TEKS

TEKS - Texas Essential Knowledge and Skills (i.e., Objectives)

UNIT 1: Value and Magnitude of Rational Numbers

This unit bundles student expectations that address the sets and subsets of real/rational numbers ordering rational numbers, and converting between standard decimal notation and scientific notation.

TOPIC 1 - REAL / RATIONAL NUMBERS

8.2A - The student will extend previous knowledge of sets and subsets using a visual representation to describe relations between sets of real numbers including the following:

• counting numbers, whole numbers, integers, rational numbers, and irrational numbers

• visual representations of the relationships between sets and subsets

• relationships between the sets of rational numbers, including the following:

  • • all counting numbers are a subset of whole numbers,, integers, and rational numbers.

    • all whole numbers are a subset of integers and rational numbers.

    • all integers are a subset of rational numbers.

    • all counting numbers, whole numbers, and integers are a subset of rational numbers.

    • not all rational numbers are in integer, whole number, or a counting number.

8.2D - The student will order a set of real numbers arising from mathematical and real-world contests, including the following:

• various forms of rational numbers (positive and negative)

• place value

• order of numbers

• number lines (horizontal and vertical)

  • • numbers increase from left to right on the horizontal number line and from bottom to top on a vertical number line

• quantifying descriptors in mathematical and real-world problem situations (e.g., between two given numbers, greatest to least, ascending to descending, tallest to shortest, warmest to coldest, fastest to slowest, heaviest to lightness, closet to farthest, oldest to youngest, etc.).

TOPIC 2 - SCIENTIFIC AND STANDARD NOTATION

8.2C - The student will convert between standard decimal notation and scientific notation including the following:

• decimal notation

• scientific notation

• powers and base

• relationships between place value and scientific notation

• format of scientific notation, including the following

  • • powers of 10

    • positive or negative integer exponents

    • positive exponents move the decimal to the right the same number of places as the exponent

    • negative exponents move the decimal to the left the same number of places as the absolute value of the exponent

    • positive or negative decimal with the exactly one non-zero digit to the left of the decimal point

    • multiplicative identity

UNIT 2: Statistics with Univariate Data

This unit bundles student expectations that address "Mean Absolute Deviation" (MAD) and generalizations of "Random Samples" of the same size from a population.

TOPIC 1 - MEAN ABSOLUTE DEVIATION and RANDOM SAMPLES

8.11B - The student will determine the "mean absolute deviation" and use the quantify as a measure of the average distance data are from the mean using a data set of no more than 10 data points, including:

• data set has less variability when the mean absolute deviation is closer to zero

• given or collected data limited to no more than 10 data points

• process for calculating the mean absolute deviation, including:

  • • find the mean of the data

    • find the absolute value of the difference between each data point and the mean

    • find the mean of the absolute differences

• relationships between mean absolute deviations and the distance of the data points on a number line

8.11C - The student will simulate the generating random samples of the same size from a populations with known characteristics to develop the notation of a random sample being representative of the population from which it was selected, including:

• random samples that are most likely to contain data that can be used to make predictions about the whole population

• developing a design for a simulation

• appropriate methods to simulate random samples from a population, including:

  • • with technology

    • calculator

    • computer model

    • random number generator

    • without technology

    • spinners (even and uneven sections)

    • color tiles

    • two-color counters

    • coins

    • deck of cards

    • marbles

    • number cubes (dice)

Unit 3A: One-Variable Equations and Inequalities

This unit bundles student expectations that address modeling, writing, and solving one-variable equations and inequalities with variables on both sides of the equal sign or the inequality sign using rational number coefficients and constants; and solving problems comparing interest rates on loans and savings accounts, loan lengths, and the total cost of repaying a loan.

TOPIC 1 - ONE-VARIABLE EQUATIONS AND INEQUALITIES

8.1A - The student will apply mathematics to problems arising in everyday life, society, and the workplace.

8.1B - The student will use a problem-solving model that includes:

• analyze given information

• formulate a plan or strategy

• determine a solution

• justify the solution

• evaluate the problem-solving process and the reasonableness of the solution

8.1C - The student will 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.

8.1D - The student will communicate mathematical ideas, reasoning, and their implications using multiple representations including symbols, diagrams, graphs, and language as appropriate.

8.1E - The student will create and use representations to organize, record, and communicate mathematical ideas, including:

• appropriate mathematical vocabulary and phrasing

8.1F - The student will analyze mathematical relationships to connect and communicate mathematical ideas, including:

• conjectures and generalizations from sets of examples and non-examples, patterns, etc.

8.1G - The student will display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication, including:

• mathematical ideas and arguments

• validation of conclusions

• displays to make work visible to others (diagrams, visual aids, written work, etc.)

• explanations and justifications

8.8A - The student will write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants, including:

• Variables

  • • one-variable on both sides of the equations or inequality

• Coefficients

  • • integers

    • decimals (positive and negative)

    • fractions (positive and negative)

• Constants

  • • integers

    • decimals (positive and negative)

    • fractions (positive and negative)

Distinguishing between equations and inequalities

• characteristics of equations

  • • equates of two expressions

    • equality of variables

    • one solution

• characteristics of inequalities

  • • shows the relationship between two expressions in terms of greater than, less than, greater than or equal to, less than or equal to, or not equal

    • inequality of the variables

    • one or more solutions

• Equality and inequality words and symbols

• Relationship of order of operations within an equation or inequality

• One-variable equations with variables on both sides from a problem situation

• One-variable inequalities with variables on both sides from a problem situation

8.8B - The student will write a corresponding real-world problem when given a one-variable equations or inequality with variables on both sides of the equal sign, using rational number coefficients and constants, including:

• corresponding real-world problem situation from a one-variable equations with variables on both sides of the equal sign

• corresponding real-world problem situation from a one-variable inequality with variables on both sides of the inequality symbol

8.8C - The student will model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real world problems using rational number coefficients and constants, including:

• Models to solve one-variable equations with variables on both sides of the equal sign (concrete, pictorial, and algebraic)

• Solutions to one-variable equations with variables on both sides of the equal sign from mathematical and real-world problem situations

• Other possible solutions

  • • one real solution

    • no solution

    • infinite solutions (all real solutions)

UNIT 3B: Interest Rates, Savings Accounts, Loans, and the Cost of Credit

This unit bundles student expectations that address solving problems comparing interest rates on loans and savings accounts, loan length, repaying a loan, and the total cost of credit.

TOPIC 2 - INTEREST RATES, SAVINGS ACCOUNTS, LOANS, AND THE TOTAL COST OF CREDIT

8.12A - The student will solve real-world problems comparing how interest rates and loan length affect the cost of credit, including:

• Credit

• Annual Percentage Rate (APR)

• Principal of a loan

• Interest

  • Simple interest for a loan

  • Compound interest for a loan

8.12B - The student will calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator, including:

• Credit

• Annual Percentage Rate (APR)

• Principal of a loan

• Collateral

• Interest

  • Simple interest for a loan

  • Compound interest for a loan

8.12D - The student will calculate and compare simple and compound interest earnings, including

• Principal of an investment

• Simple interest for an investment

• Compound interest for an investment

• Formulas for interest from the STAAR Grade 8 Mathematics Reference Materials Chart.

• Comparing simple and compound interest earnings.

SECOND NINE WEEKS 2021-2022

Unit 4: Developing an Understanding of Slope and y-Intercept

This unit ...