**SAT****® Preparation Course**

**Unit 2: Problem Solving and Data Analysis**

**Unit 2: Problem Solving and Data Analysis**

The
redesigned SAT®’s Math Test has responded to the research that has identified 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.

Students will be expected to identify quantitative measures of center, overall patterns, 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.

All Problem Solving and Data Analysis questions test the ability of students to use their math understanding and skills to solve problems they could encounter in the real world. Many of these problems are set in academic and career contexts and are likely to draw from science and social science.

Students will be expected to identify quantitative measures of center, overall patterns, 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.

All Problem Solving and Data Analysis questions test the ability of students to use their math understanding and skills to solve problems they could encounter in the real world. Many of these problems are set in academic and career contexts and are likely to draw from science and social science.

**What will my child learn?**

Students will:

SAT.PSDA.01

**Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.**The student will use a proportional relationship between two variables to solve a multistep problem to determine a ratio or rate; calculate a ratio or rate and then solve a multistep problem; or take a given ratio or rate and solve a multistep problem.

Mathematics 7 (Unit 2 - 7.RP.A.2, 7.RP.A.2.C)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 1 | Learnerator - Rates, ratios, & proportions

SAT.PSDA.02

**Solve single- and multistep problems involving measurement quantities, units, and unit conversion.**The student will solve a multistep problem to determine a unit rate; calculate a unit rate and then solve a multistep problem; solve a multistep problem to complete a unit conversion; solve a multistep problem to calculate density; or use the concept of density to solve a multistep problem.

Mathematics 6 (Unit 2 - 6.RP.A.3d)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 22 | College Board - item 25 | College Board - item 26 | Ivy Global - item 3 | Learnerator - Measurement quantities, units, & conversions

SAT.PSDA.03

**Solve single- and multistep problems involving percentages.**The student will solve a multistep problem to determine a percentage; calculate a percentage and then solve a multistep problem; or take a given percentage and solve a multistep problem.

Mathematics 7 (Unit 2 - 7.RP.A.3)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 2 | Learnerator - Multistep problems with percentages

SAT.PSDA.04

**Compare linear growth with exponential growth.**The student will infer the connection between two variables given a context in order to determine what type of model fits best.

Algebra 1 (Unit 2 - F.LE.A.1)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 5

SAT.PSDA.05

**Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related.**The student will, given a scatterplot, select the equation of a line or curve of best fit; interpret the line in the context of the situation; or use the line or curve of best fit to make a prediction.

Algebra 1 (Unit 2 - S.ID.B.6)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 3 | College Board - item 5 | College Board - item 20 | College Board - item 21 | Ivy Global - item 4 | Learnerator - Scatterplots & statistical models

SAT.PSDA.06

**Use the relationship between two variables to investigate key features of the graph.**The student will make connections between the graphical representation of a relationship and properties of the graph by selecting the graph that represents the properties described, or using the graph to identify a value or set of values.

Algebra 1 (Unit 2 - F.IF.B.4)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 6 | Learnerator - Investigating graphical relationships

SAT.PSDA.07

**Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability.**The student will summarize categorical data or use categorical data to calculate conditional frequencies, conditional probabilities, association of variables, or independence of events.

Algebra 1 (Unit 4 - S.ID.B.5) | Geometry (Unit 5 - S.CP.A.4)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 8 | College Board - item 10 | College Board - item 11 | Ivy Global - item 7 | Learnerator - Two-way tables and probability

SAT.PSDA.08

**Make inferences about population parameters based on sample data.**The student will estimate a population parameter given the results from a random sample of the population. The sample statistics may mention confidence intervals and measurement error that the student should understand and make use of, but need not calculate.

Algebra 2 (Unit 5 - S.IC.A.1)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 9

SAT.PSDA.09

**Use statistics to investigate measures of center of data and analyze shape, center, and spread.**The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation.

Algebra 1 (Unit 4 - S.ID.A.3)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 13

SAT.PSDA.10

**Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods.**The reports may consist of tables, graphs, or text summaries.

Algebra 2 (Unit 5 - S.IC.B.3 | S.IC.B.6)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 2 | College Board - item 14 | Ivy Global - item 10 | Learnerator - Data collection methods

Tools and TechnologyDesmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! NCTM's Advanced Data Grapher can be used to build and analyze data using box plots, scatterplots, histograms, stem-and-leaf plots, and bubble graphs. You can enter multiple rows and columns of data, select which set(s) to display in a graph, and choose the type of representation. |
More 4 UThe Khan Academy has produced videos of worked examples of concepts found in the Problem Solving and Data Analysis portion of the new SAT®. Khan Academy also has four official practice exams from College Board. |