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Skills available for Texas seventh-grade math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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State of Texas Assessments of Academic Readiness (STAAR) State of Texas Assessments of Academic Readiness (STAAR)
Texas Essential Knowledge and Skills (TEKS): Grade 6, Middle School Advanced Mathematics Texas Essential Knowledge and Skills (TEKS): Grade 6, Middle School Advanced Mathematics
Texas Essential Knowledge and Skills (TEKS): Grade 7 Texas Essential Knowledge and Skills (TEKS): Grade 7
Texas Essential Knowledge and Skills (TEKS): Grade 7, Middle School Advanced Mathematics Texas Essential Knowledge and Skills (TEKS): Grade 7, Middle School Advanced Mathematics

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7 One-variable expressions, equations, and relationships—foundations of one-variable relationships

7 The student applies mathematical process standards to develop concepts of expressions and equations.
- A distinguish between expressions and equations verbally, numerically, and algebraically;
- B determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and
- C generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
- Checkpoint opportunity
  - Checkpoint: Expressions with variables (6)

8 One-variable expressions, equations, and relationships—applications of one-variable relationships

8 The student applies mathematical process standards to use equations and inequalities to represent situations and solve problems.
- A write one-variable, one- and two-step equations and inequalities to represent constraints or conditions within problems;
- B write corresponding real-world problems given one-variable, one- and two-step equations or inequalities;
  - Which word problem matches the one-step equation? (6-AA.18)
- C represent solutions for one-variable, one- and two-step equations and inequalities on number lines;
- D model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts;
- E model and solve one-variable, two-step equations and inequalities; and
- F determine if the given value(s) make(s) one-variable, one- and two-step equations and inequalities true.
- Checkpoint opportunity

9 Two-variable equations and relationships—foundations of linear relationships

9 The student applies mathematical process standards to use multiple representations to describe algebraic relationships.
- A identify independent and dependent quantities from tables and graphs;
  - Identify independent and dependent variables in tables and graphs (6-CC.2)
  - Identify independent and dependent variables: word problems (6-CC.4)
- B write an equation that represents the relationship between independent and dependent quantities from a table;
  - Write a two-variable equation from a table (6-CC.9)
- C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y= kx or y = x + b; and
- D 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.
- Checkpoint opportunity

10 Two-variable equations and relationships—applications of proportional relationships.

10 The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt.

11 Geometric expressions, equations, and relationships—foundations of geometric concepts equations

11 The student applies mathematical process standards to use geometry to represent relationships.
- A model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes; and
- B write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
  - Area of quadrilaterals and triangles: word problems (6-GG.17)
  - Volume of cubes and rectangular prisms: word problems (6-HH.3)

12 Geometric expressions, equations, and relationships—applications of geometric concepts

12 The student applies mathematical process standards to use geometry to represent relationships and solve problems.
- A 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;
- B determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles where dimensions are positive rational numbers;
- C solve problems involving the volume of right rectangular prisms and triangular prisms; and
  - Volume of cubes and prisms (7-CC.5)
  - Volume of cubes and rectangular prisms: word problems (7-CC.6)
- D write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.
- Checkpoint opportunity

13 Data science—foundations of measurement and data

13 The student applies mathematical process standards to represent and analyze data.
- A distinguish between situations that yield data with and without variability; and
  - Identify statistical questions (6-JJ.1)
- B represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots.

14 Data science—applications of measurement and data

14 The student applies mathematical process standards to use numerical or graphical representations to analyze and solve problems.
- A use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution;
- B 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;
- C interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots;
- D solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents;
- E compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads; and
  - Box plots (7-GG.13)
  - Compare populations using measures of center and spread (7)
- F 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.
- Checkpoint opportunity

15 Personal financial literacy—money management

15 The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor.
- A compare the features and costs of a checking account and a debit card offered by different local financial institutions;
  - Compare checking accounts (6-LL.1)
- B identify and explain the advantages and disadvantages of different payment methods, including distinguishing between debit cards and credit cards;
  - Identify advantages and disadvantages of payment methods (6)
  - Debit cards and credit cards (6-LL.3)
- C explain why it is important to establish a positive credit history;
  - Credit reports (6-LL.4)
- D describe the information in a credit report and how long it is retained;
  - Credit reports (6-LL.4)
- E describe the value of credit reports to borrowers and to lenders;
  - Credit reports (6-LL.4)
- G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study; and
  - Paying for college (6-LL.5)
- H compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income.
  - Occupations, education, and income (6-LL.6)

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1 Mathematical process standards

1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

A apply mathematics to problems arising in everyday life, society, and the workplace;

B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

E create and use representations to organize, record, and communicate mathematical ideas;

F analyze mathematical relationships to connect and communicate mathematical ideas; and

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

2 Numeracy—foundations of rational numbers

2 The student applies mathematical process standards to represent and use rational numbers in a variety of forms.

A classify sets and subsets using a visual representation such as a Venn diagram or a hierarchy to describe relationships between sets of rational numbers;

B identify a number, its opposite, and its absolute value;

C represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers as proportional relationships;

D generate equivalent forms of fractions, decimals, and percents using real-world problems as proportional relationships, including problems that involve money;

E use equivalent fractions, decimals, and percents to show equal parts of the same whole as proportional relationships;

F locate, compare, and order integers and rational numbers using a number line;

G order a set of rational numbers arising from mathematical and real-world contexts; and

H use coordinate geometry to identify locations on a plane, including graphing points in all four quadrants using ordered pairs of rational numbers.

Checkpoint opportunity

3 Numeracy—operations with rational numbers.

3 The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions.

A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values;

B 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;

C extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

D represent integer operations with concrete models and connect the actions with the models to standardized algorithms;

E add, subtract, multiply, and divide integers fluently;

F add, subtract, multiply, and divide rational numbers;

G generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization;

H balance a check register that includes deposits, withdrawals, and transfers; and

I create and organize a financial assets and liabilities record and construct a net worth statement.

Checkpoint opportunity

4 Numeracy—applications of percents

4 The student applies mathematical process standards to solve problems involving percents as proportional relationships.

A 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

B calculate the sales tax for a given purchase and calculate income tax for earned wages.

Checkpoint opportunity

5 Proportionality—foundations of ratios and rates

5 The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations.

A give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;

B give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients;

C represent ratios and percents with concrete models, fractions, and decimals; and

D represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.

6 Proportionality—applications of ratios and rates

6 The student applies mathematical process standards to solve problems involving proportional relationships.

A apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

B calculate unit rates from rates in mathematical and real-world problems; and

C convert within and between measurement systems, including the use of proportions and the use of unit rates.

Checkpoint opportunity

7 One-variable expressions, equations, and relationships—foundations of one-variable relationships

7 The student applies mathematical process standards to develop concepts of expressions and equations.

A distinguish between expressions and equations verbally, numerically, and algebraically;

B determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and

C generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.

Checkpoint opportunity

8 One-variable expressions, equations, and relationships—applications of one-variable relationships

8 The student applies mathematical process standards to use equations and inequalities to represent situations and solve problems.

A write one-variable, one- and two-step equations and inequalities to represent constraints or conditions within problems;

B write corresponding real-world problems given one-variable, one- and two-step equations or inequalities;

C represent solutions for one-variable, one- and two-step equations and inequalities on number lines;

D model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts;

E model and solve one-variable, two-step equations and inequalities; and

F determine if the given value(s) make(s) one-variable, one- and two-step equations and inequalities true.

Checkpoint opportunity

9 Two-variable equations and relationships—foundations of linear relationships

9 The student applies mathematical process standards to use multiple representations to describe algebraic relationships.

A identify independent and dependent quantities from tables and graphs;

B write an equation that represents the relationship between independent and dependent quantities from a table;

C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y= kx or y = x + b; and

D 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.

Checkpoint opportunity

10 Two-variable equations and relationships—applications of proportional relationships.

Checkpoint opportunity

11 Geometric expressions, equations, and relationships—foundations of geometric concepts equations

11 The student applies mathematical process standards to use geometry to represent relationships.

A model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes; and

B write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.

C represent benchmark fractions and percents such as 1%, 10%, 25%, 33 ¹/₃%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers as proportional relationships;

C extend representations for division to include fraction notation such as ^a/_b represents the same number as a ÷ b where b ≠ 0