More or fewer: comparing groups before comparing numbers

Long before a child writes 7 < 9, they need to know that a pile of 7 has fewer than a pile of 9 — and why. Comparing groups is that first step, and it is where "more" and "fewer" start to mean something.

Two ways children compare

Matching. Line the two groups up, one beside the other. The group with some left over has more. This works before a child can count far, and it is the idea behind subtraction: the leftovers are "how many more."

Counting. Count each group and compare the numbers. Faster, but only works once counting is solid.

Kindergartners are expected to do both (K.CC.6), with groups up to ten.

Lifehack: set the table "wrong" — four plates and three cups. Ask if there are enough cups. Matching plates to cups shows the missing one at a glance.

The trap: big things look like more

Young children often think a spread-out row has more than a bunched-up row with the same number. It is a famous finding about how children think, and it fades with counting practice. Mixing sizes on purpose helps: three big balloons are fewer than five small ones.

On paper

Our More or Fewer? sheets scatter one picture in two colors over the page, in different-sized groups and different sizes so bigness is not a clue. Tick the color with more; from the middle level, also write how many more. The hard level adds a third color to ignore.

From groups to numbers

Once groups are easy, move to numbers: Comparing Numbers uses >, < and =, and our post on greater than and less than tricks explains why the alligator works — and when it stops working.