Is 1 m 5 cm the same as 1.5 m? Decimal measures in grades 3 and 4
Why children write 1 m 5 cm as 1.5 m, which errors with measures in decimal notation are common in grades 3 and 4, and how teachers can respond.
In brief: Children often write 1 m 5 cm as 1.5 m because they understand the decimal point as a separator between two units and put the number of centimetres directly after it. The correct form is 1.05 m, because with metres the two digits after the decimal point give the centimetres. A place value chart for measures, measuring with a tape measure and translating in both directions all help. With Mazio Math, teachers put suitable content on quantities and measuring on the class board and get a flag when a widespread misconception shows up in the class.
This article is for teachers of grades 3 and 4. It describes typical errors with lengths, masses and amounts of money written as decimals, their causes, ideas for support, and questions you can use in lessons to find out how a child interprets the decimal point.
Typical errors with measures in decimal notation
| Error | Example | Possible cause |
|---|---|---|
| Centimetres straight after the decimal point | 1 m 5 cm becomes 1.5 m. The correct form is 1.05 m. | The decimal point separates “metres” and “centimetres”, and the number of places is overlooked. |
| Reversal when reading | 2.5 m is read as 2 m 5 cm. The correct reading is 2 m 50 cm. | The digit after the decimal point is taken as the number of centimetres. |
| Wrong number of places for mass | 1 kg 25 g becomes 1.25 kg. The correct form is 1.025 kg. | The conversion factor 1000 is treated like 100. |
| The longer number counts as larger | 1.15 m is taken to be longer than 1.5 m because 15 is greater than 5. | The digits after the decimal point are read as a whole number. |
| Decimal point with time | 1.5 h is interpreted as 1 h 50 min. The correct answer is 1 h 30 min. | The conversion factor 60 is overlooked. |
The page Maths in grades 3 and 4 (in German) also lists the first example as a typical misconception in quantities and measuring.
Why the error arises
The decimal point in measures is often introduced first as a separator between two units: euros before the point, cents after it. That is a proven starting point, as long as children also see that a fixed number of places follows the decimal point. Without this knowledge, “the decimal point separates metres and centimetres” turns into the rule “the number of centimetres goes after the decimal point”.
A support module from the German Centre for Mathematics Teacher Education (DZLM) on converting units of length, area and mass describes exactly this belief, “that different units are always separated by a decimal point”. The module names a further hurdle: the conversion factors differ. Between millimetres, centimetres, decimetres and metres the factor is 10, between metres and kilometres it is 1000, and for masses it is 1000 throughout. As a representation, the module uses a place value chart for measures that also includes the intermediate units. It was written for lower secondary school, but the hurdles begin in grades 3 and 4.
Support ideas with materials
Place value chart for measures. A chart with the columns m, dm and cm shows where the 5 in 1 m 5 cm belongs: 1 metre, 0 decimetres, 5 centimetres, so 1.05 m. The zero in the decimetre column is the crucial point. For masses, the chart needs the columns kg, 100 g, 10 g and g.
Measuring with a tape measure. The children find 1.05 m and 1.5 m on the tape measure and see that almost half a metre lies between them. They measure objects in the room and record the results in both notations.
Money as a bridge. The children make €1.05 with a one-euro coin and a 5-cent coin, and €1.50 with a one-euro coin and a 50-cent coin. Because money is familiar, the rule can be carried over to lengths.
Translating in both directions. Cards showing “1 m 5 cm”, “105 cm” and “1.05 m” are matched to one another. The children invent their own traps for their partner.
Checking by converting. 1.5 m is 150 cm, 1 m 5 cm is 105 cm. Converting to centimetres shows the difference at once.
Diagnostic questions
- “Write 1 m 5 cm as a decimal. How many centimetres is that altogether?”
- “What does the zero in 1.05 m mean?”
- “Is 1.5 m longer or shorter than 1.15 m? Show me on the tape measure.”
- “How would you say 2.5 m in metres and centimetres?”
If a child converts to centimetres confidently but writes the decimal incorrectly, the link between the two notations is missing. If the child cannot convert either, it is worth going back a step to the conversion factors and to place value.
How Mazio Math supports work on measures
Mazio Math is a learning platform for primary maths lessons. The content is organised by the five content areas of the German national education standards, including quantities and measuring, and for grades 3 and 4 there are units in all five content areas. Each unit builds up a topic step by step, from first discovery to confident mastery.
Finding content. The “Curriculum” page in the dashboard shows the maths curriculum of your German federal state, where it has been added. With the “Grade 3/4” filter and a focus from the area of measures expanded, you see under “Matching content in Mazio Math” which material fits. On the shelf under “Teaching”, you can search by title, topic or competence. Tapping a card opens the detail view with the worksheet and teaching notes, where available.
A sequence for grade 4. The lesson begins with measuring in the classroom and a place value chart on the whiteboard. You then add a suitable item to the class board with the plus button. New content appears at the top as compulsory. With a note you can add a sentence, such as “Convert to centimetres to check.” The row shows how many children have finished. If a child makes a mistake, the learning assistant Mazio helps directly in the task: with a question, with highlights in the picture and, if needed, with a given partial step. He does not give the solution.
Consolidating place value. Many decimal errors are place value errors. The Basiscamp practises in worlds such as “Understanding numbers to 1000” and “Understanding numbers to 1 million” and remembers for each child which task types they have already mastered. More on this topic is on the page Place value in primary school (in German).
Misconceptions in the class. Once a week, Mazio Math checks whether a widespread misconception shows up in the class’s wrong answers. The support card explains the error in thinking with an example, lists steps for the class under “In the classroom” and suggests suitable content for the class board. You decide whether to act on the flag.
A teacher from the scientific study writes: “With Mazio Math I can quickly bring topics that often get pushed aside in lessons (geometry, measures) into my teaching.”
Next step. Register for free to create an account and look at the shelf and the curriculum view. The page Routines from the classroom shows how to respond to a misconception in the class. Using Mazio Math with a class is currently available to schools in Germany. If your school is in another country, registration records your interest.
Frequently asked questions
Why is 1 m 5 cm equal to 1.05 m?
A metre has 100 centimetres. So with metres there are always two places after the decimal point for the centimetres: first the decimetres, then the centimetres. 5 cm is 0 decimetres and 5 centimetres, so the result is 1.05 m.
Should the decimal point in measures be introduced as a separator?
As a starting point this is common and helpful, especially with money. It is important that children see early on how many places follow the decimal point and why. A place value chart for measures makes this visible.
How does Mazio Math help children practise measures in decimal notation?
Mazio Math is a learning platform for primary maths lessons. For grades 3 and 4 there are units in the content area quantities and measuring, which teachers put on the class board with a tap. If a child makes a mistake, the learning assistant Mazio helps directly in the task. The Basiscamp practises place value, on which decimal notation is built.
Why is time not written as a decimal like metres?
Because an hour has 60 minutes rather than 100. A decimal such as 1.5 h means one and a half hours, so 1 h 30 min. In grades 3 and 4, time spans are therefore usually written in hours and minutes.