Magic Bag Source:

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 435 = ?

Magic Bag - Answers

Let

Subtracting consecutive triangular numbers

Adding consecutive triangular numbers

Another clue about triangular numbers!

Note to Teacher There are two answers – the number of black balls is a triangular number and the number of white balls are the previous and next triangular numbers The number of black balls are alternate triangular numbers so students should get some answers the same Some students may spot the pattern of numbers from the lower three – but they still need to prove it!

Resources

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 45 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 66 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 91 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 120 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 153 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 190 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 231 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 276 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 325 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 378 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 435 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 496 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 561 = ? SIC_10

Magic Bag A magic bag contains some black and white balls, all of the same size, weight and shape. I put my hands in the bag and simultaneously and randomly pull out two balls. They are both the same colour and the magic bag tells me that the chance of this occurring was exactly 0.5. The bag contains a given number of black balls. Can you work out how many white ones there are? What valid combinations of black and white balls are possible? = 630 = ? SIC_10