Money in grade 2: when children count coins instead of adding values
Why children in grade 2 count coins instead of adding their values, which errors are common when calculating with money and how teachers can help.
In brief: Many children think five 10-cent coins are more money than one 1-euro coin, because they count the coins and do not add their values. Behind this lies a still uncertain distinction between number and value, which for some children persists into grade 2. Helpful approaches are exchanging, laying out amounts in different ways, bundling as with tens and ones, and estimating prices. With Mazio Math, teachers use the curriculum view to find suitable content on a topic such as money and receive flags when a widespread misconception shows up in the class.
This article is for teachers in grades 1 and 2. It shows typical errors in working with money, explains why they arise, and gives support ideas with play money as well as questions for the diagnostic conversation.
Typical errors when calculating with money
| Error | Example | Possible cause |
|---|---|---|
| Number instead of value | Five 10-cent coins are taken to be more than one 1-euro coin. | The child counts coins and does not add their values. |
| Number on the coin without the unit | €2 and 2c are treated the same; €1 and 5c make “6”. | Euros and cents are not distinguished. |
| Size of the coin as value | The 50-cent coin is taken to be worth more than the 1-euro coin because it is bigger. | The value is judged by appearance. |
| Exchanging as a gain | “When you change money, you get more.” | More coins are confused with more value. |
| Change counted up wrongly | An item costs 65c, it is paid for with €1, and the child says 45c. | An error in counting up to 100, often when bridging ten. |
The page Maths in grades 1 and 2 (in German) also names the example of the five 10-cent coins as a typical misconception. Together they make 50 cents, which is less than one euro.
Why children count coins
Money is a special kind of quantity. Lengths or weights can be measured; amounts of money cannot. The PIKAS material on understanding quantities in the area of money therefore describes exchanging amounts of money as a central component of understanding. Children with a sound sense of money can exchange amounts, represent them in different ways and distinguish between number and value in a collection of coins.
How hard this distinction is can be seen in individual interviews with children starting school, which the University of Potsdam published in its Potsdam studies on primary school research. At the start of school, most of the children interviewed could not reliably distinguish between number and value. By the end of grade 1 they managed this much better, but clear difficulties remained for a considerable share of the children. The children solved tasks with euros and cents together less well than tasks with only one unit.
In addition, the value of a coin cannot be read from its size. The 50-cent coin is bigger than the 1-euro coin, and the 5-cent coin is bigger than the 10-cent coin.
Support ideas with play money
Exchanging. The children swap a 1-euro coin for smaller coins and check that the amount stays the same. Then the other way round: many small coins become a few large ones.
Lay it another way. An amount, such as 50 cents, is laid out in several ways. Which way needs the fewest coins? Which needs the most? This separates number and value very clearly.
Bundling as in place value. Ten 10-cent coins make one euro, just as ten tens make one hundred. A table with the columns euros, 10 cents and 1 cent links money with place value.
Estimating prices. What costs about one euro, and what costs about ten euros? Reference points like these, such as a bread roll or an exercise book, give amounts a meaning.
Playing shop. The children pay at the play shop and work out the change. The change is laid out and counted up from the price, just as at a till.
Asking diagnostic questions
- Show five 10-cent coins and one 1-euro coin: “Who has more money? How did you find out?”
- “Lay out 50 cents. Can you lay out 50 cents another way too?”
- “What happens to the money when we change a coin?”
- “How much is that altogether?” with a mix of euro and cent coins. Watch whether the child counts the coins or adds the values.
If a child counts the coins, they above all need experience with exchanging and “Lay it another way”. If they add the values but make a calculation error, the error lies more in calculating with numbers up to 100.
How Mazio Math helps with the topic of quantities
Mazio Math is a learning platform for maths lessons in primary school. The content is organised by the five content areas of the German national education standards, including quantities and measuring, and designed for the two-year bands of grades 1/2 and 3/4. For grade 2 there are units in all five content areas.
Finding suitable content on money. For schools in Germany, the “Curriculum” page in the dashboard shows the maths curriculum of the school’s federal state, where it is available. Enter “money” in the search and set the filter to “Grades 1/2”. Under “Fits in Mazio Math” you can see which units, Basiscamp exercises and Knobelbox tasks match the focus; a tap opens the material in the lesson. The official document, which “To the document” opens, remains authoritative.
An example from grade 2. The children work in pairs for 20 minutes, laying out amounts with play money. Afterwards you use the plus to put suitable content on the class board. New content goes on the board as compulsory, and a note gives the children a sentence to take with them, such as “Count the values, not the coins”. The row shows you how many children have finished. A puzzle set can follow at the end: the “Competence focus” template fills it with tasks from one area, and with “Adaptive” the difficulty adapts to each child.
Consolidating calculation up to 100. Some money errors are calculation errors with numbers up to 100. The Basiscamp practises in the worlds “Numbers to 100” and “Addition and subtraction to 100”, with sections such as “Tens and ones” and “Bridging ten”. It keeps track of which types of task each child can already do confidently.
Flags on misconceptions. 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, names steps for teaching and suggests suitable content for the board. In the library you can look up common misconceptions, organised by content area. When a child makes a mistake while practising, the learning assistant Mazio helps directly in the task, with a question, with markings in the picture and, if needed, with a given partial step.
Next step. Create an account under register for free and look at the shelf and the curriculum view. Mazio Math is free for teachers. Using it with a class is currently available to schools in Germany: they can try Mazio Math with a class first and then request a quote for a licence. If your school is in another country, registration records your interest. How Mazio Math makes errors in thinking visible at class level is described in the article How Mazio Math evaluates the class’s errors in thinking.
Frequently asked questions
When do children learn to calculate with money in primary school?
Money usually features in grades 1 and 2, together with time and length. The exact distribution is set by the curriculum where you teach. When decimal notation for money is introduced differs between curricula.
A child counts the coins instead of the values. Is that a sign of dyscalculia?
Not on its own. Many children find the distinction between number and value difficult for a long time. If number sense and calculation up to 100 also remain uncertain over a longer period, it is worth taking a closer look, as described in the article on first signs of difficulties with maths in grades 1 and 2.
How do I link money with place value?
Ten 10-cent coins make one euro, just as ten tens make one hundred. A table with euros, 10 cents and 1 cent shows this bundling and prepares for decimal notation.