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Grade 10 · Core Mathematics · Lesson 7 of 14

Forming an Area Equation

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners define a dimension variable.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L740 minutes · 2 slides

KICD learning outcome (e)

Form quadratic equations in different situations.

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

  1. Define a dimension variable.
  2. Form an equation from an area constraint.
  3. Rearrange to zero form and test a non-solution.

Key vocabulary

Constraint
A condition that a mathematical model must satisfy.
The area constraint is w(w+28)=893 for this rectangle.
Standard form
A quadratic arrangement with zero on one side.
Subtracting 893 gives w²+28w−893=0 in standard form.

Lesson preview

Slide 1 · Translate the rectangleOpening · 18 min
A green rectangle is labelled with a width of w and a length of w+28 to show an area of 893 square units.
Figure 1: A green rectangle is labelled with a width of w and a length of w+28 to show an area of 893 square units.

A rectangle with width w and length w+28 has area 893 square units. Multiplying the dimensions translates the situation into an equation. The dimensions determine the product that must equal the given area. Refer to Figure 1 to see these dimensions and area labelled on the shape.

  • Define w as the width.
  • Write the length as w+28.
  • Use width times length for area.
  • Set the product equal to 893.
Worked example. Write w(w+28)=893. Expand to w²+28w=893. Subtract 893 to obtain zero form. Answer: The equation is w²+28w−893=0..

Check question: A tree nursery has a width of w metres and a length of w+28 metres. If the total area is 893 square metres, what equation represents this situation before any algebraic expansion?

  1. w(w+28)=893
  2. w+(w+28)=893
  3. 2w+2(w+28)=893
  4. w(28w)=893
Show answer

w(w+28)=893. The area of a rectangle is found by multiplying its width by its length. Therefore, the width w multiplied by the length w+28 equals the area 893.

Slide 2 · Use standard formCheck · 22 min
A flowchart shows how to rearrange the initial area equation into standard form, and a trial calculation tests a width of 20.
Figure 2: A flowchart shows how to rearrange the initial area equation into standard form, and a trial calculation tests a width of 20.

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 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