TABE 13/14 Level D Math Study Packet: Rational Numbers

This comprehensive TABE 13/14 Level D Math study packet covers five essential standards in the areas of rational number operations, irrational numbers, and proportional reasoning.

I designed Every lesson  with adult learners in mind: real-world contexts, step-by-step instruction, and professionally designed visuals that actually teach. You get a complete, print-ready resource. Your students get the depth they need to pass.

WHAT’S INCLUDED — 5 Complete Units

Unit 1 — 7.NS.3: Four Operations with Rational Numbers

Students apply all four operations — addition, subtraction, multiplication, and division — to integers, fractions, and decimals in multi-step real-world problems.

This unit brings together the sign rules from 7.NS.1 and 7.NS.2 and pushes students to use order of operations (PEMDAS) with signed numbers. Contexts include bank account balances, submarine depths, stock prices, and temperature changes.

Practice includes: computation with order of operations, multi-step word problems, and multiple choice

Unit 2 — 8.NS.2: Approximating Irrational Numbers

Students learn to distinguish rational from irrational numbers, use perfect squares to bracket and approximate square roots, and locate irrational values on a number line.

They estimate expressions such as π² and compare the size of irrational numbers without a calculator. Includes a professionally generated number line visual showing √2, √3, √5, √7, and π plotted with staggered labels.

Practice includes: approximating square roots to the nearest tenth, number line plotting, writing inequalities to compare irrational values, and multiple choice

Unit 3 — 6.RP.3: Ratio and Rate Reasoning

Students use ratio and rate reasoning to solve real-world problems with four representations: equivalent ratio tables, tape diagrams, double number lines, and equations.

Percent problems — including percent of change, discount, and markup — are covered as a natural extension of ratio reasoning. Includes color-coded ratio table, tape diagram, and double number line visuals.

Practice includes: completing ratio tables, interpreting tape diagrams, filling in double number lines, percent of change, and multiple choice

Unit 4 — 7.RP.1: Unit Rates with Fractions

Students compute unit rates when both quantities in the ratio are fractions — the most common source of confusion at this level.

The Keep-Change-Flip method is applied explicitly to unit rate problems, and students compare unit rates across different stores, speeds, and quantities to determine the better value. Includes a bar-model visual showing the division of fractions as a unit rate.

Practice includes: computing fraction unit rates, comparing rates across contexts, multi-step unit rate applications, and multiple choice

Unit 5 — 7.RP.2: Proportional Relationships (a, b, c, d)

Students recognize, represent, and interpret proportional relationships across all four representations: tables, graphs, equations, and verbal descriptions.

All four sub-standards are addressed — identifying proportional relationships (2a), finding the constant of proportionality (2b), writing y = kx equations (2c), and interpreting points on a graph including (0,0) and (1, r) (2d). A side-by-side comparison graph shows proportional vs. non-proportional relationships.

Practice includes: identifying proportional vs. non-proportional tables and equations, graphing proportional relationships, writing equations, interpreting real-world graphs, and multiple choice

📋 PACKET DETAILS

• Pages: 30+ pages of instruction and practice
• Units: 5 complete units, each with full lesson and multiple practice worksheet
• Answer Key: Complete, with step-by-step explanations for every problem including multiple choice rationale

STANDARDS ALIGNMENT

7.NS.3 Solve real-world problems using all four operations with rational numbers

8.NS.2 Approximate irrational numbers; locate on a number line; estimate expressions

6.RP.3 Ratio and rate reasoning: tables, tape diagrams, double number lines, percent

7.RP.1 Unit rates with fractional quantities in like and different units

7.RP.2a Determine whether a relationship is proportional

7.RP.2b Identify the constant of proportionality from tables, graphs, and equations

7.RP.2c Represent proportional relationships with equations in y = kx form

7.RP.2d Interpret points (x, y) on a proportional graph, including (0,0) and (1, r)

This packet builds the following CCR competencies:

Number Sense & Operations

• Apply the four operations to rational numbers in real-world, multi-step contexts
• Use order of operations with signed numbers, fractions, and decimals
• Distinguish rational from irrational numbers and approximate irrational values
• Compare irrational numbers using rational approximations
• Locate irrational numbers on a number line

Ratio, Rate & Proportional Reasoning

• Use ratio and rate reasoning to solve real-world problems
• Build and interpret equivalent ratio tables
• Construct and read tape diagrams and double number lines
• Compute unit rates involving fractional quantities in like and different units
• Recognize proportional relationships from tables, graphs, equations, and descriptions
• Identify the constant of proportionality across multiple representations
• Write and interpret y = kx equations
• Apply percent reasoning including percent of change, discount, and markup
• Solve real-world problems involving scale, maps, and equivalent ratios

Mathematical Practices

• Reason abstractly and quantitatively with real-world signed number problems
• Model with mathematics using adult-relevant contexts
• Attend to precision with fractions, decimals, and irrational approximations
• Construct viable arguments and explain mathematical reasoning in writing

WHO THIS IS FOR

✔ Adult education and ABE instructors teaching to the TABE 13/14 Level D math blueprint

✔ Workforce development programs needing documented EFL skill instruction in math

✔ Correctional education programs that need complete, self-contained, print-ready materials

✔ GED and HiSET prep instructors — the NS, RP, and NS standards in this packet overlap directly with GED Mathematical Reasoning content

✔ Individual adult learners who need a structured, visual study guide they can work through independently between class sessions