Liberia - Grade 6 - Mathematics - Multiplication in Base Five

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Subject: Mathematics

Semester: 1

Period: 2

Week: 11

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 11
Lesson Duration: 45 minutes
Week & Period: Week 11, Period 2
Topic: Multiplication in Base Five
Sub-topic: Base Five Multiplication Rules

Learning Objectives
By the end of the lesson, students should be able to:
Multiply numbers in base five
Apply carrying rules when product ≥ 5
Solve word problems in base five multiplication

Previous Knowledge
Students already know base five counting, addition, and subtraction in base five.

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 multiplication in base ten and base five addition/subtraction.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definition & Concept

The Base Five system (also known as quinary system) uses only five digits: 0, 1, 2, 3, and 4. It is a positional numeral system where the value of each digit depends on its position and is based on powers of 5.

In base five multiplication:

You multiply digits just like in base ten, but
If the product is 5 or more, you must carry over, just like in base ten but using base five rules.

Base Five Multiplication Rules

Multiply digits as usual (like in base ten).
If the result is 5 or more, divide it by 5:
- The remainder is the digit to write in the current column.
- The quotient (whole number result) is carried to the next column.
Keep place values in base five: units (5⁰), fives (5¹), twenty-fives (5²), etc.

Example 1: Multiply 23₅ × 4₅

Step-by-step:
Write:
23₅ × 4₅

Break down 23₅:
= 2×5 + 3 = 13₁₀

So, this is 13₁₀ × 4₁₀ = 52₁₀
Now convert 52₁₀ back to base 5:

52 ÷ 5 = 10 remainder 2 → write 2, carry 10
10 ÷ 5 = 2 remainder 0 → write 0, carry 2
2 ÷ 5 = 0 remainder 2 → write 2

Read from last to first: 202₂₅

✅ Answer: 23₅ × 4₅ = 202₅

Example 2: Multiply 14₅ × 3₅

Step 1: Convert both to base ten
14₅ = 1×5 + 4 = 9
3₅ = 3
9 × 3 = 27₁₀

Step 2: Convert 27₁₀ to base five:

27 ÷ 5 = 5 remainder 2
5 ÷ 5 = 1 remainder 0
1 ÷ 5 = 0 remainder 1

Answer: 102₂₅

✅ 14₅ × 3₅ = 102₅

Example 3: Multiply 12₅ × 3₅ (Direct Method)

Digits:

1 2 (base 5)

× 3 (base 5)

Step 1: Multiply 2 × 3 = 6

6 ÷ 5 = 1 remainder 1 → write 1, carry 1

Step 2: Multiply 1 × 3 = 3, plus 1 carried = 4
✅ Final Answer: 41₅

More Practice Examples

13₅ × 2₅ = ?
24₅ × 3₅ = ?
32₅ × 4₅ = ?

Word Problems (Base Five Context)

Example 1:
A student buys 3 pencils, each costing 12₅. How much does she spend?

Solution:
12₅ × 3₅ = 41₅
✅ Total cost = 41₅

Example 2:
A farmer packs 4 baskets with 23₅ oranges each. How many oranges in total?

Solution:
23₅ × 4₅ = 202₅
✅ Total = 202₅ oranges

Learners’ Activities (Expanded)

Guided Practice:
- Teacher solves one base five multiplication example on the board.
- Learners copy and solve along with the teacher.
Pair Work:
- Learners work in pairs to multiply:
  - 14₅ × 2₅
  - 21₅ × 3₅
  - 32₅ × 4₅

Group Task:
- Groups create 2 word problems involving multiplication in base five and exchange with another group to solve.
Use of Objects:
- Learners use counters (like bottle tops or sticks) to group in fives and visually simulate base five multiplication.
Game Time:
- “Multiply and Match”: Flashcards with problems and answers; learners must match base five problems to correct base five answers.

Assessment Checks

Quick Oral Questions:
- “What is 2 × 3 in base five?”
- “What do you do if the product is more than 5 in base five?”
Board Exercises:
- Multiply:
  14₅ × 2₅
  b. 12₅ × 3₅
  c. 13₅ × 4₅
Written Exercises:
- “Convert 102₅ to base ten.”
- “Solve: A pen costs 13₅. How much do 3 pens cost?”
Error Checking:
- Teacher gives a solved multiplication problem with a deliberate error.
- Learners must identify and correct the mistake.

Notes (Expanded & Detailed)

Why Base Five Multiplication?
This helps learners explore alternate number systems and strengthens understanding of place value, carrying, and digit limits.
Carrying and Conversion are Key!
Always convert results back to base five when necessary. Carrying helps preserve base five positional structure.
Use Visuals and Concrete Tools:
Abacus models, counters, or blocks grouped in fives can help visual learners understand how grouping and place value work in base five.
Connect to Real Life:
Although base five isn’t used in daily commerce, understanding it builds number sense and connects to computer science and coding principles.

Assignments

Section A: Direct Base Five Multiplication

12₅ × 3₅ = ______
21₅ × 2₅ = ______
23₅ × 4₅ = ______
13₅ × 3₅ = ______
14₅ × 4₅ = ______

Section B: Word Problems

Each basket has 14₅ How many mangoes are there in 3 baskets?
A student buys 2 books, each costing 23₅. What is the total cost?
A tray holds 13₅ How many eggs are in 4 trays?

Section C: Conversion Practice

Convert the following base ten answers to base five:
- 36
- 42
- 27

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Review base five multiplication rules, practice examples, and word problem applications.

Evaluation Method (Expanded)
Exit slip/quiz: Solve two multiplication problems in base five; teacher provides feedback.

Assignment (Expanded):
Complete five multiplication problems in base five, showing all carry-over steps.

Follow-up Activity:
Create simple word problems involving multiplication in base five using classroom objects.

Differentiation / Inclusive Strategies
Use manipulatives and visual aids for learners struggling with abstract concepts; peer-assisted learning for practice.

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