Proportional Reasoning - 1 | A

Question 3

Activity 3: Form a pair. Collect 12 countable objects or counters (it can be coins, seeds, or pebbles). Now, share them between the two of you in different ways.

Question diagram 1
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Solution
Understand the Question
  • Sharing 1212 countable objects between two people means dividing the total so that the sum of both shares equals 1212.
  • If Person 1 receives xx objects, then Person 2 receives (12x)(12 - x) objects, where xx is any whole number from 00 to 1212.

Step 1 · Identify Total Objects and Sharing Rule

Total number of objects to share: N=12N = 12Diagram 1

If Person 1 receives xx objects, Person 2 receives (12x)(12 - x) objects, where xx can be any whole number from 00 to 1212.

Step 2 · Examples of Sharing

Examples of dividing the 1212 objects into two parts: 4+8=124 + 8 = 12

6+6=126 + 6 = 12

2+10=122 + 10 = 12

Answer

The 1313 possible ways to share the 1212 objects between Person 1 and Person 2 (Person 1, Person 2) are:

  • (0,12)(0, 12)
  • (1,11)(1, 11)
  • (2,10)(2, 10)
  • (3,9)(3, 9)
  • (4,8)(4, 8)
  • (5,7)(5, 7)
  • (6,6)(6, 6)
  • (7,5)(7, 5)
  • (8,4)(8, 4)
  • (9,3)(9, 3)
  • (10,2)(10, 2)
  • (11,1)(11, 1)
  • (12,0)(12, 0)
Common Mistakes
  • Overlooking Zero: Forgetting that giving 00 objects to one person and all 1212 to the other is a valid mathematical partition.
  • Sum Mismatch: Ensuring that for every combination (x,y)(x, y), the condition x+y=12x + y = 12 is strictly satisfied.

More questions in A

Q1

Take your favourite dish. Find out all the ingredients and their respective quantities needed to make the dish for your family. Suppose you are celebrating a festival and you want to invite 15 guests. Find out the quantities of the ingredients required to cook the same dish for them.

Q2

Go to the market and collect the prices of different sizes of shampoo containers of the same shampoo and create a table like the one given below. See if the volume of shampoo is proportional to the price.

Q3

Activity 3: Form a pair. Collect 12 countable objects or counters (it can be coins, seeds, or pebbles). Now, share them between the two of you in different ways.

Q4

Solve the following Binairo puzzles:

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