Strengthening basic maths skills: planning short daily practice
Which basic maths skills primary school children need, and how teachers can secure them in lessons through short, regular daily practice.
In short: The basic maths skills of primary school include number sense, place value understanding and understanding of operations, fast mental arithmetic, and mental, informal written and formal written calculation. They are secured through understanding with concrete materials and through short, regular practice, for example ten minutes a day. In Mazio Math, the Basiscamp practises these skills step by step, and a Knobelbox set with the “Daily starter” template works well as a start to the day.
This article is for teachers and school leaders. It explains what basic maths skills include and shows what daily practice in lessons can look like.
What basic maths skills include
In Germany, the Standing Conference of the Ministers of Education (KMK) reported on the IQB Education Trend 2021 that the proportion of grade 4 pupils who fall short of the minimum standards had risen, in some cases considerably. Since then, the basics have received more attention. The German project PIKAS has published a framework for basic arithmetic skills. It names six areas:
| Area | What children should be able to do | Example grade 1/2 | Example grade 3/4 |
|---|---|---|---|
| Number sense | Understand numbers as quantity and position, connect representations | Show 17 in a twenty frame and on a number line | Place 750 on a number line to 1,000 |
| Place value | Bundle and unbundle, connect how numbers are said and written | Build 23 with tens rods | Write 3 H 14 T 2 O as a number |
| Understanding operations | Basic mental models of the operations, use relationships between tasks | Lay out 3 × 4 as three groups of four | Match a real-life situation to a division problem |
| Fast mental arithmetic | Use derivation strategies, recall basic facts | 6 + 7 via 6 + 6 + 1 | 7 × 8 via 5 × 8 + 2 × 8 |
| Calculating with numbers | Mental and informal written calculation | 45 + 30 in your head | 348 + 215 step by step |
| Calculating with digits | Use formal written methods with understanding | from grade 3 onwards | Column subtraction with exchanging |
The framework draws on a 2022 report by the KMK’s Standing Scientific Commission. According to this report, basic skills are crucial for further learning in all subjects.
Understanding before automating
Fast mental arithmetic is based on understanding. A child who has only memorised the times tables has no way of reconstructing a forgotten fact. That is why understanding with materials and pictures comes first, then deriving from core facts, and only then automating. The framework explicitly names derivation strategies for this: difficult tasks are derived from easy ones.
Planning daily practice
Short, regular practice can achieve more than one long practice lesson a week. A plan for ten minutes a day:
| Day | Content | Format |
|---|---|---|
| Monday | Flash calculation: recognising numbers quickly | In a circle, with dot arrays |
| Tuesday | Core times-table facts and deriving | Partner practice with cards |
| Wednesday | Mental arithmetic in the current number range | On the tablet or in exercise books |
| Thursday | Place value: building, writing and saying numbers | With materials |
| Friday | Review: What can I do faster now? | Short discussion, self-assessment |
Three tips: Keep the practice short and fixed in the timetable. Vary the representations so that understanding is not lost. And watch where the class gets stuck, so that you can plan the next week accordingly.
How Mazio Math helps
The Basiscamp builds calculation skills step by step, from number sense and place value through mental arithmetic and times tables to informal written and formal written methods. For grade 2 it practises in the worlds “Numbers to 100”, “Addition and subtraction to 100” and “Multiplication and division”, with sections such as “Tens and ones”, “Bridging ten” and “Equal groups”. For grades 3 and 4 there are worlds such as “Understanding numbers to 1,000” and “Calculating to 1 million”, and the formal written methods have their own sections. The Basiscamp remembers for each child which task types they have already mastered. An exercise only counts as completed when several tasks in a row are solved at the first attempt and without help. Anything that has not been practised for a while comes up again after some time.
The daily start with a Knobelbox set:
- Under “Teaching”, choose the class and tap “Knobelbox” on the shelf.
- The “Daily starter” template fills a set with 5 tasks, and the “Skill focus” template fills one from a single area. With the difficulty “Adaptive”, the set adapts to each child.
- “Save only” stores the set under “Your sets”, and “Highlight set” puts it straight on the class board.
- The row shows how many children have finished, for example “12/24”.
A practice phase in the Basiscamp: The plus on the card of a sub-world puts the whole sub-world on the board. Under “Results” you see for each area how many tasks were correct at the first attempt. “Back on the board” suggests the sub-worlds that are not yet secure.
Misconceptions in the class: Once a week, Mazio Math checks whether a misconception is showing up in the class, for example “The carry is forgotten when bridging ten”. The support card explains the error with an example, names steps for teaching and suggests suitable content for the board. You decide whether to take up the flag.
Example of a week in grade 3: From Monday to Thursday, a “Daily starter” Knobelbox set is on the board each day, with the difficulty “Adaptive”. On Tuesday, a Basiscamp sub-world on the times tables is added. On Friday you check under “Results” which areas were correct at the first attempt and use “Back on the board” to follow up in the next week. In the Collection you will also find lesson ideas from 10 minutes.
Next step: There are pages on individual topics such as bridging ten (in German) and the times tables (in German). Mazio Math in the classroom shows routines such as the daily start with a Knobelbox set. You can create a teacher account under register for free. 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
What are basic maths skills in primary school?
They are the foundations on which everything else builds: number sense, place value understanding, understanding of operations, fast mental arithmetic, and mental, informal written and formal written calculation. The PIKAS framework describes them with examples.
How long should children practise mental arithmetic each day?
Five to ten minutes a day is a common range, provided the practice takes place regularly. More important than the duration is that the children use derivation strategies and that the tasks match their level.
Can my class practise mental arithmetic briefly every day with Mazio Math?
Yes. The Basiscamp practises mental arithmetic and times tables in short exercises, and with the plus you put a sub-world on the board. A Knobelbox set with the “Daily starter” template (5 puzzle tasks) also works well as a short start to the day. With “Adaptive”, the difficulty adapts to each child.