Match them up
Which group has more? You can tell without counting either one. Pair them up: take one thing from each group and put them together, then do it again, and keep going. When one group runs out, the other still has things with no partner, so that group has more.
Take 5 cups and 3 saucers, and put one cup on each saucer. All 3 saucers get a cup, and 2 cups have no saucer. So there are more cups than saucers, and the 2 cups left without a partner are how many more.
Every square in the short row has a partner above it. The 2 squares with no partner show how many more the long row has.
More, fewer, and how many
One pairing answers both questions. The row of 5 has 2 more than the row of 3, and the row of 3 has 2 fewer than the row of 5. It is the same difference, seen from each side.
Do not judge by how long a row looks. Three saucers spread far apart can make a longer row than 5 cups packed close together, but spreading things out adds nothing. Matching one to one decides which group has more.
Worked example: Cups and Saucers Matched One to One
Question There are 5 cups and 3 saucers on a table. Dad puts one cup on each saucer. (a) Are there more cups or more saucers? (b) How many more?
1.Draw 5 counters in a row for the cups. Draw 3 counters in a row below for the saucers.
There are 5 counters in a row for the cups and 3 counters below for the saucers. 2.Join each saucer to one cup with a line. There are 3 pairs.
Join each saucer to one cup. There are 3 pairs. 3.(a) Some cups have no saucer, and every saucer has a cup. So there are more cups.
(a) Two cups have no saucer, and every saucer has a cup. There are more cups. 4.(b) Count the cups with no saucer: 1, 2. There are 2 more cups than saucers.
(b) Count the cups with no saucer: 1, 2. There are 2 more cups than saucers.
Answer: (a) There are more cups. (b) 2 more cups
Common mistakes
- Spreading the 3 saucers out so that their row looks as long as the row of cups. A longer row does not mean more things, so match them one to one.
- Saying there are 5 more cups in part (b). There are 5 cups altogether, and only the 2 cups with no saucer are the extra ones.
Worked example: Three Plates of Buns Put in Order
Question Ali has 4 buns on his plate. Mei has 2 buns on her plate. Sam has 7 buns on his plate. (a) Who has the fewest buns? (b) The plates are put in order from fewest to most. Whose plate is in the middle?
1.Draw a row of counters for each plate: 4 for Ali, 2 for Mei and 7 for Sam. All the rows start at the same line.
There is a row of counters for each plate: 4 for Ali, 2 for Mei and 7 for Sam. All the rows start at the same line. 2.(a) The row of 2 is the shortest row. Mei has the fewest buns.
(a) The row of 2 is the shortest row. Mei has the fewest buns. 3.Put the rows in order from fewest to most: 2, then 4, then 7.
The rows are in order from fewest to most: 2, then 4, then 7. 4.(b) The middle row has 4 counters. Ali's plate is in the middle.
(b) The middle row has 4 counters. Ali's plate is in the middle.
Answer: (a) Mei, with 2 buns; (b) Ali, with 4 buns. The order is 2, 4, 7.
Common mistakes
- Picking Ali for the fewest because his name comes first in the question. Look at the numbers: 2 is fewer than 4.
- Putting the plates in order from most to fewest, 7, 4, 2. The question asks for fewest to most, so start with 2.