System Authorization: Active

FRACTION HACKERS

The Ultimate Subtraction Codebook

F4

Hacker Credentials

ID: SECURE-NF4-SUB

Hacker Name (Code Name)

Hacker Station

Unit Grade Level

4th Grade + Advanced

Hacker Code of Honor

To complete this unit and defend the Fraction Fortress, you must agree to the collaborative protocols:

Think First: I will attempt task cards on vertical surfaces before writing calculations.
Support My Team: I will help my group find equivalent structures and common boundaries.
Verify My Code: I will use both area models and number lines to check my calculations.

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 1 of 6

Mission 1

Visual Subtraction

STATUS: NO REGROUPING

Objective: Master takeaway subtraction on area models and distance subtraction on number lines.

Day 1 Hack: Area Model Takeaway

Shade the starting fraction, cross out the subtraction portion, and write the remaining fraction.

Equation: \(\frac{4}{5} - \frac{2}{5} = \underline{\quad}\)

Equation: \(\frac{7}{6} - \frac{3}{6} = \underline{\quad}\)

Day 2 Hack: Number Line Distance

Mark both endpoints and jump to find the distance (difference) between them.

Distance between \(\frac{2}{8}\) and \(\frac{7}{8}\) = \(\underline{\quad}\)

01/82/83/84/85/86/87/81

Distance between \(\frac{3}{5}\) and \(\frac{9}{5}\) = \(\underline{\quad}\)

02/54/51(5/5)7/59/52(10/5)

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 2 of 6

Mission 2

Whole Breakers

STATUS: WHOLE DECOMPOSITION

Objective: Decompose whole numbers into equivalent fractions to solve subtraction problems and realistic word problems.

Day 3 Hack: Cracking Wholes

Convert 1 whole into the fraction matching your denominator, then subtract.

1. Crack 1 Whole:

\[ 1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \underline{\quad\quad} \]

2. Crack 2 Wholes:

\[ 2 - \frac{3}{4} = 1 + \frac{4}{4} - \frac{3}{4} = \underline{\quad\quad} \]

3. Crack 3 Wholes:

\[ 3 - \frac{5}{6} = 2\frac{\quad}{6} - \frac{5}{6} = \underline{\quad\quad} \]

4. Crack 4 Wholes:

\[ 4 - 1\frac{3}{8} = 3\frac{\quad}{8} - 1\frac{3}{8} = \underline{\quad\quad} \]

Day 4 Hack: Word Problem Decoding

Solve this system problem using your decomposition tools. Show work in the blank area below.

System Security: To activate the main decryption matrix, a computer requires \(2\) full petabytes of free storage. Server Area A has \(\frac{4}{10}\) of a petabyte of free space, and Server Area B has \(\frac{3}{10}\) of a petabyte. How much storage is still needed to run the process?

Write your equation, show models, and state your final answer below:

Final Space:

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 3 of 6

Mission 3

Mixed Regrouping

STATUS: REGROUP INTRO

Objective: Decompose a whole to add to a fractional part before completing the subtraction of mixed numbers.

Day 5 Hack: Mixed Numbers (No Regrouping)

Subtract whole parts first, then fractional parts.

1. Standard Subtraction:

\[ 3\frac{5}{6} - 1\frac{2}{6} = \underline{\quad\quad} \]

2. Large Number Hack:

\[ 5\frac{7}{8} - 2\frac{3}{8} = \underline{\quad\quad} \]

Day 6 Hack: Regrouping Introduction

Learn to "overcharge" your starting fraction by cracking 1 whole from your whole numbers.

Example Walkthrough:

Solve: \( 2\frac{1}{4} - \frac{3}{4} \). Since \(\frac{1}{4}\) is too small to subtract \(\frac{3}{4}\), we regroup:
• Step 1: \( 2\frac{1}{4} = 1 + 1\frac{1}{4} = 1 + \frac{4}{4} + \frac{1}{4} = 1\frac{5}{4} \)
• Step 2: \( 1\frac{5}{4} - \frac{3}{4} = 1\frac{2}{4} \)

A. Regroup and Solve:

\[ 2\frac{1}{5} - \frac{3}{5} \]

Rewrite \(2\frac{1}{5}\) as \(1\frac{\quad}{5}\)

Answer:

B. Regroup and Solve:

\[ 3\frac{2}{10} - \frac{7}{10} \]

Rewrite \(3\frac{2}{10}\) as \(2\frac{\quad}{10}\)

Answer:

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 4 of 6

Mission 4

Master Hacks

STATUS: ADVANCED REGROUPING

Objective: Solve complex mixed-number subtraction problems requiring regrouping and multi-step advanced engineering word problems.

Day 7 Hack: Advanced Regrouping Equations

Decompose, regroup, and subtract both wholes and fractional parts.

1. Regroup Wholes:

\[ 3\frac{1}{6} - 1\frac{5}{6} = \underline{\quad\quad} \]

Decompose starting number: \(2\frac{\quad}{6} - 1\frac{5}{6}\)

2. Deep Regrouping:

\[ 4\frac{3}{8} - 2\frac{7}{8} = \underline{\quad\quad} \]

Decompose starting number: \(3\frac{\quad}{8} - 2\frac{7}{8}\)

Day 8 Hack: Complex Real World Word Problem

Solve this final multi-step word problem. Show all intermediate formulas and steps.

The Core Terminal: The Fraction Fortress solar backup system holds \(5\frac{1}{10}\) gigawatt-hours of total charge. During a full mainframe lock, standard processes consume \(1\frac{4}{10}\) gigawatt-hours, and safety firewalls consume another \(1\frac{9}{10}\) gigawatt-hours. How much power remains in reserve?

Show all your step-by-step math hacks here:

Power Remaining:

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 5 of 6

Teacher Access

Hacker Solutions Key

CONFIDENTIAL ANSWER KEY

Use this secure key to review and grade students' consolidated prints. Verify calculations and models.

Mission 1 Answers

Day 1 (Area Models):

\(\frac{4}{5} - \frac{2}{5} =\) \(\frac{2}{5}\)
\(\frac{7}{6} - \frac{3}{6} =\) \(\frac{4}{6}\) (or \(\frac{2}{3}\))

Day 2 (Number Lines):

Distance from \(\frac{2}{8}\) to \(\frac{7}{8}\) = \(\frac{5}{8}\)
Distance from \(\frac{3}{5}\) to \(\frac{9}{5}\) = \(\frac{6}{5}\) (or \(1\frac{1}{5}\))

Mission 2 Answers

Day 3 (Cracking Wholes):

\(1 - \frac{3}{5} =\) \(\frac{2}{5}\)
\(2 - \frac{3}{4} =\) \(1\frac{1}{4}\)
\(3 - \frac{5}{6} =\) \(2\frac{1}{6}\)
\(4 - 1\frac{3}{8} =\) \(2\frac{5}{8}\)

Day 4 (Word Problem):

Combined storage running: \(\frac{4}{10} + \frac{3}{10} = \frac{7}{10}\) petabyte.
Remaining needed storage:
\(2 - \frac{7}{10} = 1\frac{10}{10} - \frac{7}{10} =\) \(1\frac{3}{10}\) petabytes.

Mission 3 Answers

Day 5 (No Regrouping):

\(3\frac{5}{6} - 1\frac{2}{6} =\) \(2\frac{3}{6}\) (or \(2\frac{1}{2}\))
\(5\frac{7}{8} - 2\frac{3}{8} =\) \(3\frac{4}{8}\) (or \(3\frac{1}{2}\))

Day 6 (Regrouping Intro):

\(2\frac{1}{5} - \frac{3}{5} = 1\frac{6}{5} - \frac{3}{5} =\) \(1\frac{3}{5}\)
\(3\frac{2}{10} - \frac{7}{10} = 2\frac{12}{10} - \frac{7}{10} =\) \(2\frac{5}{10}\) (or \(2\frac{1}{2}\))

Mission 4 Answers

Day 7 (Advanced Regroup):

\(3\frac{1}{6} - 1\frac{5}{6} = 2\frac{7}{6} - 1\frac{5}{6} =\) \(1\frac{2}{6}\) (or \(1\frac{1}{3}\))
\(4\frac{3}{8} - 2\frac{7}{8} = 3\frac{11}{8} - 2\frac{7}{8} =\) \(1\frac{4}{8}\) (or \(1\frac{1}{2}\))

Day 8 (Complex Problem):

Combined usage: \(1\frac{4}{10} + 1\frac{9}{10} = 2\frac{13}{10} = 3\frac{3}{10}\) gigawatt-hours.
Remaining reserve power:
\(5\frac{1}{10} - 3\frac{3}{10} = 4\frac{11}{10} - 3\frac{3}{10} =\) \(1\frac{8}{10}\) (or \(1\frac{4}{5}\)) gigawatt-hours.

Unit: Subtraction Hackers • Consolidated Print-and-Go Page 6 of 6

Fraction Hackers

Visual Subtraction

Whole Breakers

Mixed Regrouping

Master Hacks

Visual Subtraction Handout

Thin Slicing Task Cards One

Hacker Codebook Packet

Hacker Deck Slides

Whole Breakers Handout

Thin Slicing Task Cards Two

Mixed Regrouping Handout

Thin Slicing Task Cards Three

Master Hacks Handout

Thin Slicing Task Cards Four

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