Archive for the ‘Sports Science MATH’ Category

Paper Horses

YEAR HORSE JOCKEY TRAINER OWNER TIME
2014 California Chrome V. Espinoza A. Sherman Coburn & Perry 2:03.66
2013 Orb J. Rosario S. McGaughey Stuart Janney & Phipps Stable 2:02.89
2012 I’ll Have Another M. Gutierrez D. O’Neill Reddam Racing 2:01.83
2011 Animal Kingdom J. Velazquez H. G. Motion Team Valor 2:02.04
2010 Super Saver C. Borel T. Pletcher WinStar Farm 2:04.45
2009 Mine That Bird C. Borel B. Woolley Double Eagle Ranch 2:02.66
2008 Big Brown K. Desormeaux R. Dutrow IEAH Stables, Pompa et al 2:01.82
2007 Street Sense C. Borel C. Nafzger James Tafel 2:02.17
2006 Barbaro    See Video E. Prado M. Matz Roy & Gretchen Jackson 2:01.36
2005 Giacomo M. Smith J. Sherrifs Mr. and Mrs. Jerome Moss 2:02.75
2004 Smarty Jones  See Video S. Elliott J. Servis Someday Farm 2:04.06
2003 Funny Cide J. Santos B. Tagg Sackatoga Stable 2:01.19
2002 War Emblem V. Espinoza B. Baffert Thoroughbred Corp. 2:01.13
2001 Monarchos J. Chavez J. T. Ward John C. Oxley 1:59.97
2000 Fusaichi Pegasus K. Desormeaux N. Drysdale Fusao Sekiguchi 2:01.12

 Ratios & Proportional Relationships

  • 6.RP.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
  • 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship.
  • 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. [Includes parts a, b, c, and d]

 The Number System

  • 6.NS.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
  • 6.NS.2 – Fluently divide multi-digit numbers using the standard algorithm.
  • 6.NS.3 – Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  • 6.NS.4 – Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
  • 6.NS.5 – Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
  • 6.NS.6 – Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [Includes parts a, b, and c]
  • 6.NS.7 – Understand ordering and absolute value of rational numbers. [Includes parts a, b, c, and d]
  • 6.NS.8 – Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

 Expressions & Equations

  • 6.EE.1 – Write and evaluate numerical expressions involving whole-number exponents.
  • 6.EE.2 – Write, read, and evaluate expressions in which letters stand for numbers. [Includes parts a, b, and c]
  • 6.EE.3 – Apply the properties of operations to generate equivalent expressions.
  • 6.EE.4 – Identify when two expressions are equivalent.
  • 6.EE.5 – Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • 6.EE.6 – Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
  • 6.EE.7 – Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
  • 6.EE.8 – Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
  • 6.EE.9 – Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

 Geometry

  • 6.G.1 – Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • 6.G.2 – Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
  • 6.G.3 – Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
  • 6.G.4 – Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
  • 6.SP.1 – Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
  • 6.SP.2 – 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.
  • 6.SP.3 – Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  • 6.SP.4 – Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • 6.SP.5 – Summarize numerical data sets in relation to their context. [Includes parts a, b, c, and d]

 

 

 

  • 6.NS.1 – Dividing Two Fractions
  • 6.NS.1 – Dividing Fractions and Mixed Numbers
  • 6.NS.1 – Dividing Fractions and Whole Numbers
  • 6.NS.2 – Dividing Multi-Digit Numbers
  • 6.NS.3 – Estimate All Operation Answers: Multi-Digit Decimals
  • 6.NS.3 – Add/Subtract/Multiply/Divide: Multi-Digit Decimals
  • 6.NS.4 – Identifying the Least Common Multiple
  • 6.NS.4 – Identifying the Greatest Common Factor
  • 6.EE.2a – Identifying Expressions that Represent Situations
  • 6.EE.2b – Parts of an Expression
  • 6.EE.2a – Translate Addition Sentences into Algebraic Expressions
  • 6.EE.2a – Translate Subtraction Sentences to Algebraic Expressions
  • 6.EE.2a – Translating Multiplication Sentences to Algebraic Expressions
  • 6.EE.2a – Translating Division Sentences to Algebraic Expressions
  • 6.EE.2c – Using Order of Operations to Evaluate Expressions
  • 6.EE.3 – Identify Equivalent Expressions: Distributive Property
  • 6.EE.4 – Identifying Equivalent Expressions by Evaluation
  • 6.EE.5 – Using Substitution to Determine Solutions
  • 6.RP.1 – Representing Ratios
  • 6.RP.2 – Expressing Unit Rate
  • 6.RP.3a – Ratio Tables and Graphs
  • 6.RP.3b – Solving Problems Involving Unit Rate
  • 6.RP.3d – Converting Measurement Units Using Ratio Reasoning
  • 6.RP.3c – Expressing Percents
  • 6.RP.3c – Percent Relationships
  • 6.RP.3c – Solving Percent Word Problems
  • 6.G.1 – Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.A.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

6.RP.A.3

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

 

6.RP.A.3a

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

 

6.RP.A.3b

Solve unit rate problems including those involving unit pricing and constant speed.

  • 6.NS.1 – Dividing Two Fractions
  • 6.NS.1 – Dividing Fractions and Mixed Numbers
  • 6.NS.1 – Dividing Fractions and Whole Numbers
  • 6.NS.2 – Dividing Multi-Digit Numbers
  • 6.NS.3 – Estimate All Operation Answers: Multi-Digit Decimals
  • 6.NS.3 – Add/Subtract/Multiply/Divide: Multi-Digit Decimals

John Brenkus and the “Sport Science” team break down why Little League World Series pitcher Mo’ne Davis can reach 70 mph with her fastball.

6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.
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How to Calculate Miles Per Hour in Pitching

by Axl J. Amistaadt, Demand Media

The “fastest pro pitcher of all time” will inevitably change over the years as records are eventually broken by the latest and greatest, and the point will ever be contested eternally by players, fans, historians and researches. All-time great Nolan Ryan’s rocketing Aug. 20, 1974, fastball pitch against the Detroit Tigers was entered into the Guinness World Records “officially” at 100.9 miles per hour. According to power-hitting Hall of Famer Reggie Jackson, “Every hitter likes fastballs just like everybody likes ice cream. But you don’t like it when someone’s stuffing it into you by the gallon. That’s how you feel when (Nolan) Ryan’s throwing balls by you.” Surprise your friends at the next game by calculating pitching miles per hour using simple math that’s easy enough for a middle school kid to learn.

Items you will need

  • Measuring tape
  • Stopwatch

Step 1Measure the distance from where the ball will be thrown to home plate with a tape measure. It’s 60.6 feet to the plate from the pitcher’s mound on a Major League diamond, but the distance varies between leagues and playing levels.

Step 2Clock the pitch’s travel time with a stopwatch. This is the time that it takes for the ball to travel from the pitcher’s hand to when it reaches home plate — a half second, for example.

Step 3Calculate the average speed of the pitched ball with the equation S = D / T. The speed in feet per second is represented by S, the travel distance is D, and the time it took for the pitch to reach the plate is T. The pitch’s speed in this example is 60.6 / 0.50 = 121.2 feet per second.

Step 4Divide the seconds in an hour (3,600) by feet per mile (5,280). The conversion ratio is 0.682. Convert the pitch’s speed per second into miles per hour using the formula M = S x (3,600 / 5,280). M represents the ball’s speed in miles per hour, with S being its speed in feet per second. The speed in this example is formulated as 121.2 x 0.682 = 82.65 miles per hour.

Step 5Figure the pitch’s speed in miles per hour directly from its travel speed in seconds and the distance. Though slightly more involved, it’s a bit quicker. In the equation M = (D / T) x (3,600 / 5,280), M represents the speed in miles per hour, D represents the distance in feet and T represents the travel time in seconds. This formulation for the pitch’s average speed is (60.6 / 0.50) x (3,600 / 5,280) = (121.2 x 0.682) = 82.65 miles per hour in this example.

Sport Science: Gymnastics

Posted: October 20, 2016 in Sports Science MATH

4.MD.C.6

MP5

MP6

Measure angle openings precisely by using a protractor

6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.EE.2b
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

6.EE.2c
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

7.NS.2d
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.3
Solve real-world and mathematical problems involving the four operations with rational numbers.

7.G.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.