Lesson

Breaking up numbers into parts, often by place value, can help with addition. Do you know how to partition a number by place value?

We're going to write 56\,713 in expanded form.

a

Fill in the number expander for 56\,713.

56\,713=⬚ \, \text{ Ten-Thousands }⬚ \, \text{ Thousands }⬚ \, \text{ Hundreds }⬚ \, \text{ Tens }⬚ \, \text{ Units}

Worked Solution

b

56\,713=⬚+⬚+⬚+10+3

Worked Solution

Idea summary

We can use a place value table to write numbers in expanded form.

Place value is something we need to know when solving addition, whether working across our page, or using a vertical algorithm. Let's see how it helps us, including regrouping.

Let's find the value of 705 + 205, by partitioning the numbers.

a

Fill in the box with the missing number.

705 = 700 + ⬚

Worked Solution

b

Fill in the box with the missing number.

205 = ⬚ + 5

Worked Solution

c

Find the value of 705 + 205.

Worked Solution

Idea summary

To add large numbers, we can first partition the numbers and then add their partitions.

We can use vertical algorithms to work with larger numbers as well, as we do in this video.

Find the value of 19\,292 + 34\,131.

Worked Solution

Idea summary

We often call on different methods when we solve addition problems, so remember to use things such as:

bridge (build) to 10

partitioning numbers

number lines

place value

vertical algorithms

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations