Math // Number Representation & Place Value

The multiples of 10

Understand that the multiples of 10 (10, 20, 30 … 90) represent one to nine tens and 0 ones

Ages
6 to 7
Type
Concept
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

Can the learner explain that 60 means 6 tens and no ones — and that this is why the ones column has a zero as a placeholder?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Explain that 30 means 3 tens and 0 ones
  • Represent 50 using 5 tens rods and no unit cubes
  • Match decade numbers to their tens representation

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • A Ten Is Ten OnesRequired

    Number Representation & Place Value // Ages 6 to 7

    Understanding decade numbers as 'some tens and 0 ones' requires the concept of a ten

  • Counting in 2sHelpful

    Counting & Cardinality // Ages 5 to 7

    Skip counting in tens supports recognising decade numbers

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The multiples of 10

Ages 6 to 7 // Concept

Leads to

1 topic
  • Subtracting multiples of 10Required

    Addition & Subtraction // Ages 6 to 7

    Subtracting multiples of 10 requires understanding decade numbers as tens

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 6-7 (Y2), help children understand that the multiples of 10 (10, 20, 30 … 90) each represent a whole number of tens with zero ones — e.g. 30 is 3 tens and 0 ones. The key insight is that the 0 in a decade is an active place-holder marking the empty ones column, not 'nothing', and that decades are simply the 'whole tens, no ones' case of ordinary two-digit place value. Build quantities with tens rods, anchor to skip-counting in tens, and contrast a decade with a nearby non-decade so the 0 earns its meaning.

Common misconceptions

  • Treating the 0 in a decade as meaningless ('nothing there') rather than as a place-holder marking zero ones.
  • Reading the tens digit as its face value — saying 30 is 'three' rather than 'three tens/thirty'.
  • Decade-word confusion — mixing thirteen with thirty, fifteen with fifty, because the '-teen' and '-ty' endings sound alike.
  • Believing decades are a separate kind of number unrelated to ordinary two-digit numbers, rather than the ones-is-zero case of tens-and-ones.
  • Miscounting the rods and losing track that each rod is worth ten, not one, when skip-counting.

Useful representations

  • Tens rods alone in the tens column with a visible 0 in the ones column
  • Bead string / number track marked in tens for skip-counting
  • 0-100 number line with decade stops highlighted
  • Tens|ones place-value chart showing 'n tens, 0 ones'
  • Gattegno/place-value chart row of decades (10, 20 … 90) linking each to n×10

Teaching practices

  • Build decades with tens rods ONLY and write a 0 in the ones column so the child sees the ones place is filled by zero, not absent — this is the seed of the place-holder idea.
  • Anchor to skip-counting in tens on a bead string or number track so '3 tens' and 'thirty' and the third stop line up as the same thing.
  • Contrast a decade with an adjacent non-decade (40 vs 43) so the 0 earns its meaning as 'no ones', not 'nothing'.
  • Name the decade words carefully (thirty, forty, fifty) and connect the '-ty' to 'tens', flagging the thirteen/thirty and fifteen/fifty confusions.
  • Use the tens|ones chart to show that reading only the tens column gives the decade name — reinforcing column-based reading of two-digit numbers.

Activities to try

  1. 1

    Building decades with tens rods and a visible zero

    Why it works: A decade is a whole number of tens with the ones column filled by zero; the 0 is a place-holder that keeps the tens digit in the tens place and marks that there are no ones. Decades are not a separate kind of number — they are the ones-is-zero case of tens-and-ones.

    1. Set up a tens|ones chart (drawn or physical) with two columns.
    2. Add tens rods one at a time into the tens column, placing no unit cubes; after each rod, say the count aloud: 'ten, twenty, thirty …' and write the numeral (10, 20, 30).
    3. Each time, write a 0 in the ones column so the empty ones place is seen, not left blank.
    4. Build 30 with three rods and say '30 is 3 tens and 0 ones'; build 50 with five rods and say '50 is 5 tens and 0 ones'.
    5. Rebuild 30 with three rods, then add a single loose ones cube and read what you have: 30 becomes 31. Describe what the 0 was doing before you added the cube.
  2. 2

    Decade reference chart — tap, reveal, and lift the flap

    Why it works: Each decade numeral maps to a count of tens, a decade name (ten, or a '-ty' word from twenty to ninety), and a zero in the ones column; the tens digit tells you which decade it is.

    1. Work from a chart of the nine decades (10, 20 … 90).
    2. For a chosen decade (e.g. 30), reveal its three tens rods, the words '3 tens, 0 ones', and the spoken name 'thirty'.
    3. Use a 'where did the ones go?' prompt (e.g. a lift-the-flap or cover) to answer: there are zero ones, and the 0 marks that.
    4. Read across several decades to notice that reading only the tens column gives the decade name.
  3. 3

    Consolidation: sequence, match, and justify the zero

    Why it works: Children can recognise and justify decades across different representations, and can avoid confusing '-teen' words with '-ty' words.

    1. Put the decade numerals in order smallest to largest (10, 20 … 90).
    2. Match each decade numeral to a picture of the correct number of tens rods.
    3. Fill in blanks such as '30 = __ tens' and '50 = 5 tens and __ ones'.
    4. Choose and explain the meaning of the 0 in a decade (zero ones / place-holder), not 'nothing'.
    5. Distinguish sound-alike pairs: thirteen vs thirty, fifteen vs fifty — say which is 'teen' (ten and some) and which is 'ty' (whole tens).

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.NBT.2.c

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