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Grade 10 · Core Mathematics · Lesson 13 of 13

Why Indices and Logarithms Matter

A Grade 10 Core Mathematics CBE lesson from the sub-strand Indices and Logarithms. In it, learners recognise how indices organise repeated growth and scale.

Strand Numbers and AlgebraSub-strand Indices and LogarithmsLesson code 10CM-12-L1340 minutes · 2 slides

KICD learning outcome (g)

Appreciate the use of indices and common logarithms in mathematical computations.

By the end of this lesson, learners should be able to

  1. Recognise how indices organise repeated growth and scale.
  2. Recognise how logarithms simplify large computations.
  3. Choose and justify a representation for a new computation.

Key vocabulary

Scale
The relative magnitude of a quantity or change.
A power of ten communicates scale compactly.
Pattern
A repeated or predictable mathematical arrangement.
Equal factors reveal a power pattern.
Efficiency
Achieving a result with sensible effort and resources.
Logarithms can make repeated multiplication more efficient.
Computation
A mathematical process used to obtain a result.
A log computation can estimate a large power.

Lesson preview

Slide 1 · Compact notation reveals structureOpening · 20 min
A blue ribbon showing repeated multiplication of twos rolls up into a smaller orange square tile showing the same value written in index notation.
Figure 1: A blue ribbon showing repeated multiplication of twos rolls up into a smaller orange square tile showing the same value written in index notation.

Indices expose repeated multiplication, scale, and dimension in a form that can be compared quickly. A well-chosen index representation helps a learner notice patterns that would be hidden inside long strings of ordinary multiplication.

  • Indices make repeated growth easier to read and compare.
  • Powers describe dimensions in area and volume.
  • A compact expression can preserve exactness while making repeated structure easier to compare.
  • The base and exponent each carry useful information.
Worked example. Count the four equal factors. Use the base 2 and exponent 4. Compare the compact form with the original product. Answer: 2⁴ records the same exact value while showing the repeated-factor structure..

Check question: What information does the exponent preserve when repeated multiplication is written in compact index notation?

  1. How many times the base is used as a factor
  2. The sum of the bases added together
  3. The product of the base and the exponent
  4. The number of digits in the final evaluated result
Show answer

How many times the base is used as a factor. The exponent communicates repetition without listing every multiplication sign, showing exactly how many times the base is used as a factor.

Slide 2 · Logarithms make large work manageablePractice · 20 min
A diagram shows how indices and logarithms provide two different calculation routes that lead to a single computed result for practical applications.
Figure 2: A diagram shows how indices and logarithms provide two different calculation routes that lead to a single computed result for practical applications.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 12 lessons in this sub-strand
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All 13 lessons in Indices and Logarithms

  1. 1Reading Repeated Factors as IndicesExpress numbers in index form
  2. 2Index Forms with a Specified BaseExpress numbers in index form
  3. 3Discovering Product and Quotient LawsDerive the laws of indices using factors
  4. 4Power of a Power and Identity CasesDerive the laws of indices using factors
  5. 5Indices in Measurement and DesignApply the laws of indices in different situations
  6. 6From Powers of Ten to Common LogsRelate index notation to logarithm notation to base 10
  7. 7Interpreting Base-Ten LogarithmsRelate index notation to logarithm notation to base 10
  8. 8Reading Common Logarithms in TablesDetermine common logarithms of numbers from mathematical tables and calculators
  9. 9Comparing Table and Calculator LogarithmsDetermine common logarithms of numbers from mathematical tables and calculators
  10. 10Logarithms for Multiplication and DivisionApply common logarithms in multiplication, division, powers and roots of numbers
  11. 11Logarithms for Powers and RootsApply common logarithms in multiplication, division, powers and roots of numbers
  12. 12Integrated Logarithmic ComputationApply common logarithms in multiplication, division, powers and roots of numbers
  13. 13Why Indices and Logarithms MatterAppreciate the use of indices and common logarithms in mathematical computations