Lesson Planning to Verify Distributive Laws



Subject Mathematics

Grade 5th

Students` Learning Outcomes

  • The students will be able to:

o   Verify distributive laws.

Information for Teachers

Distributive law w. r. t subtraction:

First number x (Second Number + Third Number)

= (First Number x Second Number) + (First Number x Third Number)

Distributive law w.r.t multiplication:

First Number x (Second Number x Third Number)

= (First Number x Second Number) – (First Number x Third Number)

Explanation of Distributive Law:

Over Addition:

o   The word “Distributive” refers to the distribution of a common multiplier among the terms of an additive expression. For example:  2( 3 + 4 + 5) = 2 x 3 + 2 x 4 + 2 x 5 = 6 + 8 + 10

o   To verify the distributive law, we note that 2 (3 + 4 + 5) is the same as 2(12) or 24. Also, 6 + 8 10 is 24.

Over Subtraction:

o   3(8 – 5) = 3 x 8 – 3 x 5.

While teaching the lesson the teacher should consult with the textbook at all steps where and when applicable.

Material / Resources

Writing board, chalk /marker, duster, textbook


  • Tell the students if:

o   If row one (left) of the class there are 18 students and each have 3 notebooks in their bags for today.

o   In the middle row there are 20 students and each have 3 notebooks in their bags for today.

o   In the third (right) of the class there are 15 students and each have 3 notebooks in their bags for today.

o   How many notebooks do we have altogether?

o   If they give you answers appreciate them and also ask how did they get that answer?

o   Some would say 18 x 3 + 20 x 3 + 15 x 3 or find if somebody says 3 x (18 + 20 +15) by giving a reason that everybody has three notebooks for today! [Done in numbers unit as well)

o   If no one gives 3 x (18 + 20 +15), write on the board yourself and ask if it gives the same answer or not.

o   Introduce it as distributive property of multiplication over addition.


Activity 1

What does the word ‘distributive’ means? [Divide the load or burden among parts / members]

Ask them / giving different examples:

o   Tell students to bring 10 kg of stones for class activity each group of the class. Group A of 14 members brought 1 / 2 kg each and group B of 6 members brought 1 / 2 kg each. 

o   Three packs of sweets are lying in my room and 5 in my mother`s room, each of it weighs 1 / 2 kg. What is the total weight of sweets we have at home?

[ 1 / 2(3 + 5) = 1 / 2 x 3 + 1 / 2 x 5 = 3 / 2 + 5 / 2 = 4]

o   Explain the distributive law of multiplication by drawing circles on the board.

o   Ask students to count and observe the answers are same in both ways.

o   Use sample whole numbers for explanation and later apply it on the fractions.

o   The dot (.) shows multiplication: 

Activity 2

Ask for the example we just did, can I say that 4. (8 + 3) is the same as 4 x 8 + 4 x 3. (Yes)

What is the difference?

Why it`s not distributive law?

Conclude the discussion on that we can`t interchange the operations (addition by multiplication)

Split the class into groups.

Ask students write all the example questions done as yet and replace the addition sign with subtraction.

Does if the distribution law holds for subtraction as well or not, apply on the questions and explain?

Later ask them to create three questions for distributive law of multiplication over subtraction.

Collect the question slips, shuffle them up.

Distribute three per group and ask them to prove and verify the distributive law for the questions given by your class fellows.

Students have got enough application of distributive law over addition and subtraction. Now they are ready to apply it for fractions.

Activity 3

Call two students on board who are confident at fraction operations.

Divide the board into two columns.

Ask them to turn around to the class and not look at board.

You write the following on either side:

o   3 / 4 (2 / 3 + 6 / 7)

o   3 / 4 x 2 / 3 + 3 / 4 x 6 / 7

Say the both students:

o   You are given four minutes to solve.

o   Your time will begin as soon as you turn around.

o   You have to solve and find the answer.


Let the whole class clap and encourage.

SAY STOP!!!!!  So as the time is up.

Let the whole class observe that answer is the same on both sides of the board.

Reinforce the distributive law of addition over multiplication for fractions as well.

Recall fraction is also a number on number line not two numbers separated by a horizontal line.

Invite few more pairs to apply fraction distributive laws over addition and subtraction both. So there are once few examples are done its time for individual work.

Your turn:

  • Give an example such as; 13 / 7 + 16 / 7 = 1 / 7 x 13 + 1 / 7 x 16 = 1 / 7 (13 + 16)
  • Ask it`s you turn, them to write an example of distributive property for fractions with same denominators.
  • Say students to write few examples on board as well.

Sum up / Conclusion

  • Repeat the distributive law with the help of this example:

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

4 x 53 = 200 + 12

212 = 212

  • Say students: this is an example of distributive law over addition. If we change (50 + 3) into (50 – 3) then it will become an example of distributive law over subtraction.




  • Write down two questions related to this law and distribute into groups, such as; solve it by using distributive laws. 



  • Collect the responses and encourage.

Follow up

  • Assign questions from the textbook.
  • Solve by using distributive law and explain each step.


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