Skip to content
Request a demo

Grade 10 · Core Mathematics · Lesson 8 of 14

A Consecutive-Integer Equation

A Grade 10 Core Mathematics CBE lesson from the sub-strand Quadratic Expressions and Equations. In it, learners represent consecutive integers with one variable.

Strand Numbers and AlgebraSub-strand Quadratic Expressions and EquationsLesson code 10CM-13-L840 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. Represent consecutive integers with one variable.
  2. Translate a product into a quadratic equation.
  3. Interpret the constant after rearrangement.

Key vocabulary

Consecutive
Following one another with a difference of exactly one.
The integers k and k+1 are consecutive.
Standard form
A quadratic equation written with zero on one side.
The product model becomes k²+k−3782=0 after rearrangement.

Lesson preview

Slide 1 · Represent the pairOpening · 18 min
A number line displays consecutive integers k and k + 1, showing their product as an equation equal to 3782.
Figure 1: A number line displays consecutive integers k and k + 1, showing their product as an equation equal to 3782.

One integer can be named k, so the next consecutive integer is k+1. Their product gives a natural quadratic model. The named consecutive integers make the product condition explicit. Use Figure 1 to see how the product of these consecutive integers forms an explicit equation.

  • Define k as the smaller integer.
  • Write the next integer as k+1.
  • Use multiplication for the product.
  • Set the product equal to 3782.
Worked example. Let the smaller integer be k. The next integer is k+1. Set k(k+1)=3782. Answer: The product equation is k(k+1)=3782..

Check question: If k represents an integer, what represents the next consecutive integer?

  1. k+1
  2. 2k
  3. k−1
  4. k2
Show answer

k+1. Consecutive integers differ by exactly one. Therefore, the integer that immediately follows k is k+1.

Slide 2 · Rearrange and interpretCheck · 22 min
A four-step diagram demonstrates forming a quadratic equation from an area model, rearranging it into standard form, and checking the solution.
Figure 2: A four-step diagram demonstrates forming a quadratic equation from an area model, rearranging it into standard form, and checking the solution.

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
See the school projectorWhatsApp us

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