To answer a question about a collection, first sort it: put things that are the same in one group, using one rule such as colour, shape or kind. Then count each group, touching each object once. Last, compare the counts. The group with the biggest count has the most and the smallest count has the fewest. Big pictures do not mean more, so always count. To find how many more, line the two groups up one to one and count the extras with no partner.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- sort
- put things that are the same in one group
- most
- the group with the biggest count
- fewest
- the group with the smallest count
- how many more
- how many extra one group has after matching it with another
Worked examples
Buttons sorted into rows: red 4, blue 6, yellow 3. How many red buttons are there?
- 1.Find the Red row.
- 2.Touch each red button once as you count: 1, 2, 3, 4.
= 4
Mixed-up fruit: 3 big bananas, 5 apples, 2 pears and 4 oranges. Which kind of fruit is there the most of?
- 1.Sort the fruit into groups by kind.
- 2.Count each group: bananas 3, apples 5, pears 2, oranges 4.
- 3.The bananas are drawn big, but big pictures do not mean more.
- 4.5 is the biggest count, so apples are the most.
= Apples
Fruit sorted into rows: apples 7, pears 4. How many more apples than pears are there?
- 1.Count each row: apples 7, pears 4.
- 2.Line the rows up: 4 apples match the 4 pears, and 3 apples have no partner.
- 3.7 − 4 = 3.
= 3
Blocks: 3 red squares, 2 blue squares, 1 yellow square and 4 red circles. Sort by shape. How many squares are there?
- 1.Sort by shape only: a square is a square whatever its colour.
- 2.Count every square, red, blue and yellow: 3 + 2 + 1.
- 3.There are 6 squares. The red circles stay out of the group.
= 6
For parents
Method: Sort, count, compare
What to say: What rule are we sorting by? How many are in this group? Which group has the most, and how do you know?
Common mistakes:
- Counts every object in the picture instead of only the group the question asks about.
- Counts the wrong group, such as the row next to the one asked about or a different kind in the mix.
- Misses one object in the group while counting, so the count is one too small.
- Counts one object twice, so the count is one too big.
- Answers "how many more" with the count of the bigger group instead of the difference.
- Answers "how many more" with the count of the smaller group.
- Adds the two groups together when asked how many more one has than the other.
- Sorts by both attributes at once, so counts only the asked-for objects that also look alike (e.g. only the red squares).
- Mixes up "most" and "fewest", choosing the group at the wrong end.
- Judges which group has the most (or fewest) by how big the pictures are or how much space they take, not by counting.