Grade 10 · Core Mathematics · Lesson 5 of 13

Indices in Measurement and Design

A Grade 10 Core Mathematics CBE lesson from the sub-strand Indices and Logarithms. In it, learners select an index law for area, volume, or quotient-based dimension problems.

Strand Numbers and AlgebraSub-strand Indices and LogarithmsLesson code 10CM-12-L540 minutes · 2 slides

KICD learning outcome (c)

Apply the laws of indices in different situations.

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

Select an index law for area, volume, or quotient-based dimension problems.
Keep units and powers consistent while calculating.
Interpret and verify a simplified power in context.

Key vocabulary

Dimension: A measurable direction such as length, width, or height.; A rectangular panel has two dimensions contributing to area.
Volume: The space occupied by a three-dimensional object.; A cube with side 2 metres has volume $2^{3}$ cubic metres.
Scale factor: A multiplier that changes a measurement proportionally.; A scale factor of $5^{2}$ multiplies each displayed length.
Area factor: The multiplier affecting area when each length scales.; Doubling both lengths makes the area factor $2^{2}$ .

Lesson preview

Slide 1 · Area and volume use repeated dimensionsOpening · 18 min

Figure 1: A square and a cube demonstrate how to calculate area and volume by raising the dimensions given in index form to a power.

Many measurements naturally create powers because equal lengths are multiplied. A square uses two dimensions and a cube uses three, so index laws can simplify scaled dimensions before a numerical answer is found. Study Figure 1 to see how index laws can simplify these scaled dimensions.

Area multiplies two lengths with compatible units.
Volume multiplies three lengths with compatible units.
Repeated scaling can be represented as powers.
The final power should still match the context.

Worked example. Area is side × side, so write (

3^{2}

)(

3^{2}

). Add exponents: 2 + 2 = 4. State area as

3^{4}

square centimetres. Answer: $3^{4}$ cm².

Check question: A storage box is designed as a perfect cube with a side length of $2^{3}$ units. What power of $2$ represents the volume of this box?

$2^{9}$
$2^{6}$
$2^{27}$
$6^{9}$

Show answer

$2^{9}$ . The volume of a cube is found by multiplying its length, width, and height. Since all sides are equal, the volume is $2^{3} \times 2^{3} \times 2^{3}$ . According to the laws of indices, when multiplying terms with the same base, we keep the base and add the exponents: $3 + 3 + 3 = 9$ . Therefore, the volume is $2^{9}$ cubic units.

Slide 2 · Recover a Dimension with a QuotientPractice · 22 min

Figure 2: A rectangular diagram shows how to divide an area by its width using the laws of indices to find the missing length.

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

See the school projector WhatsApp us

Indices in Measurement and Design

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

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 13 lessons in Indices and Logarithms