## Math Education Standards

#### SfA and Math Education Standards

Statistics for Action situates opportunities for practicing math skills into a dramatic community context: One where people's health, homes, and childrens are on the line. Even if your students are not directly experiencing environmental contamination, the high stakes, drama, and politics involved may be more engaging than a typical math workbook problem.

Many SfA activities feature different versions within one activity (all building the same skill or concept, but with different data sets or environmental media). Pick the one that fits best; if only one version fulfills the education standard, it will be specified below.

SfA activities are an application for math and critical thinking skills. Activities can be used at the beginning of a unit to spark interest, and/or at the end of a unit as synthesis activities. Many activities combine different math ideas, so some of the standards below are grouped together. Hover over the colored buttons to expand the text of the particular standard. The Career and College Readiness Standards are based on the Common Core State Standards. The biggest change is that adult ed eliminates grade levels and replaces them with five levels, A-E. Educators can reference the purple button for the level for adults and then the red button for the precise standard.

The color code used is:

#### Basic Math Operations

Compare to Standards - Participants compare environmental test results to health-based standards by dividing one by the other. They generate statements like “The arsenic in sample SB-08 was 12.8 times the screening level.” Then they create a number line and arrange the results along that line.

GED Quantitative Assessment Target Q.1.b
Perform addition, subtraction, multiplication, and division on rational numbers
GED Quantitative Assessment Target Target Q.1.h
Identify absolute value or a rational number as its distance from zero on the number line and determine the distance between two rational numbers on the number line, including using the absolute value of their difference.
GED Quantitative Assessment Target Q.2.a
Solve single-step or multistep real-world arithmetic problems involving the four operations with rational numbers, including those involving scientific notation.
Mathematics » Grade 7 » The Number System » A.3
Solve real-world and mathematical problems involving the four operations with rational numbers
Mathematics » Grade 6 » The Number System » B.2
Fluently divide multi-digit numbers using the standard algorithm. Mathematics » Grade 6 » The Number System » B.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Mathematics » Grade 6 » The Number System » C.7c
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
NRC Scientific Practices 4 & 5
4. Analyzing and interpreting data.
5. Using mathematics and computational thinking.
Level C and D » The Number System Reading, Anchor 7

Exposed! - Participants read about four children who spend time at or near a contaminated place. Then they guess which child has the longest exposure, and verify by calculating it. Involves addition and multiplication.

GED Quantitative Assessment Target Q.1.b
Perform addition, subtraction, multiplication, and division on rational numbers
GED Quantitative Assessment Target Q.2.a
Solve single-step or multistep real-world arithmetic problems involving the four operations with rational numbers, including those involving scientific notation.
Mathematics » Grade 7 » The Number System » A.3
Solve real-world and mathematical problems involving the four operations with rational numbers
Standard for Math Practice 1
Make sense of problems and persevere in solving them.
Standard for Math Practice 4
Model with mathematics.
NRC Scientific Practices 1, 5, & 7
5. Using mathematics and computational thinking.
7. Engaging in argument from evidence.
Level D » The Number System

As Toxic As…? - Participants explore the toxicity of an unfamiliar contaminant by dividing its health-based standard by the same standards for more familiar contaminants like lead, mercury, arsenic, and cyanide. They generate statements like “Benzo[a]pyrene is 50 times as toxic as arsenic in water.” The activity also shows inverse proportionality: Contaminants with smaller health-based standards are generally more toxic.

GED Quantitative Assessment Target Q.1.b
Perform addition, subtraction, multiplication, and division on rational numbers
GED Quantitative Assessment Target Q.2.a
Solve single-step or multistep real-world arithmetic problems involving the four operations with rational numbers, including those involving scientific notation.
Mathematics » Grade 7 » The Number System » A.3
Solve real-world and mathematical problems involving the four operations with rational numbers
Mathematics » Grade 7 » Expressions and Equations » B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Standard for Math Practice 6
Attend to precision.
NRC Scientific Practices 5 & 8
5. Using mathematics and computational thinking.
8. Obtaining, evaluating, and communicating evidence.
NRC Scientific Practices 5 & 8
5. Using mathematics and computational thinking.
8. Obtaining, evaluating, and communicating evidence.
Level D » The Number System Level D» Expressions and Equations

#### Unit Rates, Unit Conversions, Proportional Scaling

Limits and LevelsA set of fact sheets for common limits and levels people encounter in environmental science. Most are a rate/ratio like milligrams per liter, mg/kg/day, microgram per cubic meter, etc. If the units are unfamiliar, more info can be found in the fact sheets in Common Units. There are no specific activities for the fact sheets, but they can be used to supplement other activiites, or to practive converting/scaling between different kinds of units.

GED Quantitative Assessment Target Q.3.a
Compute unit rates
Mathematics » Grade 6 » Ratios & Proportional Relationships 3d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
NRC Scientific Practices 5
Using mathematics and computational thinking.
Level D » The Number System Reading, Anchor 7» Level C, D, E

Converting Between Units - Participants practice converting part per million or parts per billion to either mg/kg and µg/kg (for soil) or mg/L and µg/L (for water).

GED Quantitative Assessment Target Q.3.a
Compute unit rates
GED Quantitative Assessment Target Q.3.b
Use scale factors to determine the magnitude of a size change. Convert between actual drawings and scale drawings
Mathematics » Grade 6 » Ratios & Proportional Relationships 3d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Mathematics » High School » Numbers & Quantities 3d
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas
NRC Scientific Practices 5
Using mathematics and computational thinking.
Level D » The Number System Level E » Number and Quantity: Quantities

Exposed! - See Above. Convert hours per year to average hours per day.

GED Quantitative Assessment Target Q.3.a
Compute unit rates
NRC Scientific Practices 5
Using mathematics and computational thinking.
Level D » The Number System Level E » Number and Quantity: Quantities

#### Multi-step arithmetic problems using percents, ratios, and averages.

Memorable Messages – In the activity as written, participants look at examples of how one numerical fact can be presented in many different ways (percents, ratios, etc.). They discuss the ones they find most powerful. Multiple calculations and proportional reasoning are needed to change “The legal limit for arsenic in drinking water is 10 µg/L” to “One ounce of arsenic could contaminate enough drinking water to fill an Olympic-sized swimming pool.” An instructor can follow by having students make their own memorable messages, or trace back how to get from the original fact to the favorite message. The session also includes the resource Benchmark Numbers, which gives ideas for using familiar, local, or impressive objects as pseudo-units.

GED Quantitative Assessment Target Q.3.a
Compute unit rates
GED Quantitative Assessment Target Q.3.b
Use scale factors to determine the magnitude of a size change. Convert between actual drawings and scale drawings
GED Quantitative Assessment Target Q.3.c
Solve multistep, arithmetic, real-world problems using ratios or proportions including those that require converting units of measure.
GED Quantitative Assessment Target Q.3.d
Solve two-step, arithmetic real world problems involving percents.
Mathematics » Grade 6 » Ratios & Proportional Relationships 3d
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Standard for Math Practice 4
Model with mathematics.
NRC Scientific Practices 5 & 8
5. Using mathematics and computational thinking.
8. Obtaining, evaluating, and communicating evidence.
Level D » The Number System Speaking and Listening, Anchor 2 » Levels C, D, E Anchor 5 » All Levels Writing, Anchor 8 » Levels C, D, E

Common Units: Physical units like cubic meters, liters, and kilograms can be used for fun ratio and scaling activities. For example, you can take a fact from the fact sheet like, “A typical person breathes one cubic meter of air in two hours” and then ask, “How many hours of air are there in this room for the 20 people here?” Follow by measuring the room, calculating its volume in cubic meters, and then scaling.

GED Quantitative Assessment Target Q.3.c
Solve multistep, arithmetic, real-world problems using ratios or proportions including those that require converting units of measure.
GED Quantitative Assessment Target Q.3.d
Solve two-step, arithmetic real world problems involving percents.
Mathematics » Grade 7 » Geometry 7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Standard for Math Practice 4
Model with mathematics.
Standard for Math Practice 5
Use appropriate tools strategically.
Level D » Geometry

Finding Newsworthy Data - Participants read a data set, and use a set of tips to find the most newsworthy facts in the data (usually a ratio between numbers in the data or a rate increase or decrease). Then they practice different ways of expressing those facts using direct comparison, ratios, percents, percent increase/decrease, and orders of magnitude.

GED Quantitative Assessment Target Q.3.c
Solve multistep, arithmetic, real-world problems using ratios or proportions including those that require converting units of measure.
GED Quantitative Assessment Target Q.3.d
Solve two-step, arithmetic real world problems involving percents.
GED Quantitative Assessment Target Q.7.a
Reading and interpreting graphs, charts, and other representations.
Mathematics » Grade 6 » Ratios & Proportional Relationships 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, or equations.
Mathematics » Grade 7 » Ratios & Proportional Relationships 1-3
1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
2. Recognize and represent proportional relationships between quantities.
3. Use proportional relationships to solve multistep ratio and percent problems.
NRC Scientific Practices 1, 4, 5, & 8
4. Analyzing and interpreting data.
5. Using mathematics and computational thinking.
8. Obtaining, evaluating, and communicating evidence.
Level D » The Number System Anchor 5 » All Levels

Inside Averages - Participants start with a stated average, and six different graphic (column chart) representations of data that could have that average. They match each graph with a common questionable practice (provided) used for finding an average.  They then approach the problem from the reverse angle – starting with an average and then imagining a data set that could match it. Graph paper is provided to highlight the graphic-area method of determining an average. You can supplement with the video Averages Can Be Political – A 1-min video describing how averages used in environmental testing might not always be the best way to present what's really going on. The example used is tests of trihalomethanes in Miami drinking water.

GED Quantitative Assessment Target Q.8
Measuring the center of a statistical data set.
Mathematics » Grade 3 » Measurement and Data 3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
Mathematics » Grade 6 » Statistics and Probability 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.
NRC Scientific Practices 4, 5, & 6
4. Analyzing and interpreting data.
5. Using mathematics and computational thinking.
6. Constructing explanations.
Level B » Measurement and Data Level B » Statistics and Probability

#### Reading, interpreting, and making graphs and charts.

Memorable GraphsParticipants are given a numerical fact in words, along with five different ways to depict it graphically. They decide which they find most compelling and why. Then they discuss principles of making a compelling graphic depiction of data.

GED Quantitative Assessment Target Q.7.a
Reading and interpreting graphs, charts, and other representations.
Standard for Math Practice 4
Model with mathematics.
Mathematics » Grade 7 » Ratios & Proportional Relationships 2
Recognize and represent proportional relationships between quantities.
Mathematics » Grade 3 » Measurement and Data 3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.
Mathematics » High School » Statistics & Probability » Interpreting Categorical & Quantitative Data 1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
NRC Scientific Practices 4 & 8
4. Analyzing and interpreting data.
8. Obtaining, evaluating, and communicating evidence.
Level B » Measurement and Data Level D » The Number System Level E » Statistics and Probability

Finding Newsworthy Data - See above. The versions Public Health Data and Pesticides on Food present data in graphs for participants to analyze.

Inside Averages - See above.

Limits and Levels: Cancer Slope FactorContains a very challenging line graph. See if participants can relate the graph to the text in the resource.

GED Quantitative Assessment Target Q.7.a
Reading and interpreting graphs, charts, and other representations.
Level B » Measurement and Data Level D » The Number System Level E » Statistics and Probability (for all three above)