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Counting and number sense

Number sense is the difference between knowing that 47 comes after 46 and knowing where 47 sits — that it is nearly fifty, that ten more is fifty-seven, that it is four tens and seven ones. The counting comes first, but the sense is what everything later is built on.

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Ten more, without counting

What is 10 more than 47?

  1. 47 is four tens and seven ones.
  2. Ten more adds one to the tens and changes nothing else.
  3. Four tens becomes five tens; the seven ones stay.
  4. The answer is 57.

Worth knowing. Counting on ten fingers from 47 also gets there, and it is worth noticing out loud that it is slower. The point of this question is to stop counting.

Counting back over a ten

What is 5 less than 32?

  1. Count back two to reach 30, which is the tricky part done first.
  2. Three left to go.
  3. Three back from 30 is 27.
  4. The answer is 27.

Worth knowing. Splitting the jump at the ten is the same move as bridging in addition. A child who does it here will recognise it later, which is why it is worth naming.

Where it usually goes wrong

  • Counting on in ones when the step is ten, which works and takes ten times as long.
  • Changing the ones digit as well when adding ten, so 47 and 10 becomes 58.
  • Losing the count over a ten, so 5 less than 32 comes out as 28.

The Professor adds ten by moving one finger up the tens column and leaving the ones alone. It is not cheating. It is the whole idea.

Practise it

All level paths

Questions teachers and parents ask

Why practise "ten more" separately from adding ten?

Because Common Core asks for it mentally, without counting (1.NBT.C.5), and that is a different skill from running the column algorithm. A child who can answer it as a fact — the tens digit goes up, the ones stay — has understood place value. A child who lines up 47 and 10 and adds has only understood addition.

When should counting on replace counting from one?

As soon as it will. Counting from one to add 3 to 47 is fifty counts instead of three, and the habit gets in the way for years. Kindergarten already asks for counting forward from a given number (K.CC.A.2).

What is skip counting for?

It is multiplication before multiplication has a name. A child who can count by fours has the four times table in a form they can use, and the step from "4, 8, 12, 16" to "4 x 4 is 16" is a short one.

Where this shows up

Standards

  • K.CC · Counting and cardinality
  • K.NBT · Number and operations in base ten
  • 1.NBT · Number and operations in base ten
  • 2.NBT · Number and operations in base ten

Formats