Addition and Subtraction in Base Five

Grade 6 · Mathematics

Semester 1 | Period 2 | Week 9

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Subject: Mathematics

Semester: 1

Period: 2

Week: 9

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 9
Lesson Duration: 45 minutes
Week & Period: Week 9, Period 2
Topic: Addition and Subtraction in Base Five
Sub-topic: Base Five Arithmetic

Learning Objectives
By the end of the lesson, students should be able to:
Add numbers in base five
Subtract numbers in base five
Apply base five arithmetic in word problems

Previous Knowledge
Students already know base five counting and conversion to/from base ten.

Instructional Materials
Mathematics textbook for Grade 6, counters, chart paper.

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher reviews counting in base five and previous conversion exercises.

B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes

Topic: Addition and Subtraction in Base Five

Definition and Conceptual Overview

The Base Five (Quinary) Number System uses only the digits 0, 1, 2, 3, and 4. Each position in a number represents a power of 5, just as in base ten we use powers of 10.

When adding or subtracting in base five, we apply the same column-wise method as in base ten, but we carry or borrow when the result reaches 5 (not 10, as in base ten).

 

Addition in Base Five

  • Method:
  1. Add digits starting from the rightmost digit.
  2. If the sum is 5 or more, subtract 5 and carry 1 to the next column.
  3. Continue with the next column, including any carry.
  • Example 1:
    245+135

Let’s align and add column-wise:

     2  4

  + 1  3

  _____

    • Right column: 4+3=7
      Since 7 ≥ 5, subtract 5: 7−5=2, carry 1
    • Left column: 2+1+1=4

Final answer: 425

  • Example 2:
    325+215
    • Right: 2+1=3
    • Left: 3+2=53 + 2 = 53+2=5; since 5 ≥ 5, subtract 5 → 0, carry 1
    • New digit added to the front: 1

Final answer: 1035

Subtraction in Base Five

  • Method:
  1. Subtract digits starting from the right.
  2. If the top digit is smaller than the bottom digit, borrow 1 from the next column (worth 5 in that position).
  3. Adjust the digit and continue.
  • Example 1:
    325−145

Let’s align:

    3  2

  - 1  4

  ____

    • Right: 2−4; borrow 1 from 3 (left column), making it 2. Add 5 to the 2 → becomes 2+5=7
    • Now: 7−4=3, and left: 2−1=1

Final answer: 135

  • Example 2:
    435−145
    • Right: 3−4 → not possible → borrow 1 (from 4), becomes 3. 3+5=8, so 8−4=4
    • Left: 3−1=2

Final answer: 245

 

Word Problems Using Base Five

  • Example 1: A student groups pencils into bundles of 5. She has 325 pencils. Her friend gives her 125 more. How many pencils does she now have?
    • 325+125=445=445 pencils.
  • Example 2: A farmer had 435 sacks of rice. He sold 145. How many are left?
    • 435−145=245=245 sacks remain.

 

Learners’ Activities (Expanded)

  • Activity 1: Base Five Addition Drills
    Learners practice several base five additions using two-digit numbers, such as:
    • 135+215
    • 245+115
    • 345+125
  • Activity 2: Base Five Subtraction Drills
    Learners solve subtraction problems:
    • 325−145
    • 435−215
    • 315−125
  • Activity 3: Word Problem Creation (Peer Task)
    In pairs, learners create their own word problems using base five numbers and swap with other groups to solve.
  • Activity 4: Peer Review
    Learners swap notebooks and check each other's answers using step-by-step working.

 

Assessment Checks

Oral Questions:

  • “What is 325+215?” → 1035
  • “What is 435−145?” → 245

Quick Written Quiz:

  1. Add the following base five numbers:
    125+235
    b. 315+145
  2. Subtract the following base five numbers:
    345−125
    b. 445−135
  3. Solve:
    A boy had 335 marbles and gave away 145. How many marbles does he have left?

 

Notes (Expanded & Detailed)

  • Base five arithmetic strengthens the concept of place value, carrying, and borrowing outside of the familiar base ten system.
  • It builds flexibility in number thinking and prepares students for understanding other number systems used in computing (binary, octal).
  • Practicing addition and subtraction in base five helps develop procedural fluency and deeper understanding of mathematical structure.
  • Learners often make mistakes by carrying at 10 instead of 5, so practice and repetition are key.
  • Word problems give real-life context and support conceptual understanding, not just computation.

Assignments

  1. Convert and Solve:
    • Convert the following to base five, then add: 7+6, 10+13
  2. Solve in Base Five:
    • 245+135= ?
    • 345−115= ?
  3. Word Problem:
    • A group of students collects sticks. One collected 125, another collected 235. How many did they collect altogether?
  4. Challenge:
    • A basket had 445 fruits. After giving away some, 215 fruits remained. How many were given away?

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Review rules for addition and subtraction in base five with examples.

Evaluation Method (Expanded)
Exit slip/quiz: Solve two addition and two subtraction problems in base five. Teacher checks and gives feedback.

Assignment (Expanded):
Complete five addition and five subtraction problems in base five.

Follow-up Activity:
Create word problems involving addition/subtraction in base five using classroom objects.

Differentiation / Inclusive Strategies
Use counters and charts; provide step-by-step guidance for learners needing extra support.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☐ Medium ☐ Low