Add and Subtract with Numbers in Standard Form

To add and subtract with numbers in standard form, students apply various skills and knowledge of different topics. They need to be equally confident converting large numbers to standard form as they write small numbers from standard to ordinary form. Column subtraction and addition may seem basic skills, but they become more complex when many zeros are added.

Converting Between Ordinary and Standard Form

Add and Subtract with Numbers in Standard Form

When I teach how to add and subtract numbers in standard form, I use the starter activity to ensure students know how to convert between ordinary and scientific numbers. I asked them to arrange two sets of numbers in ascending order. I don’t mind if students write all the numbers in scientific or ordinary form as both are relevant and necessary to the lesson. Depending on the class, I may use the first set as an example and ask the students to attempt the second set on mini-whiteboards. It is necessary to allow sufficient time for this as the rest of the lesson becomes very difficult without it.

Using Standard Form

Add and Subtract with Numbers in Standard Form

There are two ways to add and subtract with numbers in standard form.  The first is to write them both as the same There are two ways to add and subtract with numbers in standard form. The first is to write them both as the same power of ten and add or subtract the decimals. When adding numbers in standard form, they both need to be written with the same power of ten. I find this approach best for more able students as it requires them to work with decimals rather than integers.

Add and Subtract with Numbers in Standard Form

Here both numbers are converted to ordinary form Here both numbers are converted to ordinary form to use the column method of addition or subtraction. This is a common approach as students are more comfortable working with integers than decimals.

Adding Greater Challenge

Whenever these questions appear in exam papers, they involve positive powers often, but I like to include negative powers to add a greater level of challenge and interest. I also want to have a mixture of addition and subtraction questions. I do this because the challenge is not in arithmetic but in converting standard to ordinary form and consolidates this skill.

Click here to view the video.

I work thI worked through the questions on the second slide with the class. After demonstrating a few solutions, I asked the students to attempt a few on their mini-whiteboards. I leave them to decide whether to use the standard or ordinary form method. Typically, only the more able students try to add and subtract the numbers while in standard form. After sufficient practice, I asked the class to work through the questions on the third slide. I encourage all students to check their work on calculators rather than waiting for me to provide answers. I find this helps maintain the pace of the lesson as students get instant feedback.

Challenge in the Plenary

Add and Subtract with Numbers in Standard Form

I leave about 12 minutes for the plenary. I like this question as it brings together multiple skills. Students begin by working out the total land area of Asia, Africa, and North America, then subtracting that from the global land area. I ask the class to attempt this on their mini-whiteboards so I can assess progress and feedback. For an additional challenge, I provide the approximate populations of each continent so students can calculate population densities.

Addition and subtraction of numbers in standard form is a free lesson that you are welcome to download. Like all lessons available at Mr. Mathematics, it includes an online version, PowerPoint, Notebook, Flipchart, and differentiated worksheet. In addition, solutions are provided for the lesson plan and worksheet.


About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.


How to Simplify Surds

To introduce what a surd is students learn about the difference between rational and irrational numbers. Using square factors students progress from simplifying surds to evaluating fractions and products.

Mr Mathematics Blog

Solving Problems with Non-Right-Angled Triangles

How to teach solving problems with non-right angled triangles.

Nth Term of Picture Sequences

How to work out the nth term of a picture sequence.

Using Box Plots to Interpret Sets of Data

How to compare datasets using box and whisker diagrams.