3. Multiplication and division

Lesson

Let's practice breaking apart the number in this problem to help us get ready for this lesson.

We want to find 2 \times 45.

Use the area model to complete the following:

\displaystyle 2\times 45 | \displaystyle = | \displaystyle 2\times \left(40+5\right) |

\displaystyle = | \displaystyle 2\times ⬚ + 2\times5 | |

\displaystyle = | \displaystyle ⬚ + ⬚ | |

\displaystyle = | \displaystyle ⬚ |

Worked Solution

Idea summary

If we have a number sentence such as 5\times 12 it can be rewritten as 5\times 10 + 5\times 2.

We can use some of the multiplication strategies we know to solve multiplication of larger numbers.

How can some of these strategies be used on larger numbers, do you think?

Find the product of 65 \times 97.

Worked Solution

Idea summary

We can multiply two digit numbers by two digit numbers using the standard algorithm by partitioning one of the numbers.

Let's take a look at how we divide a 4 digit number by a single digit number, using a few different strategies we've learnt.

Find the value of 1209 \div 3.

Worked Solution

Idea summary

Division is when we share a total into a number of groups, or find out how many items each group has. It is the reverse of multiplication.

We often hear and use the language "twice as big as", or "ten times bigger than", but how do we work this out?

The image below shows a row of squares.

a

How many times more circles are shown below compared to the squares?

Worked Solution

b

How many times more triangles are shown below compared to the squares?

Worked Solution

Idea summary

The vertical algorithm method is really useful for solving multiplication and division problems, but we also have other strategies if we need them, including:

estimating the answer first

using the area or arrays method

partitioning our number

using the distributive property of multiplication

looking for patterns

finding the factors of our numbers

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies

Solve problems involving division by a one digit number, including those that result in a remainder

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems

Use equivalent number sentences involving multiplication and division to find unknown quantities