Celebrate Pi Day! 3.14.15 9:26:53

Pi day is March 14th and many schools will be celebrating on Friday.  How will your school mark the big day?  Here are some resources and suggestions.

1. News Hour wants to know how you're celebrating Pi Day, tweet about it!
2. The Math Forum @ Drexel activities to celebrate Pi Day.
3. Teach π.org - A one-stop Pi Day stop for teachers and number lovers.
4. The Joy of π
5. CNN - How America Celebrates Pi Day
6. Pi Day Challenge
7. Pi Day.org
8. Exploratorium: Pi Day
9. How to Celebrate Pi Day
10. Celebrate Pi Day on Math  Goodies
11. Tween Us
12. How to Type the π Symbol
13. Fun Facts about our Favorite Irrational Number
14. Visnos Interactive Teaching Resource

Tangram Tales

Fifth grade self-contained teachers were looking for tangram activities for their classes.  I suggested creating a class tangram story like the one above.
Here are some additional tangram resources.

• Story on one page with tangram pictures - http://teachersnetwork.org/teachnet-lab/ps101/chornik/grandfather.htm
• Smart Exchange activities - http://exchange.smarttech.com/details.html?id=9bfd751c-ca5d-4733-9748-475963892d53
• Interactive Online Tangram - http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html
• Tangram Thinking Games - http://www.mathplayground.com/tangrams.html
• Tangram Game - http://pbskids.org/cyberchase/math-games/tanagram-game/
• ABCya Tangrams - http://www.abcya.com/tangrams.htm
• Tangram House - http://www.puzzlechoice.com/pc/Tangramx.html

Bad Dates, Ratios, Rates, and Proportions

The sixth grade math teachers were looking for ways to integrate technology into their lessons on ratios and proportions.  This is what I came up with.

1. BBC Lesson, Activity, and Test - http://www.bbc.co.uk/bitesize/ks3/maths/number/ratio/revision/1/
2. Matching equivalent ratios (allow popup) - http://www.harcourtschool.com/activity/con_math/g05c27.html
3. Fruit Loops - http://tothesquareinch.wordpress.com/2011/12/31/fruit-loop-ratios/
4. Common Core Assessment: Truffles (with sample responses)- http://www.insidemathematics.org/assets/common-core-math-tasks/truffles.pdf
5. Ratios on AAA math - http://aaamath.com/rat.html
• Determining Ratios - http://aaamath.com/rat62b-findratios.html#section2
• Determine the number based on the ratio practice - http://www.aaamath.com/B/g62a_rx1.htm#section2
• Determine the ratio practice - http://www.aaamath.com/B/g62b_fx1.htm#section2
6. Ratio Blasters - http://www.arcademicskillbuilders.com/games/ratio-blaster/ratio-blaster.html
7. Ratio Stadium - http://www.arcademics.com/games/ratio-stadium/ratio-stadium.html
8. Musical Ratios - http://csdt.rpi.edu/latino/rhythm/rhy_intr.htm
9. Homework help - http://www.mathvillage.info/node/91
10. Ratios and Proportions Whiteboard lesson - https://www.wisc-online.com/learn/formal-science/mathematics/gem2004/ratios-and-proportions
11. Ratios and Proportions - http://www.math.com/school/subject1/lessons/S1U2L2GL.html
12. Dirt Bike proportions - http://www.arcademics.com/games/dirt-bike-proportions/dirt-bike-proportions.html
13. Ratios, Rates, and Percentages on Kahn Academy - https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic
14. Percents on AAA math - http://www.aaamath.com/pct.html

Lessons and Projects

http://kuna6th.weebly.com/ratio-and-proportion-lessons.html

http://ellienix.blogspot.com/2013/05/ratios-and-proportionsand-goldfish.html

4-1-14 Probability Probably Matters

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 7: STATISTICS PT. 2

Investigate chance processes and develop, use, and evaluate probability models.		RESOURCES
7.SP.5.	Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.	What is Probablility? Math is Fun Khan Academy Math Goodies
7.SP.6.	Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.	Coin Toss Probability PBS Coin Toss Interactivate Toss Interactivate Spinner BBC Dice
7.SP.7.	Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?	Marbles Experimental Probability Math is Fun: DATA Probability of Events Math Goodies BrainPop Math is Fun: Advanced
7.SP.8.	Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?	Tree Diagram Lesson Tree Diagram Lesson 2 Relative Frequency Table example List Example Throwing Dice Theory Random.org Rolling the Dice Learnzillion Virtual Nerd YouTube Lesson

11-15-2012 Function, Function, What's your Function?

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: FUNCTIONS

FUNCTIONS
By the end of Grade 8	Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.
Define, evaluate, and compare functions.			RESOURCES
	8F.A.1	Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.	Algebra Puzzle Algebraic Reasoning Algebra vs The Cockroaches  Equation Match  Explore Families of Functions Function Machine Late Delivery Linear Function Machine Mystery Operations Number Cruncher Patterns & Functions Positive Linear Function Machine Solve Equations Spy Guys Interactive - Balancing Equations Teacher Dodgeball  Whole Number Cruncher
	8F.A.2	Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
	8F.A.3	Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.			RESOURCES
	8F.A.4	Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.	Virtual Manipulatives: Algebra Save Our Dumb Planet Linear Equation Problem Solver  Practice Lessons Practice with Solving Inequalities Equation of a Line: Slope-Intercept Form Find the graph that best matches the linear equation Linear Equation Test Linear function  Linear function and Graph Linear Functions Part A: Basics: Slope and Intercept Part B: Finding the Equation of a Line  Graphing linear equations Linear Equation Solver Linear Equation Solvers  The Linear Equations Solver Applet Linear Equation Solver Linear Equation Solver Rags to Riches Game Solving Equations with Variables on Both Sides  Writing Equation of a Line Linear functions: Rate of Change of linear Functions Grand Slam Math Late Delivery Math at the Mall Math in Daily Life: How do numbers affect everyday decisions? Thinking Blocks  Word Problems with Katie
	8F.A.5	Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

4-28-2012 Choreographing Curriculum

Teching the CCCS

Visual and Performing Arts

Grades 5-8

Performance: Dance

1.3 Performance: All students will synthesize those skills, media, methods, and technologies appropriate to creating, performing, and/or presenting works of art in dance, music, theatre, and visual art.
A.  By the end of grade 8, those students choosing DANCE as their required area of specialization demonstrate COMPETENCY in the following content knowledge and skills.			RESOURCES
Movement dynamics and qualities emphasize time, space, and energy.Movement affinities and effort actionsimpact dynamic tension and spatial relationships.	1.3.8.A.1	Incorporate a broad range of dynamics and movement qualities in planned and improvised solo and group works by manipulating aspects of time, space, and energy.	Arts Alive Dance Words Teaching Dynamics Space Space, Time, Energy The Dancer's Blog Elements of Dance Teaching Elements of Dance Choreography Assessment Modern Dance Create-A-Line-Dance Dance Lesson of the Month Dance and Literature Laban Movement Analysis What is a Lyrical Dance? Lyricism Video
Dance may be used as a symbolic language to communicate universal themes and varied points of view about social, political, or   historical issues in given eras.	1.3.8.A.2	Choreograph and perform cohesive dance works that reflect social, historical, and/or political themes.
Foundational understanding of anatomical and kinesthetic principlesis a contributing factor to dance artistry. Artistry in dance requires rhythmic acuity.	1.3.8.A.3	Choreograph and perform movement sequences that demonstrate artistic application of anatomical and kinesthetic principles as well as   rhythmic acuity.
Technology and media arts are often catalysts for   creating original choreographic compositions.	1.3.8.A.4	Use media arts and technology in the creation and performance of short, original choreographic compositions.

4-16-2012 Teching the CCCS - Grade 8 Solving Linear Equations

Mathematics     Grade 8     Expressions & Equations
Formulate and reason about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.  Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems   to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
Analyze and solve linear equations and pairs of simultaneous linear equations.			Resources
	8.EE.7. Solve linear equations in one variable.	Give examples of linear equations in one variable with one   solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, ora = b results (where a and b are different numbers).	Algebra Help Save the Zogs Balance Beam Balance Beam II Linear Equation Solver Easy Algebra Equations and Inequalities Linear Equation Study Guide Word Problem Equations One Unknown One Step Equations
		Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.	Regents Linear Equations Transparent Algebra Expanding Expressions Expanding and Simplifying Expansion and Factorization
	8.EE.8. Analyze and solve pairs of simultaneous linear equations.	Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.	Virtual Math Lab Linear Relationships Intersection of 2 lines Math Matters Simultaneous Equations
		Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.  For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.	2 Equation Drills Linear Equations Solver Linear Equation Solver II Web Calculator 2 Equations, 2 Unknowns Substitution Method Systems Tutorial
		Solve real-world and mathematical problems leading to two linear equations in two variables.  For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.	Word Problems that lead to Simultaneous Equations Graphing Systems Algebra Class Word Problems Pump Up! Worksheets