Subject Mathematics

Grade 5th

Students` Learning Outcomes

  • Verify Distributive Laws

Information for Teachers

  • Distributive law collects multiplication and addition subtraction operations;
  • o   Distributive Law w.r.t addition x(b + c) = a x b + a x c
  • o   Distributive law w.r.t subtraction a x ( b – c) = a x b – a x c


  • While teaching the lesson, the teacher should consult textbook at all steps where in and whenever applicable.



  • Write ‘Distributive Laws’ on the top of the board.
  • Ask students if they have any idea what it is?
  • Tell students that this law (sometimes called property) states that you get the same answer when you multiply a number by a group of numbers added together as when you do each multiplication separately, such as; 3 x (2 + 4) = 3 x 2 + 3 x 4 so the “3” can be “distributed” over the “2 + 4” into 3 times 2 and 3 times 4.
  • Show it with help of the following figure:


  • Repeat this activity for subtraction.



Activity 1

  • Draw the following shape on the board and tell students that this figure represents the area of rectangle with length b + c and width a. 


  • Hence area of this rectangle is = a x (b + c) or a( b + c)
  • This can be split into two parts as follows; 



  • Now the sum of the area of both rectangles is a b + a c because both are parts of that rectangle, so we can write; a (b + c) = a b + ac
  • Give paper strips to students in groups to verify it for themselves.

Activity 2

  • Tell students that it is very convenient to use distributive law for quick multiplication.
  • Tell students that I want to multiply 12 x 19, and I used a quick method to do it. I multiplied 12 by 20. Well 12 x 20 is easy, it`s 240. But, I added one more 12 than I needed, so i`ll take it away from 240 to give me 228. =
  • Similarly ask students how to do;

4 x 27

= 4(20 + 7)

= 4(20) + (7)

= 80 + 28 = 108

  • Solve 2 more examples.


Activity 3

  • Now divide students in two groups.
  • Each group will suggest a multiplication sum like given in the examples of previous activity, for the other group as challenge.
  • Other group will solve in their notebooks.
  • Each group will solve at least 5 questions.
  • Help students if they are unable to do any question.
  • These multiplication sums can be selected from textbook exercise as well.

Sum up / Conclusion

  • The Distributive Laws lets you multiply a sum by multiplying each added separately and then add the products.
  • Quick multiplication can be done through distributive laws.
  • The Distributive Property helps with mental math.
  • A quick multiplication is;

4 x 53

= (4 x 50) + (4 x 3)

= 200 + 12 = 212


  • Students will be given following statement questions to apply their understanding of Distributive Law.

Follow up


  • Assign some questions from textbook to do as homework.






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