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Posted: August 22, 2017 in Advance, Off the Beaten Math
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      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.
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1. Identify independent and dependent variables

2. Relate independent and dependent variables using a function table

3. Show the relationship between variables using a graph

4.  Relate variables using an equation

5. Solve for missing values in rate problems using a table

 

(6.RP.A.1) Understand ratios and using ratio language to describe a ratio relationship

Lessons:

Tenmarks Assignments:

  • 6.RP.1Representing Ratios

 

(6.RP.A.2) Understand unit rate and use rate language in the context of a ratio relationship

Lessons:

TenMarks Assignments:

  • 6.RP.2 Expressing Unit Rate

 

6.RP.3a-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.

 Lessons:

Isolation Drills:

 

TenMarks. Assignments:

  • 6.RP.3a Ratio Tables and Graphs

 

6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed.

Lessons:

Isolation Drills:

 

TenMarks Assignments:

  • 6.RP.3b Solving Problems Involving Unit Rate

 

6.RP.A.3c nFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Lessons:

Isolation Drills:

TenMarks Assignments:

  • 6.RP.3cExpressing Percents
  • 6.RP.3cPercent Relationships
  • 6.RP.3cSolving Percent Word Problems

6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Lessons:

Convert measurement units using ratio tables

Isolation Drills:

none

TenMarks Assignments:

  • 6.RP.3d Converting Measurement Units Using Ratio Reasoning

Rates, Ratio, and Proportions

Statistics

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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]

 

 

 

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Scores:

6.G.1 Find the area41 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.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.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.

materials

Barbie Bungee Jump EXCEL Spreadsheet

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

6.EE.2a
Write expressions that record operations with numbers and with letters standing for numbers.

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).

6.EE.3
Apply the properties of operations to generate equivalent expressions.

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.

School Hall Drop Zone= .5m (mortar) + 7.5b (blocks)  144-181 inches

School Roof Drop Zone= 7.5v (vertical bricks) + .5m(mortar) + 2h(horizontal bricks)