007. Division with Remainders and Short Division

Learning Intentions

• To know that a division of two numbers can result in a quotient and a remainder, and the result can be written as a mixed numeral if there is a remainder
• Use mental strategies to Solve quotients
• Apply the short division algorithm to divide positive integers

Pre-requisite Summary

• Understanding division as sharing and grouping
• Knowledge of multiplication facts (– times tables)
• Understanding that division is the inverse of multiplication
• Ability to partition numbers into multiples of a divisor
• Understanding place value when dividing multi-digit numbers

Worked Examples

Worked Example 1

Express the result with a remainder and as a mixed numeral:

a)

b)

Worked Example 2

Use mental strategies:

a)

b)

c)

Worked Example 3

Use mental strategies with remainders:

a)

b)

Worked Example 4

Use the short division algorithm:

a)

b)

Worked Example 5

Use the short division algorithm:

a)

b)

Problems

Problem 1

a)

b)

Problem 2

a)

b)

c)

Problem 3

a)

b)

Problem 4

a)

b)

Problem 5

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Write with remainder and as a mixed numeral:

a)

b)

c)

Exercise 2.

Use mental strategies:

a)

b)

c)

Exercise 3.

Use mental strategies with remainders:

a)

b)

c)

Exercise 4.

Use short division:

a)

b)

c)

Exercise 5.

Use short division:

a)

b)

c)

Exercise 6.

Divide:

a)

b)

c)

Reasoning

Exercise 7.

Explain why remainder .

Exercise 8.

A student writes . Explain the mistake.

Exercise 9.

How can multiplication help Check ?

Exercise 10.

Why must the remainder always be less than the divisor?

Problem-solving

Exercise 11.

students are placed into groups of . How many groups and how many left over?

Exercise 12.

A teacher shares pencils equally among classes. How many pencils per class?

Exercise 13.

A farmer packs eggs into cartons of . How many full cartons and how many eggs remain?

Exercise 14.

A library divides books equally onto shelves. How many per shelf?

Exercise 15.

A factory produces items and packs them into boxes of . How many boxes?

Potential Misunderstandings

• Students may write the remainder larger than the divisor
• Students may confuse the remainder with a decimal rather than a fraction
• Students may place the remainder incorrectly when writing a mixed numeral
• Students may divide each digit separately without considering place value
• Students may forget to carry the remainder to the next place value in short division
• Students may not check answers Use multiplication

Next: 008. Rounding and Estimation Strategies