Summary Tables of Texas Adult Education Content Standards & Benchmarks

Created by M.J. Ochoa, Far West GREAT Center
July 2008 (revised January 2009)

ABE/ASE CONTENT STANDARDS
USE MATH TO SOLVE PROBLEMS AND COMMUNICATE

  • Understand, interpret, and work with pictures, numbers and symbolic information.
  • Define and select data to be used in solving the problem. 
  • Determine the degree of precision required by the situation.
  • Apply knowledge of mathematical concepts and procedures to figure out how to answer a question, solve a problem.
  • Make a prediction or carry out a task that has a mathematical dimension using appropriate quantitative procedures, and verify the results are reasonable.
  • Communicate results using a variety of mathematical representations, including graphs, charts, tables, and algebraic models.  

ABE/ASE Content Standards: Use Math to Solve Problems and Communicate

  LEVEL 1
BEGINNING ABE LITERACY
LEVEL 2
BEGINNING BASIC EDUCATION
LEVEL 3
LOW INTERMEDIATE BASIC EDUCATION
LEVEL 4
HIGH INTERMEDIATE BASIC EDUCATION
LEVEL 5
LOW ADULT SECONDARY EDUCATION
LEVEL 6
HIGH ADULT SECONDARY EDUCATION
RECOGNIZE AND COMPARE NUMBERS

(M1.1) Count and read whole numbers between 0 and 10.

Example: Label days of the week with numbers.

(M1.2)
• Count and read whole numbers between 0 and 1000.
• Identify place value system.

Example: Label days of the month with numbers.

(M1.3)
• Compare and order fractions.
• Identify mixed numbers.
• Compare and order decimals.

Example: Given 0.1, 0.2, 0.02, 0.001, order the decimal from greatest to least.

(M1.4) Recognize and use equivalencies between fractions, decimals, and percents.

Example: Is ½ of a pizza the same as 50% of a pizza?

(M1.5) Compare, convert and order non-equivalent forms of commonly used fractions, decimals and percents.

Example: Analyze effects of deductions on earnings and project annual income.

(M1.6) Compare, convert and order non-equivalent forms of commonly used fractions, decimals, and percents.

Example: Make a decision about how to consolidate bills and credit card payments.

MATHEMATICAL SYMBOLS

(M2.1) Identify and use mathematical symbols (+,-,=) and words that represent those symbols.

Example: Use mathematical symbols to represent three plus five.

(M2.2)
• Identify simple fractions.
• Identify and use mathematical symbols (x, ÷) and words that represent those symbols for multiplication and division.

Example: Measure ingredients for simple recipes using benchmark fractions.

(M2.3) Identify and use mathematical symbols (<,>, ≠) and words that represent those symbols.

Example: Compare prices from different advertisements, e.g., school supplies, groceries, clothing.

(M2.4) Identify and use mathematical symbols (≥, ≤) and words that represent those symbols.

Example: Decide which product to buy based on a comparison of nutritional information.

(M2.5)
• Identify and use mathematical symbols [√, Ð, °, ()] and words that represent those symbols.
• Identify and compute powers and roots.

Example: Given the area of a square flower bed, what is the length of one side?

(M2.6)
• Identify and use mathematical symbols (n√, [], {}) and words that represent those symbols.
• Understand the meaning of absolute value. (e.g.,
|-8|=8)

Example: A mountain is 1000 feet above sea level and 250 feet below. The absolute values would be:
1000+|-250|=1250 feet

NUMBER LINE AND GRIDS

(M3.1) Plot natural numbers on a horizontal number line.

Example: Plot the first five days of the week using the number line.

(M3.2) Plot natural numbers on a vertical number line.

Example: Plot daily temperature on a vertical number line over a set period of time.

(M3.3)
• Plot points in Quadrant I of a coordinate grid.
• Read and understand integers (positive and negative numbers) as showing direction and change on both horizontal and vertical number lines.

Example: Plot age and weight of their children on a growth chart.

(M3.4) Plot points in all four quadrants of a coordinate grid.

Example: Plot the path of hurricanes based on given coordinates.

(M3.5)
• Identify positive and negative slopes on a coordinate grid.
• Graph linear equations.

Example: Given this equation:
Y=3x+2

What is the slope of the line?

(M3.6) Find slope and distance on a coordinate grid.

Example: Given the points (0,2) and (3, -4) find the slope of a line.

APPLICATION OF MATHEMATICAL OPERATIONS

(M4.1) Model and apply meanings of addition (such as counting or combining) and subtraction (such as taking away or separating inverse operations) of one-digit whole numbers.

Example: Add the ages of two 3-year olds and one 2-year old.

(M4.2) Model and apply meanings of addition and subtraction of two- and three-digit whole numbers.

Example: Add the ages of any three ninth graders.

(M4.3)
• Model and apply meanings of addition and subtraction of decimals.
• Model meanings of multiplication and division (inverse operations) using facts through 12 x 12.

Example: Balance a checking account.

(M4.4) Model and apply meanings of four basic math operations (i.e., addition, subtraction, multiplication, division) using whole numbers, fractions and decimals.

Example: Divide a restaurant check evenly for a group of 5 people.

(M4.5) Model and apply meanings of addition, subtraction, multiplication and division using integers.

Example: Develop a budget for a home or business.

(M4.6) Use four basic operations with exponents, including addition and subtractions of like terms and multiplication and division of monomials.

Example: Fill out personal or business income tax forms.

CURRENCY

(M5.1) Identify U.S. currency and coins.

Example: Sort coins into like piles, and then determine the value of each pile.

(M5.2) Count and make change using U.S. coins and currency up to $1.00.

Example: Sort coins into like piles, and then determine the value of each pile.

(M5.3) Count and make change using all U.S. coins and currency.

Example: How much change would you get back if you buy a $29.95 money order from a $50.00 bill?

(M5.4)

Concept mastered

(M5.5)

Concept mastered

(M5.6)

Concept mastered

MEASUREMENTS

(M6.1) Identify common units of measurement: length, volume, time, and temperature.

Example: Read a school calendar.

(M6.2) Identify the instruments used to measure common units of measurement: length, volume, time, and temperature.

Example: Read a thermometer.

(M6.3) Measure whole units with appropriate tools: length, weight, volume, time, and temperature.

Example: Which tool would you use to measure the number of feet of baseboard that will be needed for a room?

(M6.4) Measure fractional unit with appropriate tools: length, weight, volume, time, and temperature.

Example: Read a fuel gauge.

(M6.5) Convert units within length, weight, volume, time, and temperature.

Example: Reduce or expand a recipe.

(M6.6) Apply appropriate units and instruments of length, weight, volume, time, and temperature to solve a variety of problems.

Example: Design a “dream” house.

AREA, PERIMETERS, AND ANGLES

(M7.1) Recognize and identify simple two- and three- dimensional shapes.

Example: Identify the shape of the classroom.

(M7.2) Calculate the perimeter of polygons.

Example: Design a garden with a specific amount of fencing.

(M7.3) • Identify and define all angles including supplementary, complementary and vertical angles
. • Find the third interior angle of triangles.


Example: Find a right angle and an acute angle within the classroom.

(M7.4)
• Calculate the area of squares, rectangles, and triangles.
• Identify parallel lines, perpendicular lines, and intersecting lines.


Example: Determine the area of a rectangular room for carpeting or tile.

(M7.5)
• Calculate area of polygons.
• Calculate circumference and area of circles.
• Calculate volume of rectangular solids and cylinders.
• Apply the Pythagorean Theorem.


Example: Plan and measure shelves.

(M7.6) Use basic trigonometric functions – sine, cosine, and tangent.

Example: Design a living room to scale.

USING RATIOS, PROPORTIONS, AND PERCENTS

(M8.1)

Concept introduced at Level 3.

(M8.2)

Concept introduced at Level 3.

(M8.3) Identify and write simple ratios and proportions.

Example: What is the ratio of males to females in the classroom?

(M8.4) Identify and write ratios and proportions within word problems.

Example: One minute is to 60 seconds as 60 minutes is to ___ seconds.

(M8.5) Use ratios, proportions, and percents to solve word problems.

Example: If a flagpole is 12 feet tall and casts a shadow of 6 feet, and a man casts a shadow of 3 feet, how tall is the man?

(M8.6) Use ratios, proportions, and percents to solve multi-step, algebraic problems.

Example: A man drives 180 miles in 3 hours. Find his average speed and how far he could drive in 9 hours.

PROBABILITIES

(M9.1)

Concept introduced at Level 4.

(M9.2)

Concept introduced at Level 4.

(M9.3)

Concept introduced at Level 4.

(M9.4) Determine simple probabilities.

Example: Flip a coin. What is the probability of landing heads?

(M9.5) Use simple probabilities to predict outcomes.

Example: What is the probability of drawing a nine from a deck of cards?

(M9.6) Use probabilities with dependent events to predict outcomes.

Example: If a drawer contains 6 pairs of socks (2 brown, 2 black, 2 red), what is the probably of drawing a black pair and a brown pair in order without placing the first pair?

GRAPHS AND CHARTS

(M10.1) Identify key features of simple everyday graphs and charts.

Example: Interpret a simple graph (e.g. in a child’s height and weight chart).

(M10.2) Collect data and construct simple everyday graphs and charts.

Example: Develop a schedule for how and when to take medication according to a doctor’s order.

(M10.3) Collect and interpret data to construct graphs, schedules, and tables, and diagrams.

Example: Choose a phone plan by comparing rates and constant costs.

(M10.4) Collect and interpret data to construct more complex graphs, schedules, tables, and diagrams.

Example: Develop a yearly budget and illustrate expenses by creating a chart or graph.

(M10.5) Collect, interpret, represent and draw implications from graphs, schedules, tables, and diagrams.

Example: Read and interpret aquifer table/chart to determine water restriction.

(M10.6) Interpret, represent and identify trends and/or make inferences and draw conclusions from complex graphs, schedules, tables, and diagrams.

Example: Choose which car to buy based on published consumer information.

AVERAGES

(M11.1)

Concept introduced at Level 4.

(M11.2)

Concept introduced at Level 4.

(M11.3)

Concept introduced at Level 4.

(M11.4) Find mean, range, median, and mode.

Example: Track temperatures for one week and find the mean, median, mode, and range.

(M11.5) Find mean, range, median, and mode.

Example: Determine your readiness for the GED by finding your average score on the GED official practice test.

(M11.6)

Concept mastered at Level 5.

ORDER OF OPERATIONS AND LINEAR EQUATIONS

(M12.1)

Concept introduced at Level 2.

(M12.2) Read and solve simple addition and subtraction equations.

Example: 3 + x = 8

(M12.3) Use order of operations (i.e., multiplication, division, addition, subtraction), to evaluate expressions.

Example:
10 – 2 * 3 + 7 + 12 ÷ 6= ?

(M12.4)
• Solve linear equations with one variable using division, addition, subtraction, and distributive property.
• Write simple linear equations from the given word problems.

Example: Tom is twice as old as Tammy. Tammy is 6 years old. How old is Tom?

(M12.5)
• Use order of operations (i.e., parentheses, exponents, multiplication, division, addition, subtraction – PEMDAS) to evaluate expressions with variables, including common formulas.
• Express numbers in scientific notation.

Example: Given: d = r * t and r=4, t=6. Find d.

(M12.6)
• Solve linear equations with one variable using strategies such as the distributive property and /or transposition.
• Add and subtract polynomials.
• Factor binomials and trinomials using strategies such as greatest common factor, difference of two squares, and/or
x2 + bx + c form.

Example: Factor x2 + 5x - 6

PATTERNS AND SEQUENCES

(M13.1) Recognize patterns and sequences using colors, shapes, and numbers.

Example: 2, 4, 6, __, 10, 12 …

(M13.2) Construct simple patterns and sequences.

Example: à, ð, à, __,à, …

(M13.3) Construct patterns using arithmetic sequences.

Example: 3, 5, 7, 9, 11,…

(M13.4) Construct patterns using geometric sequences.

Example: 3, 6, 12, 24, 48, …

(M13.5) Construct complex patterns and sequences.

Example: n, 2n, 4n, 8n, …

(M13.6) Determine the missing terms from arithmetic and/or geometric sequences.

Example: n, n+2, __, n+6,…

ROUNDING AND ESTIMATION

(M14.1) Round to the nearest 10.

Example: Is 6 closer to 1 or 10?

(M14.2)
• Round to the nearest 100 or 1000.
• Use estimation to check the answer of one-step word problems.

Example: Is 565 closer to 500 or 600?

(M14.3) Round to specified place value including decimals.

Example: Is 3.674 closer to 3.6 or 3.7?

(M14.4) Apply the concept of rounding and estimation to solve multi-step problems.

Example: Estimate the sum of 2.75 + 33.1 + 8.49 + 4.11 to the nearest tenth.

(M14.5)

Concept mastered.

(M14.6)

Concept mastered.