005. Multiplication Laws and Algorithms

Learning Intentions

• To understand the commutative and associative laws for multiplication
• Use mental strategies to Solve products
• Apply the multiplication algorithm to find the product of a single digit number by a positive integer

Pre-requisite Summary

• Understanding multiplication as repeated addition
• Knowledge of basic multiplication facts (– times tables)
• Understanding place value (ones, tens, hundreds, thousands)
• Ability to partition numbers (e.g., )
• Understanding of distributive reasoning (breaking numbers apart)

Worked Examples

Worked Example 1

Use multiplication laws to Simplify:

a) and

b) and

Worked Example 2

Use mental strategies:

a)

b)

Worked Example 3

Use mental strategies:

a)

b)

Worked Example 4

Use the multiplication algorithm:

a)

b)

Worked Example 5

Use the multiplication algorithm:

a)

b)

Problems

Problem 1

a) and

b) and

Problem 2

a)

b)

Problem 3

a)

b)

Problem 4

a)

b)

Problem 5

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Use the commutative law:

a)

b)

c) Explain the relationship

Exercise 2.

Use the associative law:

a)

b)

c) Compare the results

Exercise 3.

Use mental strategies:

a)

b)

c)

Exercise 4.

Use mental strategies:

a)

b)

c)

Exercise 5.

Use the multiplication algorithm:

a)

b)

c)

Exercise 6.

Use the multiplication algorithm:

a)

b)

c)

Reasoning

Exercise 7.

A student says . Explain why this is true.

Exercise 8.

Which is easier to Calculate mentally? Explain:

a)

b)

Exercise 9.

Show two different ways to calculate Use mental strategies.

Exercise 10.

Explain why breaking into works.

Problem-solving

Exercise 11.

A box holds pencils. How many pencils are in boxes?

Exercise 12.

A bus carries passengers per row. There are rows. How many passengers?

Exercise 13.

A teacher gives stickers to each of students. How many stickers are given?

Exercise 14.

A factory makes toys per minute. How many toys in minutes?

Exercise 15.

A farmer plants trees in each row. There are rows. How many trees?

Potential Misunderstandings

• Students may think multiplication is not commutative (believing )
• Students may confuse associative and commutative laws
• Students may incorrectly regroup when multiplying (e.g., forgetting to carry)
• Students may multiply digits without considering place value
• Students may omit multiplication by in numbers such as
• Students may incorrectly partition numbers when using mental strategies

Next: 006. Multiplying by Powers of Ten and Algorithms