006. Multiplying by Powers of Ten and Algorithms

Learning Intentions

• multiply by a power of ten by adding zeros to the end of a number
• Apply the multiplication algorithm to Solve the product of any two positive integers

Pre-requisite Summary

• Understanding place value and how digits shift when multiplied by
• Recognising powers of ten:
• Recall of single-digit multiplication facts
• Ability to multiply a number by a single digit Use the written algorithm
• Understanding column alignment and place value in written multiplication

Worked Examples

Worked Example 1

Multiply by powers of ten:

a)

b)

c)

Worked Example 2

Multiply by powers of ten:

a)

b)

c)

Worked Example 3

Use the multiplication algorithm:

a)

b)

Worked Example 4

Use the multiplication algorithm:

a)

b)

Problems

Problem 1

a)

b)

c)

Problem 2

a)

b)

c)

Problem 3

a)

b)

Problem 4

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Multiply by powers of ten:

a)

b)

c)

Exercise 2.

Multiply by powers of ten:

a)

b)

c)

Exercise 3.

Multiply using the algorithm:

a)

b)

c)

Exercise 4.

Multiply using the algorithm:

a)

b)

c)

Exercise 5.

Multiply:

a)

b)

c)

Exercise 6.

Multiply:

a)

b)

c)

Reasoning

Exercise 7.

Explain why multiplying by adds two zeros to a number.

Exercise 8.

A student writes . Explain the mistake.

Exercise 9.

Why must the second line in the multiplication algorithm shift one place left?

Exercise 10.

Compare and . How are they related?

Problem-solving

Exercise 11.

A factory produces items per day. How many items in days?

Exercise 12.

A school buys boxes of pencils with pencils in each. How many pencils?

Exercise 13.

A warehouse stores cartons with items each. How many items?

Exercise 14.

A printer produces pages per hour. How many pages in hours?

Exercise 15.

A farm plants trees in each section. There are sections. How many trees?

Potential Misunderstandings

• Students may append zeros incorrectly (e.g., adding zeros to the wrong number)
• Students may believe multiplying by changes digits rather than shifting place value
• Students may forget to shift the second partial product in the algorithm
• Students may misalign digits when adding partial products
• Students may ignore multiplication by zero within a number (e.g., )
• Students may incorrectly count the number of zeros when multiplying by powers of ten

Next: 007. Division with Remainders and Short Division