Math help from the Learning Centre

Multiplication is more than just a mechanical process. Understanding different strategies enhances problem-solving skills in algebra, calculus, and real-world applications.

Why Not Just Memorize or Use the Standard Algorithm?

• Memorizing times tables is useful, but insufficient for complex calculations and mental flexibility

• The standard multiplication algorithm works but isn’t always the most efficient.

• Alternative strategies can simplify large numbers, reduce errors, and improve mental math skills.

 

Application:

Consider how multiplication is used in data science, physics, finance, nursing, and engeineering - often requiring breaking down problems rather than direction computation.

Repeated Addition & Iterative Thinking

Multiplication can be viewed as an iterative process: foundational loops in programming and recursive functions in computer science.

Example: \(4 \times 3\)

\(3 +3+3+3=12\)

 

Example: You invest $1,000 in a savings account that earns 5% simple interest per year. How much money will you have after 4 years using repeated addition?

Interest for 1 year:

Interest \(= 1000 \times 0.05 = 50 \)

After 1 year: \($1000 + 50 = $1050\)

Use repeated addition for 4 years:

Year 2: \($1050 + 50 = $1100\)

Year 3: \($1100 + 50 = $1150\)

Year 4: \($1150 + 50 = $1200\)

Final Amount After 4 Years: $1200

 

Scaling & Proportional Reasoning

Rescaling numbers makes computation easier and is used in economics and physics.

Example: \(49 \times 26 \)

We can rewrite as 

\((50 \times 26) - (1 \times 26) = 1300 - 26 = 1274 \) 

 

Example: \(102 \times 17 \)

We can rewrite as 

\((100 \times 17) + (2 \times 17) = 1700 + 34 = 1734 \) 

 

Doubling and Halving 

Halving one factor and doubling another preserves the product but simplifies calculations.

Example: \(16 \times 25\)

We divide 16 by 2 and multiple the 2 to 50 and rewrite as:

\(8 \times 50 = 400\)

 

Example: \(48 \times 15\)

\(24 \times 30 = 720\)

 

Distributive Property and Algebraic Expansion

Break numbers into smaller, manageable parts can speed up calculations.

Example: \(38 \times 7\)

\(= (30 \times 7) + (8 \times 7)\)

\(=210 + 56 = 266\)

 

Example:  \(232 \times 46\)

\(= (200 \times 46) + (30 \times 46) + (2 \times 46)\)

\(= (200 \times 40) + (200 \times 6) + (30 \times 40) + (30 \times 6) + (2 \times 46)\)

\(=8000 + 1200 + 1200 + 180 + 92 = 10,672\)

 

Reflection

Which multiplication strategy do you think is most useful for you?

Can you think of a real-world example where mental math strategies would be useful?