform calculations involving multiplication of 2 and 3 digit numbers.
Standard(s): [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama) [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama) [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics (9  12)
Title: Napier's Bones  A Useful Calculation Tool
Description: This lesson deals with John Napier's historical contributions to the field of mathematics. Focus is given to Napier's Bones or Rods. Students will create a set or will use an online interactive set to perform calculations involving multiplication of 2 and 3 digit numbers.
Thinkfinity Lesson Plans
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Title: Reflect on This
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In this lesson, from Illuminations, students investigate reflections in a plane using mirrors (or other reflective materials) and a geometry utility. They apply their findings to examination of interior angles of regular polygons.
Standard(s): [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Reflect on This
Description: In this lesson, from Illuminations, students investigate reflections in a plane using mirrors (or other reflective materials) and a geometry utility. They apply their findings to examination of interior angles of regular polygons. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Measuring Shadows
Description:
In this Science NetLinks lesson, students determine the pattern (length and direction) of shadows cast by sunlight during a several month period. They develop an interpretation of the daily and seasonal patterns and variations observed.
Standard(s): [S1] (6) 1: Identify global patterns of atmospheric movement, including El Niño, the Gulf Stream, the jet stream, the Coriolis effect, and global winds that influence local weather. [S1] (6) 8: Describe how Earth's rotation, Earth's axial tilt, and distance from the equator cause variations in the heating and cooling of various locations on Earth. [MA2013] (6) 26: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [6SP2] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [SID3] [MA2013] AL1 (912) 44: Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. [SID5] [MA2013] MI1 (912) 1: Critique ancient numeration systems and applications, including astronomy and the development and use of money and calendars. (Alabama) [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Measuring Shadows
Description: In this Science NetLinks lesson, students determine the pattern (length and direction) of shadows cast by sunlight during a several month period. They develop an interpretation of the daily and seasonal patterns and variations observed. Thinkfinity Partner: Science NetLinks Grade Span: 6,7,8
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Title: Using a Calculator for Finding the Equation of a Function
Description:
To determine the function of best fit for a set of data, students should recognize which category of function bests fit the data and know how to use technology to obtain a function. Students will use linear regression to find the best function. This lesson teaches these skills and prepares students for the subsequent lesson(s), in which they will collect their own data.
Standard(s): [MA2013] ALC (912) 4: Determine maximum and minimum values of a function using linear programming procedures. (Alabama) [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Using a Calculator for Finding the Equation of a Function
Description: To determine the function of best fit for a set of data, students should recognize which category of function bests fit the data and know how to use technology to obtain a function. Students will use linear regression to find the best function. This lesson teaches these skills and prepares students for the subsequent lesson(s), in which they will collect their own data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Podcasts
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Title: Logarithmic and Exponential Functions TV
Description:
This website has different videos explaining how to graph logarithmic and exponential functions.
Standard(s): [MA2013] AL1 (912) 23: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [MA2013] AL2 (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama) [MA2013] PRE (912) 18: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7]
Logarithmic and Exponential Functions TV
http://www.mathtv.co...
This website has different videos explaining how to graph logarithmic and exponential functions.
Thinkfinity Learning Activities
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Title: Hospital Locator
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In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.
Standard(s): [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Hospital Locator
Description: In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: IGD: Angle Bisector
Description:
This student interactive, from Illuminations, helps students understand and investigate angle bisectors. Students read a definition and then construct an angle bisector using the interactive tool. Finally, students take a closer look at the properties of angle bisectors by answering a set of questions and then checking their answers.
Standard(s): [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: IGD: Angle Bisector
Description: This student interactive, from Illuminations, helps students understand and investigate angle bisectors. Students read a definition and then construct an angle bisector using the interactive tool. Finally, students take a closer look at the properties of angle bisectors by answering a set of questions and then checking their answers. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: IGD: Euler Line
Description:
This student interactive, from Illuminations, helps students understand and investigate Euler lines. Students read a definition and then construct the Euler line of a triangle using the interactive tool. They learn that the Euler line involves three points associated with triangles: the circumcenter, orthocenter, and centroid.
Standard(s): [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [GC3] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: IGD: Euler Line
Description: This student interactive, from Illuminations, helps students understand and investigate Euler lines. Students read a definition and then construct the Euler line of a triangle using the interactive tool. They learn that the Euler line involves three points associated with triangles: the circumcenter, orthocenter, and centroid. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: IGD: Simson Line
Description:
This student interactive, from Illuminations, helps students understand and investigate a triangle s Simson line, which is the line passing through the feet of the perpendiculars dropped from P to the three sides of a triangle. Students construct the Simson line for a given triangle using the interactive applet.
Standard(s): [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [GCO13] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [GC3] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: IGD: Simson Line
Description: This student interactive, from Illuminations, helps students understand and investigate a triangle s Simson line, which is the line passing through the feet of the perpendiculars dropped from P to the three sides of a triangle. Students construct the Simson line for a given triangle using the interactive applet. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

