3-31-2014 GRADE 8 LINEAR EQUATIONS AND PROPORTIONS

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: linear equations and proportions

Mathematics     Grade 8
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 ory-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.
Understand the connections between proportional relationships, lines, and linear equations.			Resources
	8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.	For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.	Utah Core Standards Resources IXL Practice Scatter Plot Excel Calculating Slope Save Our Dumb Planet Slope and Intercept Slope and y-Intercept Cab Fares
	8.EE.6. Use similar triangles to explain why the slope m is the same between any two            distinct points on a non-                vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.		T-chart  Graphing Slope Linear Equation Test Linear Function Graphing Equations and Inequalities Linear Function and Graph Line Plotter Slope of a Line Determining Slope Slope Tutorial

3-28-14 8th Grade Solving Linear Expressions and Proportions

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: SOLVE Linear expressions and proportions

Mathematics     Grade 8     Expressions & Proportions
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 ory-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.
Understand the connections between proportional relationships, lines, and linear equations.			Resources
	8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.	For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.	Utah Core Standards Resources IXL Practice Scatter Plot Excel Calculating Slope Save Our Dumb Planet Slope and Intercept Slope and y-Intercept Cab Fares
	8.EE.6. Use similar triangles to explain why the slope m is the same between any two            distinct points on a non-                vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.		T-chart  Graphing Slope Linear Equation Test Linear Function Graphing Equations and Inequalities Linear Function and Graph Line Plotter Slope of a Line Determining Slope Slope Tutorial

3/27/2013 Statistically Speaking

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: GEOMETRY

Grade 6 Statistics and Probability
Develop understanding of statistical variability.		RESOURCES
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. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.	Recognize Statistical Questions Forming a Statistical Question Recognizing Statistical Questions Writing Statistical Questions
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.	Center, Spread, and Shape Describing Distributions Distributions Quiz Leap Frog Marbles Practice with Data Understanding Probability Theoretical Probability Handling Data Handling All That Data
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.	Jupiter is Average Mean and Median Interactive Mean Green Machine Central Tendency Worksheets Measures of Spread Braining Camp: Median Medians The Party is Here Send in the Trolls Chances
Summarize and describe distributions.
6.SP.4.	Display numerical data in plots on a number line, including dot plots, histograms, and box plots.	Reading Charts and Graphs Stem and Leaf Plots Stem and Leaf Stem and Leaf Lesson STem and Leaf Box and Whisker Box Plot Braining Camp: Box Plots Box Plotter Box and Whisker Plot The Pizza Palace Bar Graph Bar Graphs Graphing Calculator Collecting and Analyzing Data Quiz Data Interpretation Games Exploring Histograms Histogram Line Graphs Line Graph Line Graph Lesson Long Distance Airplanes Push Ups
6.SP.5.	Summarize numerical data sets in relation to their context, such as by: ·         Reporting the number of observations. ·         Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. ·         Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. ·         Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.	Wolfram Alpha Interpreting Graphs Steppin Out Math Project Collecting Data Activity Explaining Your Results Using Graphs to Understand Data What Percentage of Your Class is...

4-13-2012 Teching the CCCS Grade 8 Proportions and 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 ory-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.
Understand the connections between proportional relationships, lines, and linear equations.			Resources
	8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.	For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.	Utah Core Standards Resources IXL Practice Scatter Plot Excel Calculating Slope Save Our Dumb Planet Slope and Intercept Slope and y-Intercept Cab Fares
	8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.		T-chart  Graphing Slope Linear Equation Test Linear Function Graphing Equations and Inequalities Linear Function and Graph Line Plotter Slope of a Line Determining Slope Slope Tutorial

2-6-2012 5 Great Graphing Tools

Graphing On Line

In preparation for working with a group of seventh graders on a graphing project, I went in search of the best tools online for students under the age of 13.  Here is what I found.

1. Rich Chart Live - This site is easy to use, has many options, and allows to publish in various ways with no sign-up, sign-in, or registration!  I will be using this with a seventh grade, self-contained, math class project.
2. Chartle.net - While not as "pretty" as Rich Chart Live, this is also easy to use, requires no registration for instant chart creation, and allows the user to publish, share, or embed..
3. Hohli - While I wouldn't choose this one for my class, it is a very clean site, no distractions, no registration and allows for publication.  It seems less self explanatory.  Here is a Youtube video on how to make a Hohli chart - http://youtu.be/RJB9K6MYfPo 
4. ChartGo Line Graphs - No sign up required and allows you to save, share, or embed.
5. Pretty Graph - This site does not require registration and allows the user to save, create a PDF, or email completed graphs.  All data must be uploaded to the site from a database or excel.

1-14-2012 CCCS Ratios and Proportional Relationships Grade 7

Continuing my way through the standards, offering links, lessons, and ideas to help teach the 

Core Curriculum Content Standards

Math Grade 7

Ratios and Proportional Relationships

STRAND	CPI	SKILLS	RESOURCES
Ratios and Proportional Relationships	The goal -     Students will connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems.	More specifically, students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.	Dirt Bike Proportions Ratio Blaster Ratio Stadium Math 6 Spy Guys
Understand ratio concepts and use ratio reasoning to solve problems.
·	1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.	For example, If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.	Ratios  Ratio Workout Practice More Practice Determine the Ratio Rate Demos Rate Tutorial Unit Rate Practice Scale Measures Converter
	·    2.Recognize and represent proportional relationships between quantities.	For example, Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.	Ratios and Proportions Introduction Proportion Mini-lesson Ratio and Proportion Videos Matching Equivalent Ratios Proportion Workout
		Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.	Rhythm Wheels Ratio and Proportion Ratio Tables and Proportions Ratio Tables and Proportions Video Unit Rate Problems
		Represent proportional relationships by equations.  For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.	Proportional Relationships Proportion Word Problems Linear Equation
		Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.	Understanding Slope Slope as a Unit Rate Interpret Slope
	3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.		Ratios, Rates, Percents, and Proportion Ratio, Proportion, Percent, Probability Lessons Percent Wheel Percent and Proportions Lesson Percentage Lessons With a Calculator

Please post a comment below if you have a site or lesson idea to share for teaching this standard.  I would love your input!