Transfer and difference

In an earlier lesson, the extra part of the longer bar was the difference. Today, we will see why giving shells changes the difference by twice as many. Mei has 30 shells and Kavin has 18 shells. How many shells must Mei give Kavin so they have equal numbers of shells? Mei has 30 shells. Kavin has 18 shells. The question asks how many shells Mei must give Kavin. Mei has more. This extra part of her bar is the difference. 30 minus 18 is 12. The difference is 12 shells. Mei gives some shells away, so her bar gets shorter. Kavin gets those same shells, so his bar gets longer. So the gap closes from both ends. The 12 is shared into 2 equal parts. 12 divided by 2 is 6. So Mei must give Kavin 6 shells. Check: Mei gives 6 shells; 30 minus 6 is 24, and 18 plus 6 is 24, so both have 24.

Siti has 14 more shells than Bala. Siti gives Bala 5 shells. How many more shells does Siti have than Bala now? Try it first. Pause if you like. Bala's number of shells is not given. Siti has 14 more shells than Bala. Siti has 14 more shells. Siti gives Bala 5 shells, so her bar gets shorter. Bala gets those same 5 shells, so his bar gets longer. How many more shells does Siti have now? Look at the gap that is left. Siti has 5 fewer, and Bala has 5 more. So the difference gets smaller by 2 times 5. 2 times 5 is 10. 14 minus 10 is 4. So Siti has 4 more shells than Bala now. Check: Siti gives Bala 5 shells; the difference is 14 minus 5 minus 5, which is 4.

Ravi has 34 shells. Wei Jie has 20 shells. Ravi gives Wei Jie some shells. Then Ravi has 4 more shells than Wei Jie. How many shells does Ravi give Wei Jie? Try it first. Pause if you like. Ravi has 34 shells. Wei Jie has 20 shells. Find the difference at first. 34 minus 20 is 14. The difference at first is 14 shells. Ravi gives some shells away, so his bar gets shorter. Wei Jie gets those same shells, so his bar gets longer. Ravi has 4 more shells now. The two dotted parts show how much smaller the difference gets. 14 minus 4 is 10. Both people change by the same number of shells. 10 divided by 2 is 5. So Ravi gives Wei Jie 5 shells. Check: Ravi gives 5 shells; 34 minus 5 is 29, and 20 plus 5 is 25, so 29 minus 25 is 4. When one person gives shells to the other, the difference changes by twice as many.