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Rice University School Mathematics Project
 

Deconstructing the Language of Mathematics in the Revised TEKS for Grades 4-6

Mathematics teachers who participated in Rice University School Mathematics Project's 2014 Spring Networking Conference on February 1 provided material for this wonderful resource for K-12 Texas mathematics teachers. Attendees identified mathematical terms new to their grade level in the revised TEKS; these terms are bold typed.  

TEKS Revised Language   Reporting Category
4.2A Interpret the value of each place-value position as 10 times the position to the right and as 1/10 the value of the place to its left.
Number and Operations
4.2B Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation
and numerals
.

Number and Operations
4.2H Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line.
Number and Operations
4.3A Represent a fraction a/b as a sum of fractions 1/b.
Number and Operations
4.3B Decompose fractions into a sum of fractions with the same denominator.
Number and Operations
4.3C Determine if two given fractions are equivalent.
Number and Operations
4.3D Compare fractions with different numerators and denominators using the symbols >, =, or <.
Number and Operations
4.3E Represent and solve addition and subtraction of fractions with equal denominators.
Number and Operations
4.3F Evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4 and 1.
Number and Operations
4.4A Add and subtract both whole numbers and decimal values to the hundredths place using the standard algorithm.
Number and Operations
4.4D Multiply a 4-digit by 1-digit number and a 2-digit number by a 2-digit number.
Number and Operations
4.4E Represent the quotient of up to a 4-digit whole number divided by a 1-digit whole number using arrays, area models, or equations.
Number and Operations
4.4F Use strategies and algorithms, to divide up to a four-digit dividend by a one-digit divisor .
Number and Operations
4.4H Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
Number and Operations
4.6A Identify points, rays, lines, line segments, angles, and perpendicular and parallel lines.
Geometry and Measurement
4.6C Apply knowledge of right angles to identify acute, right, and obtuse triangles.
Geometry and Measurement
4.7A Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle.
Geometry and Measurement
4.7B Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. 
Geometry and Measurement
4.7C Use a protractor to determine the approximate measure of angles in degrees to the nearest whole number..
Geometry and Measurement
4.7D Draw an angle with a given measure.
Geometry and Measurement
4.10 Financial literacy terms
Personal Financial Literacy
5.3B Multiply with fluency a 3-digit number by a 2-digit number using the standard algorithm.
Number and Operations
5.3C Solve with proficiency for quotients of up to a 4-digit dividend by a 2-digit divisor using strategies and the standard algorithm.
Number and Operations
5.3D Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models.
Number and Operations
5.3E Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers.
Number and Operations
5.3F Represent quotients of decimals to hundredths, up to 4-digit dividends and 2-digit whole number divisors, using objects and pictorial models, including area models.
Number and Operations
5.3G Solve for quotients of decimals to the hundredths, up to 4-digit dividends and 2-digit whole number divisors, using strategies and algorithms, including the standard algorithm.
Number and Operations
5.3H Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations.
Number and Operations
5.3I Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models.
Number and Operations
5.3J Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models.
Number and Operations
5.3K Add and subtract positive rational numbers fluently.
Number and Operations
5.3L Divide whole numbers by unit fractions and unit fractions by whole numbers.
Number and Operations
5.4C Generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph.
Algebraic Reasoning
5.4D Recognize the difference between additive and multiplicative numerical patterns given in a table or graph.
Algebraic Reasoning
5.4E Describe the meaning of parentheses and brackets in a numeric expression.
Algebraic Reasoning
5.4F Simplify numerical expressions that do not involve exponents, including up to two levels of grouping.
Algebraic Reasoning
5.4H Represent and solve problems related to perimeter and/or area and related to volume.
Algebraic Reasoning
5.5 Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.
Geometry and Measurement
5.7 Solve problems by calculating conversions within a measurement system, customary or metric.
Geometry and Measurement
5.8C Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table.
Geometry and Measurement
5.9A Represent categorical data with bar graphs or frequency tables and numerical data including data sets of measurements in fractions or decimals with dot plots or stem-and-leaf plots.
Data Analysis
5.9B Represent discrete paired data on a scatterplot.
Data Analysis
5.9C Solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.
Data Analysis
5.10 Financial literacy terms
Personal Financial Literacy
6.2A Classify whole numbers, integers, and rational numbers using visual representations such as a Venn diagram to describe relationships between sets of numbers.
Number and Operations
6.2B Identify a number, its opposite and its absolute value.
Number and Operations
6.2C Locate, compare and order integers and rational numbers using a number line.
Number and Operations
6.2D Order a set of rational numbers, arising from mathematical and real world contexts.
Number and Operations
6.2E Extend representations for division to include fraction notation such as  a/b represents the same number as a ÷ b where b does not equal 0.
Number and Operations
6.3A Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values.
Number and Operations
6.3B Determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one.
Number and Operations
6.3C Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Number and Operations
6.3D Add, subtract, multiply, and divide integers fluently.
Number and Operations
6.3E Multiply and divide positive rational numbers fluently.
Number and Operations
6.4A Compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive
and multiplicative relationships.

Proportionality
6.4B Apply qualitative and quantitative reasoning to solve prediction and comparison real-world problems involving ratios and rates.
Proportionality
6.5A Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.
Proportionality
6.5B Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole including the use of concrete and pictorial models.
Proportionality
6.6A Identify independent and dependent quantities from tables and graphs.
Expressions, Equations and Relationships
6.6C Represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.
Expressions, Equations and Relationships
6.7A Generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.
Expressions, Equations and Relationships
6.7B Distinguish between expressions and equations verbally, numerically, and algebraically.
Expressions, Equations and Relationships
6.7C Determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.
Expressions, Equations and Relationships
6.7D Generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
Expressions, Equations and Relationships
6.8A Extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle.
Expressions, Equations and Relationships
6.9A Write one-variable, one-step equations and inequalities to represent constraints or conditions within problems.
Expressions, Equations and Relationships
6.9B Represent solutions for one-variable, one-step equations and inequalities on number lines.
Expressions, Equations and Relationships
6.9C Write corresponding real-world problems given one-variable, one-step equations or inequalities.
Expressions, Equations and Relationships
6.10A Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts.
Expressions, Equations and Relationships
6.10B Determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.
Expressions, Equations and Relationships
6.11 Graph points in all four quadrants using ordered pairs of rational numbers.
Measurement and Data
6.12A Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots.
Measurement and Data
6.12B Use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution.
Measurement and Data
6.12C Summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution.
Measurement and Data
6.12D Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each
category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.

Measurement and Data
6.13A Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots.
Measurement and Data
6.13B Distinguish between situations that yield data with and without variability.
Measurement and Data
6.14 Financial literacy terms
Personal Financial Literacy