Add and Subtract with Numbers in Standard Form

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

Converting Between Ordinary and Standard Form

When I teach how to add and subtract with numbers in standard form I use the starter activity to make sure students know how to convert between ordinary and scientific numbers. I ask them to arrange two sets of numbers in ascending order.  I don’t mind if students choose to 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 important to allow sufficient time for this as without it the rest of the lesson becomes very difficult.

Using 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 power of ten and add or subtract the decimals. To add the numbers in standard form both numbers need to written using the same power of ten. I find this approach is 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 to use the column method of addition or subtraction.  This is a common approach as students are more comfortable working with integers than decimals.

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

I work through the questions on the second slide with the class.  After demonstrating a few solutions I ask 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 attempt to add and subtract the numbers while in standard form. After sufficient practice I ask 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 I leave about 12 minutes for the plenary.  I like this question as it brings together multiple skills.  Students first must find the total land area of Asia, Africa and North America then subtract 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 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 which you are welcome to download.  Like all lessons available at Mr Mathematics it includes a detailed lesson plan, PowerPoint, Notebook, Flipchart and differentiated worksheet.  Solutions are provided for the in the lesson plan and worksheet.

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