Learning Goals and Objectives

     State Standards in Georgia are undergoing the national push to become in line with the national curriculum that has been put forth.  In this push the state of Georgia has moved from the Georgia Performance standards to the Common Core curriculum.  In this effort to become more progressive the effects have been to move key mathematics concepts around through different grade levels.  There has been a shuffle of concepts to be in line with the national standards.   Understandably, this reform will become a good thing in the future once all students are at the same place or ahead across the county.  However, in the meantime there will be students who will be caught in the shuffle of the curriculum.  Thus, by doing so, students will be left with gaps of information from students moving up a grade level and curriculum being shifted down. 

     The Georgia performance standards state that sixth grade students will be taught and will learn ratios and the language of ratios.  Students will be able to use the language of ratios and proportions to solve problems of unit rate.  They read as taken from the Georgia education website:

     MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

MCC6.RP.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, for equations.

MCC6.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.

• Analyze and describe patterns arising from mathematical rules, tables, and graphs

MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours?  At what rate were lawns being mowed?

MCC6.RP.3c Find 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. (Not addressed in the unit).

MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (Not addressed in this unit).

     By the end of this unit the learning goals are students will be able to use ratio and proportions to describe relationships among numbers.  Students will be able to use ratios and rates to solve real world problems.  Students will be able to create a dual number line as a strategy to solve problems.  The unit will focus on real world applications of ratios and proportions and developing a basic understanding of these things.

   The learning goals are as follows:

1)  Given 10 word problems students will correctly set up ratios at least 7 out of ten times. 

2) Students will also be given 10 proportions and will correctly set up a dual number lineout of 10 times to show rate of change. 

3)  Given 10 word problems students will set up and solve proportions by cross multiplying. 

4) Lastly, given 10 real world applications (word problems) students will find unit rates and apply them to missing values in proportions seven out of 10 times. 

     This unit is designed to move students from a surface understanding of fractions into a deeper understanding of ratios and thus proportions.  With this understanding students will be able to use the language of mathematics to communicate the state standards of ratio language.  Also, these skills will lend themselves to being able to create a dual number line aspect and use these techniques to solve real world applications and gain a greater of the standard as well as gain greater ability to process questions dealing with a unit rate.

     Cognitively students will need to have processing and reasoning skills.  Students will need to use deductive and inductive reasoning to solve real world application and problems.  As sixth graders some will have developed the ability to move from concrete to abstract reasoning and some will have to use manipulatives to help them understand the concepts in the case that the reasoning abilities are not yet developed by the student.  

References

Georgia Standards. (2012). Georgia performance standards [Data file]. Retrieved from https://www.georgiastandards.org/Common-Core/Documents/Large-Print-MATH-CCGPS-Grade-6.pdf