Introducing Standard Form

Differentiated Learning Objectives

  • All students should convert numbers bigger than one to and from standard form.
  • Most students should convert numbers bigger or less than one to and from standard form.
  • Some students should convert fractions to and from standard form.

Links to Lesson Resources (Members Only)

Starter/Introduction

At the start of the lesson, students recap multiplying and dividing numbers by a power of ten. Some students may benefit from a place value grid, while others will use mental methods. Students could check their solutions using the ×10x or EXP button on their calculators.

 Prompts / Questions to consider

  • How can we use the place value table to convert a power of ten to a decimal multiplier?
  • Which is bigger, dividing by 102 or multiplying by 10-3?

Introducing Standard Form

When introducing standard form, discuss how calculations with very big or small numbers can be more accessible by writing numbers in standard form. After the classroom discussion, students work in pairs or small groups to think of five industries that operate with numbers in standard form.

Next, demonstrate how to convert ordinary numbers to standard form, as shown in the tutorial below.

After working through questions a) and b), students could attempt questions from the Interactive Excel file on mini-whiteboards to assess understanding. When demonstrating why numbers less than 1 involve a negative power of ten it may be helpful to refer back to the rules of indices. 

Students could work through the questions on the third slide and then progress through the worksheet when ready. Please encourage students to check their work using the scientific form on their scientific calculators.

 Prompts / Questions to consider

  • How does the power of ten determine the place value of the decimal?

Plenary

The plenary includes two common exam-style questions. Have students attempt these questions on mini-whiteboards to assess progress and give feedback. For example, more able students could write the sun’s diameter in cm or mm and the radius of the hydrogen atom in km.

 Prompts / Questions to consider

  • What would be the diameter of the sun in cm or mm?
  • How can we write the radius of a hydrogen atom in cm or km?

Differentiation

More able students could focus on correcting numbers not written in standard form. For example, 0.025 × 10-1 becomes 2.5 × 10-3. Less able students may benefit from additional practise writing numbers bigger than 1 in standard form before moving on to negative powers of ten.

Additional Resources

Problem Solving
Working with Standard Form
Revision
Writing Numbers in Standard Form
4 Part Lesson
Writing Numbers in Standard Index Form

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