First degree equations with an unknown


  • Video presentation (related to balance) Discussion
  • Using a balance to visualize the properties of equality (students’ activity)
  • Presenting the properties of equality with mathematical symbols)
  • Solving equality (by students)

Learning objectives:

Students learn to solve A grade equality

Advisable age of students:

(Flexible according to the curriculum of specific country)  13

Previous knowledge:

  • use of variables,
  • distributive property,
  • operations with algebraic representations

scales, balls, wooden toys in the shape of a cube, and parallelepiped, finger paints

PHASE A  Visualisation (15 min)

The lesson started with a video showing a balancer (Nick Wallenda Chicago tightrope walk) between two skyscrapers (2-3 min). Then a discussion followed about balance (how important it is) throughout the ride. We made references to the video and what it might be related to the math lesson.

PHASE B     Artistic action and experimentation  (35 min)

A balance scale with two trays was placed at the classroom seat. By placing various objects, we brought it into a position of balance. The objects were wooden cubes, balls, paint cans, etc. The students with the help of the teacher managed to balance the scale. Then, they were asked to make changes to the masses of the two pans of the scale so that the scale (target) would again balance. The students, gradually and by experimenting with the scales, managed to discover the properties of equality. That is, they added, subtracted, multiplied or divided the same objects to both trays so that the even balance was always maintained. The next step was to record in the table the properties of equality as a general scientific conclusion. That is, if:

a=b then a+c=b+c

a=b then a-c=b-c

a=b then a*c=bx*

a=b then a/c=b/c

PHASE   C     Reflexion and debate       (45min)

The next goal was to solve the first-degree equation, i.e. the calculation of an unknown which in our example was the mass of a wooden rectangular parallelepiped, knowing the masses of known colored cylinders (25gr each).

The students with appropriate permissible movements based on the properties of equality and having on the seat similar wooden parallelepipeds as well as similar cylinders managed to leave the wooden parallelepiped on one balance disk and only cylinders with known masses on the other balance disk. (the goal was in any case to maintain the balance.  So, the solution of the equation was achieved.

That is: x* 25=x/3+5*25

Multiply by 3: 3(x+25)=3(x/3+5*25)


Then subtract an x:


Then subtract 3*25:


Divide by 2: x=6*25

so x=150

So, it was found that the mass of the rectangular parallelepiped was 150gr.

Then the students solved other examples of equations in order to better understand and consolidate the lesson.

Comments, possible derivations, and prolongations of the proposal:

Each lesson plan can have more phases and each phase can be divided in further sub-phases in order to reach the learning objectives

References and links:

First degree equations with an unknown

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