Sum and difference

In the last lesson, we drew bars of equal units and found one unit. Then we used one unit to answer the question. Today, we will set the difference aside, so the two bars make equal units. Mei and Kavin collected 24 shells altogether. Mei collected 6 more shells than Kavin. How many shells did Mei collect? Mei collected 6 more shells than Kavin. So we draw Kavin's bar first, as 1 unit. Mei's bar is as long as Kavin's, and 6 more. The 6 more shells are only in Mei's bar. Together, they collected 24 shells. The question asks for Mei's shells. Let us set the 6 more shells aside. We will not count them for now. Now Mei's bar and Kavin's bar are equal. They make 2 units. Without the 6, the 2 units are 24 minus 6. 24 minus 6 is 18. To find 1 unit, we share 18 equally between the 2 units. 18 divided by 2 is 9. So each unit is 9 shells. Mei has 1 unit and the 6 more shells. 9 plus 6 is 15. So Mei collected 15 shells.

Nisha and Jun Wei have 21 shells altogether. Nisha has 5 more shells than Jun Wei. How many shells does Jun Wei have? Try it first. Pause if you like. Nisha has 5 more shells than Jun Wei, so Jun Wei's bar is 1 unit. Nisha's bar is as long as Jun Wei's, and 5 more. The 5 more shells are only in Nisha's bar. Together, they have 21 shells. The question asks for Jun Wei's shells. Set the 5 more shells aside, and 2 equal units are left. 21 minus 5 is 16. Jun Wei has just 1 unit. 16 divided by 2 is 8. So Jun Wei has 8 shells.

Farid and Ling have 58 shells altogether. Farid has 12 more shells than Ling. How many shells does Farid have? Try it first. Pause if you like. Farid has 12 more shells than Ling, so Ling's bar is 1 unit. Farid's bar is as long as Ling's, and 12 more. The 12 more shells are only in Farid's bar. Together, they have 58 shells. The question asks for Farid's shells. Set the 12 more shells aside, and 2 equal units are left. 58 minus 12 is 46. Half of 4 tens is 2 tens, and half of 6 ones is 3 ones. So 46 divided by 2 is 23. So each unit is 23 shells. Farid has 1 unit and the 12 more shells. 23 plus 12 is 35. So Farid has 35 shells. Set the difference aside, and the two bars make equal units. Find one unit, then add the difference back for the bigger bar.