Math // Measurement

Converting measurement units (age 9+)

Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
2 codes

Quick check

If the learner needs to convert 3.5 kg to grams, can they do it confidently — and also fill in a simple two-column table showing the same measurements in kg and g?

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.
  • Convert 3.5 km to 3,500 m
  • Complete a conversion table for cm and mm: (1,10), (2,20), (3,30)...
  • Express 2 kg 350 g as 2,350 g

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
  • Converting measurement unitsRequired

    Measurement // Ages 8 to 9

    Y4 unit conversion is prerequisite to systematic metric conversions with tables

  • Multiplying and dividingHelpful

    Multiplication & Division // Ages 9 to 10

    ×÷ by 10/100/1000 supports metric unit conversions

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Converting measurement units (age 9+)

Ages 9 to 10 // Method

Leads to

3 topics

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

Year 5 pupils (age 9–10) learn the relative sizes of units within one system (metric km/m/cm/mm, kg/g, l/ml; and time units hr/min/sec, which are not metric) and convert between metric units, expressing a measurement in a smaller unit and recording equivalents in conversion tables. Metric conversion is applied place value: converting to a SMALLER unit means multiplying (there are more of them); converting to a LARGER unit means dividing (there are fewer of them). The two persistent hazards are choosing the wrong operation and manipulating zeros/decimals mechanically ('add a zero') instead of moving the digits across a fixed decimal point. The core activity is a live place-value transformation where digits slide across a fixed point, supported by table-building, mixed-unit recomposition, and targeted practice that probes direction and zero errors. (Note: the digit-sliding by 10/100/1000 applies to the metric units; hr/min/sec relate by ×60 and are included only in the 'relative sizes' knowledge.)

Common misconceptions

  • Confuses when to multiply and when to divide (converts to a smaller unit by dividing, or vice versa).
  • 'Adds a zero' or manipulates zeros mechanically, which breaks with decimals (3.5 km → '350 m' or '3.50 m' instead of 3500 m).
  • Treats a mixed unit as concatenation (2 kg 35 g → '235 g'), a two-separate-numbers error.
  • Fills a conversion table by copying a pattern without understanding the ×10 relationship.

Useful representations

  • Place-value / Gattegno chart showing digits sliding across a fixed decimal point
  • Conversion tables (e.g. cm→mm: 1→10, 2→20, …)
  • Double number line linking two units
  • Bar showing a mixed unit (2 kg + 350 g) recomposed as one unit

Teaching practices

  • Anchor the multiply/divide decision in REASONING about unit size, not a rule: 'which unit is bigger? there are fewer of the bigger unit, so to reach it I divide' — the rule is exactly what pupils reverse (Oak National Academy).
  • Teach conversion as multiplying/dividing by 10, 100, 1000, and talk about the DIGITS moving (one/two/three places) while the decimal point stays fixed — never 'move the decimal point' or 'add a zero' (NCETM Spine 2.29).
  • Secure fluency with ×/÷ by 10/100/1000 BEFORE layering on conversion, to avoid overload.
  • Use a place-value chart / Gattegno chart so pupils SEE the digits shift and the value change (the 1 in 1.75 km becomes the 1 thousand in 1750 m).
  • Build conversion tables and read them as a set of equivalent multiplications; include mixed-unit forms (2 kg 350 g = 2350 g) and always add a reasonableness check (bigger or smaller number than we started with?).

Activities to try

  1. 1

    Slide the digits across a fixed decimal point

    Why it works: The number grows (or shrinks) because the DIGITS move a fixed number of places, not because zeros are 'added' — so 3.5 km can never become 3.50 m.

    1. Enter a measurement such as 3.5 km and choose the target unit (metres).
    2. Before computing, answer the prompt: 'Is a metre bigger or smaller than a kilometre — so will there be MORE metres or FEWER?' State whether this means multiply or divide.
    3. Watch (or physically move, using a place-value chart or Gattegno chart) every digit slide three places left while the decimal point stays nailed in place, so 3.5 becomes 3500, with place-holder zeros dropping in where needed.
    4. Repeat for a case that keeps the decimal visible, e.g. 1.75 km to m, naming where each digit lands (the 1 becomes 1 thousand, giving 1750 m).
    5. Do at least one divide case too, e.g. 4500 m to km, moving digits three places right to give 4.5 km.
  2. 2

    Build and check conversion tables

    Why it works: A conversion table is a repeated multiplication by the same factor, not a copied number pattern — understanding the factor lets you extend or correct any row.

    1. Complete a cm→mm table: 1→__, 2→__, 5→__, 10→__ and say what you multiply by for each row.
    2. Read the completed table aloud as a set of equivalent multiplications ('each centimetre is ten millimetres — I'm multiplying by 10').
    3. Check each row against the ×10 relationship and flag any row that breaks the pattern, explaining why it is wrong.
    4. Build a second table for a different pair of units (e.g. kg→g, ×1000) to see the same structure with a different multiplier.
  3. 3

    Recompose a mixed unit into one smaller unit

    Why it works: A mixed unit is recomposed by converting the larger part and ADDING, not by writing the two numbers side by side — so 2 kg 35 g = 2035 g, not 235 g.

    1. Express 2 kg 350 g as a number of grams, showing the step 2 kg = 2000 g, then 2000 + 350 = 2350 g.
    2. Test the tricky case 2 kg 35 g: decide whether it equals 235 g or 2035 g and justify using place value.
    3. Use a bar (2 kg + loose grams recomposed as one quantity) to make the missing hundreds place visible when the loose amount is small.
    4. State a check: the combined gram total must include the thousands from the kilograms.

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
4.MD.1
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/3.1a

Math // Measurement

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