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The Rates of Ratios in Today's World
Transcript of The Rates of Ratios in Today's World
*Answer keys and rubrics are also provided in these documents. *See attached Microsoft Word documents (in email).
Assessments- Paragraph response, quiz, and exit slip.
* See "Outline & Assessments" document.
How do you know whether to use rates or ratios when solving real-world problems? The main standard requires students to use
reasoning skills in order to solve both mathematical and
real-world problems that involve rates and ratios. In order for
students to correctly reason when using these two topics, they need to know
when to use each one.
By solving rate problems that include unit pricing and constant speed,
students will see how rate relates to real world problems as well as be able to
perform the skills needed to solve these problems. By using converting ratio
measurement units, students will be further practicing their multiplication
and division skills. They will also be determining when it is appropriate to use
each mathematical process for converting.
Student evaluation of which method to use when converting measurement
ratios will help them evaluate the best way to solve problems involving rates.
When students can master these two concepts, they will be able to effectively
solve both real-world and mathematical problems with rates and ratios. How do you use rate to solve a problem that
involves pricing? Constant speed? Why is it better to use rate (rather than ratio) when solving a problem involving pricing or constant speed? How do you know when to multiply or divide when measuring ratios? Big Ideas Pre-Test & Post-Test Outline & Assessments Focus Standards Rates and ratios help us solve everyday complications.
Because not everything can be
measured equally (the same), you
need to know how to convert these
measurements to best meet your needs. Meeting Student Needs Enrichment CCSS.Math.Content.6.RP.A.3 Use ratio & rate reasoning to solve real-world & mathematical problems. 3.b: Solve unit rate problems including those involving unit pricing & constant speed. 3d: Use ratio reasoning to convert measurement units; manipulate & transform units appropriately when multiplying or dividing quantities. Bloom's Taxonomy 6.RP.A.3 6.RP.A.3b 6.RP.A.3d Skills Concepts Use
mathematical reasoning problems Skills Concepts Solve
Involving unit rate problems unit pricing
constant speed Level 5 or 6: Evaluating or Creating Use fits into the Apply category because the student has to try to use the (rate and ratio) information in a new way- solving problems.
Solve fits into the Evaluate & Create categories, depending on problem that is being solved. If the problem is simply going through a sequence of steps to find an answer, then "solve" only hits the Evaluate category. If the problem is taking the steps, or answer, and adding on or making something new, then "solve" hits the Create category. Level 5 or 6: Evaluating or Creating Solve, again, fits into the Evaluate and Create categories, pending on the type of problem that is being solved. If the problem is going through the sequence of steps to find an answer, then "solve", again, only hits the Evaluate category. If the [unit rate] problems take the steps and adds to them, or makes something new, then "solve" hits the Create category.
Involving fits either into the Analyzing or Evaluating category, depending on the type of problem. This parallels the same type of thinking as separating "solve" , but does so at a lower level Bloom's because students need to be able to decide which methods are best to use in each problem. They will either use a unit pricing method or a constant speed method. Level 4: Analyzing Use fits into the Apply category because students are
going to use [ratio] reasoning to figure out problems- they
apply that knowledge to solve a problem.
Convert falls into the Apply category as well because students are
taking their understanding of different topics and applying
(converting) them to problems, whether they are real-world or mathematical problems.
Manipulate/transform [units] fits into the Create category because students are transforming ideas and concepts into new ones. They are not just deciding between which concepts to use, but are adding to (or taking away from) each concept to make it work to solve
problems. They are creating something new out of what they were
Multiply/divide [quantities] fits into the Apply and Analyze
categories because students are using these concepts to work
through problems (apply), but they are also deciding
which concepts to use in order to determine the
most efficient way to solve a problem
(analyze). Skills Concepts Use
Multiplying/ Dividing ratio
unit rate problems
quantities problems Essential Question Essential Question What is the best way to solve a ratio problem that requires you to convert units? Essential Question I chose these big ideas and essential questions because they relate directly to the three standards that I chose. Students need to understand how these concepts can be used in real-life and how to best use prior knowledge when trying to solve these types of problems. Remediation Low Reading Level English Learner This student would still work at the same pace as the rest of the class unless he/she demonstrated a lack of mathematical knowledge. I would use examples from this child's native country, as well as allow for some written responses to be written in the native language. However, by sixth grade, the student should be somewhat proficient in English, so my expectations at this age would be higher than at a third grade level. No questions or key words will be written in the native language unless there is a clear cognitive delay. I would have this student work with my enrichment student in an attempt to have the [enrichment] student help explain each problem and set up steps (during activities). I would also have this student visit an online website that helps explain processes better, and would give the student opportunities to do more problems. If the student is lacking in multiplication and division skills, I would have activities such as "memory" or "around the world" games for this child to participate in more often.