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Grade 10 · Core Mathematics · Lesson 11 of 14

A Triangular Sign Model

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners model a triangular area with one variable.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L1140 minutes · 4 slides

KICD learning outcome (g)

Apply quadratic equations to real life situations.

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

  1. Model a triangular area with one variable.
  2. Solve and reject a negative physical root.
  3. Report and verify dimensions with units.

Key vocabulary

Model
A mathematical representation of a situation and its constraints.
The sign model is one-half h(h+17)=559.
Feasible
Possible within the conditions of the real situation.
Only h=26 is feasible for a physical sign height.
Dimension
A measurable length that describes the size of a shape.
The sign dimensions are height 26 cm and base 43 cm.
Reflection
A reasoned statement about what a method reveals or why a choice is valid.
The final report explains why the chosen root is physically meaningful.

Lesson preview

Slide 1 · Define the triangular modelOpening · 8 min
A diagram of a triangular sign labelled with a height of h cm, a base of h+17 cm, and an area of 559 cm².
Figure 1: A diagram of a triangular sign labelled with a height of h cm, a base of h+17 cm, and an area of 559 cm².

A triangular road safety sign must be highly visible to passing drivers. Regulations demand a height of h cm, base h+17 cm, and a 559 cm² area. One variable links both dimensions, helping engineers model sizes responsibly.

  • State that all lengths are in centimetres.
  • Use one-half base times height.
  • Write the area condition.
  • Keep units in the final report.
Worked example. Use one-half h(h+17)=559. Multiply by two and expand to h²+17h=1118. Move 1118 to obtain h²+17h−1118=0. Answer: The model is h²+17h−1118=0..

Check question: In the triangular sign model, what is the main purpose of defining the base as h+17 rather than using a second variable like b?

  1. It allows us to form a quadratic equation with only one unknown variable.
  2. It ensures the area of the triangle is automatically calculated in cm².
  3. It guarantees that the height of the sign will not be a negative value.
  4. It means the base is exactly 17 times longer than the height.
Show answer

It allows us to form a quadratic equation with only one unknown variable. By relating the base to the height (h) using the stated difference, we avoid needing a second variable and can solve for h using the given area constraint.

Slide 2 · Solve and filter rootsModel · 12 min
A number line showing a mathematically valid root at 26 and a rejected root at negative 43.
Figure 2: A number line showing a mathematically valid root at 26 and a rejected root at negative 43.

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.

  • All 4 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 13 lessons in this sub-strand
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All 14 lessons in Quadratic Expressions and Equations

  1. 1Building Quadratic Expressions from DimensionsForm quadratic expressions from different situations
  2. 2Four Products on a NoticeboardForm quadratic expressions from different situations
  3. 3Deriving a Square Identity by AreaDerive the quadratic identities from the concept of area
  4. 4Restoring a Difference-Square AreaDerive the quadratic identities from the concept of area
  5. 5Nearby Bases for Mental SquaringApply quadratic identities in numerical cases
  6. 6Factor Pairs and GroupingFactorise quadratic expressions from different situations
  7. 7Forming an Area EquationForm quadratic equations in different situations
  8. 8A Consecutive-Integer EquationForm quadratic equations in different situations
  9. 9Solving by FactorisationSolve quadratic equations by factorisation
  10. 10Exact Roots with Signed FactorsSolve quadratic equations by factorisation
  11. 11A Triangular Sign ModelApply quadratic equations to real life situations
  12. 12Planning a Rectangular TankApply quadratic equations to real life situations
  13. 13Exploring Quadratic Models for a Community MuralExplore the use of quadratic equations in real life situations
  14. 14Exploring a Community Greenhouse FrameExplore the use of quadratic equations in real life situations