PSDA - Problem Solving and Data Analysis Module Overview

Problem Solving and Data Analysis

image Rate and Ratio word cloud The redesigned SAT's Math Test has responded to the research evidence identifying what is essential for college readiness and success by focusing significantly on problem solving and data analysis: the ability to create a representation of a problem, consider the units involved, attend to the meaning of quantities, and know and use different properties of operations and objects. Problems in this category will require significant quantitative reasoning about ratios, rates, and proportional relationships and will place a premium on understanding and applying unit rate.

Interpreting and synthesizing data are widely applicable skills in postsecondary education and careers. In the redesigned SAT's Math Test, students will be expected to identify quantitative measures of center, the overall pattern, and any striking deviations from the overall pattern and spread in one or two different data sets. This includes recognizing the effects of outliers on the measures of center of a data set. In keeping with the need to stress widely applicable prerequisites, the redesigned SAT emphasizes applying core concepts and methods of statistics, rather than covering broadly a vast range of statistical techniques.

Finally, the redesigned SAT's Math Test emphasizes students' ability to apply math to solve problems in rich and varied contexts and features problems that require the application of problem solving and data analysis to solve problems in science, social studies, and career-related contexts.

Essential Questions

How are ratios, rates and proportional relationships related?
How can you use a proportion or scale drawing to solve a problem?
How does solving a problem differ when percentages or measurements are involved?
How are linear, quadratic and exponential models the same and how do they differ?
What are the key features of each of these types of graphs?
How does a two-way table help us organize categorical data?
How can sample data help us draw conclusions about a population?
What are the significant features of a set of data and how do we calculate them?
What are some ways to make inferences and justify conclusions from data?

Key Terms

1. Rate - A comparison of two quantities that have different units of measure.

2. Ratio - A comparison of two quantities that have the same unit of measure.

3. Proportion - An equation which states that two ratios are equal.

4. Scale Drawings - Drawings that represent real objects or places. Scale drawings are in proportion to the real objects that they represent and the scale is given as a ratio.

5. Quadratic Equation - An equation of degree 2, which has at most two solutions. The general form of a quadratic equation is LaTeX: ax^2+bx+c=0 $ax^2+bx+c=0$ . Graphs of quadratic equations are called parabolas.

6. Exponential Function - A function of the form LaTeX: y=ab^x+c $y=ab^x+c$ , where both a and b are greater than 0 and b is not equal to 1. The c is a constant allowing the graph to shift vertically up and down.

7. Categorical Data - Data that is sorted or divided into different categories, according to the attributes of the data.

8. Relative Frequency - The ratio of the actual number of favorable events to the total possible number of events; often taken as an estimate of probability

9. Conditional Probability - The probability of an event A, assuming that B has already occurred.

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