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Grade 10 · Core Mathematics · Lesson 12 of 14

Planning a Rectangular Tank

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners translate a tank footprint into an equation.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L1240 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. Translate a tank footprint into an equation.
  2. Solve and filter roots with units.
  3. Verify a resource-planning dimension pair.

Key vocabulary

Footprint
The length-and-width plan of a structure viewed from above.
The tank footprint satisfies x(x+29)=1122 in square metres.
Feasible root
A solution that satisfies both the equation and the physical context.
x=22 is the feasible root for the tank width.
Verification
A deliberate comparison between a model prediction and the stated condition.
The verification 22×51=1122 matches the tank area.
Planning report
A concise statement connecting a mathematical result to an actionable decision.
The report recommends a 22 m by 51 m tank because its area is 1122 m².

Lesson preview

Slide 1 · Translate the tank constraintOpening · 8 min
A rectangular diagram shows a tank footprint with a width of x, a length of x+29, and an area of 1122 square metres.
Figure 1: A rectangular diagram shows a tank footprint with a width of x, a length of x+29, and an area of 1122 square metres.

A tank footprint has width x metres, length x+29 metres, and area 1122 square metres. The area condition creates a quadratic equation. The product of the dimensions must reproduce the stated footprint.

  • Define x as the width in metres.
  • Write the length as x+29 metres.
  • Multiply the dimensions.
  • Set the product equal to 1122.
Worked example. Write x(x+29)=1122. Expand to x²+29x=1122. Move 1122 to obtain x²+29x−1122=0. Answer: The equation is x²+29x−1122=0..

Check question: In the equation x(x+29)=1122, what does the value 1122 represent in the context of the tank?

  1. The area of the tank footprint in square metres.
  2. The perimeter of the tank footprint in metres.
  3. The volume of the tank in cubic metres.
  4. The length of the tank footprint in metres.
Show answer

The area of the tank footprint in square metres. The equation multiplies the width (x) by the length (x+29). The product of a rectangle's width and length gives its area, which is 1122 square metres.

Slide 2 · Solve and filterModel · 12 min
A sorting machine separates a negative mathematical root of negative 51 from a positive, buildable root of 22.
Figure 2: A sorting machine separates a negative mathematical root of negative 51 from a positive, buildable root of 22.

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