Mixed-ability grade 1: differentiating maths in the first months
How teachers can differentiate maths in a mixed-ability grade 1 class when children start school with very different understandings of number.
In short: In a mixed-ability grade 1 class, it helps to look closely in the first weeks at what each child already knows about numbers and then to work on shared topics with open tasks. Materials such as the twenty frame, two-colour counters and shake boxes carry the teaching, supplemented by short daily practice. Digital practice plays a minor role in the first months. Mazio Math also has units for grade 1.
Some children count to 10 on their first day at school, while others already calculate with numbers up to 100. This article shows how you can differentiate maths in the first months of grade 1 without splitting the class into many individual plans.
What the children bring with them
Before you differentiate, it is worth looking at the starting point. In its framework for basic arithmetic skills, the German project PIKAS describes number sense, among other things: understanding numbers as quantities and as positions, connecting representations such as the dot field and the number line, and using relationships between numbers. In the first weeks of grade 1, the differences show up mainly in these areas.
| Observation | What it can show | What can help in lessons |
|---|---|---|
| The child counts three counters one by one. | Quantities are not yet grasped at a glance. | Recognising quantities shown briefly in a five frame |
| The child counts confidently to 20 but does not know how many counters there are. | Counting and quantity are not yet connected. | Counting while pointing, stressing the last number as the quantity |
| For 7, the child immediately says “5 and 2”. | Numbers are already seen as parts and a whole. | Finding partitions systematically |
| The child works out 8 + 5 mentally. | Well advanced in the number range to 20 | Open tasks with a larger number range, explaining reasoning |
A conversation with materials in the first two to three weeks is often enough to see where each child stands. Keep brief notes of your observations, for example in a dated list.
Differentiating with shared tasks
In grade 1, many individual plans take a lot of energy and separate the children. An information paper from PIKAS on arithmetic teaching in the first years of school recommends a balance between learning in one’s own way and learning from one another. Learning activities should offer easy ways in and at the same time hold questions that lead further.
Examples of such tasks in the first months:
- Shake box: A tin contains two-colour counters. After shaking it, the child counts how many are red and how many are blue. Each child chooses their number, whether 5, 10 or 20, and looks for all the partitions.
- Numbers in the classroom: The children look for things in the room that there are three, five or ten of, and show them with counters.
- Quick look: You show a twenty frame with counters only briefly. The children say how many there were and how they saw them.
- Making patterns: The children continue a pattern of counters and invent their own.
Each of these tasks can be solved with small numbers and extended with larger ones. Afterwards, the children compare their methods in the circle.
A sequence for a grade 1 maths lesson
- Opening in the circle (10 minutes): Quick look with the twenty frame, three to four rounds.
- Working phase (20 minutes): Shake box with a number the child chooses. You walk around and ask follow-up questions, for example: “Have you found them all? How do you know?”
- Sharing (10 minutes): Two children show their partitions. The class puts them in order, for example from 0 and 10 to 10 and 0.
- Close (5 minutes): Each child draws their favourite partition in their exercise book.
Children who are already well ahead get an extra question: “How many partitions does 20 have? Can you find a rule?” Children who are still counting work with 5 and the five frame.
When to look more closely
If a child goes on calculating by counting for months, even with small quantities, it is worth looking more closely. You will find guidance in the article on signs of difficulties with arithmetic in grades 1 and 2.
What Mazio Math offers for grade 1
Mazio Math is a learning platform for primary school maths lessons. The content is organised by the five content areas of the German national education standards and designed for the two-year bands of grades 1/2 and 3/4. There are units for grade 1 too. In the first months of grade 1, working with materials comes first.
If you would like to use Mazio Math later in the school year:
- First look at a unit the way a child sees it. Tapping a card on the shelf opens the details with the worksheet and teaching notes, where available. “Open & play” shows the unit from the children’s point of view. Nothing you do there counts as a result.
- For grade 2 there are units in all five content areas, such as “Calculating in the hundred field” or “The dot grid”. The Basiscamp practises in worlds such as “Numbers to 100”, with sections such as “Tens and ones” and “Bridging ten”. Check whether a piece of content fits what your class is currently learning.
- If it does, use the plus to put it on your class board. The children see it on their devices straight away.
Logging in for children who cannot read yet: Each child logs in with their own eight-character access code or their access card. “Print cards” creates an A4 sheet of access cards to cut out, each with a code, a QR code and an animal. The children can scan their card instead of typing in the code. You do not need to enter names.
Help with mistakes: If a child makes a mistake, 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. The children answer only by tapping one of the answers offered.
Next step: The page Maths in grades 1 and 2: topics, hurdles and content (in German) shows which content is available for grade 2. How two year groups practise together is described in the article Practising maths across grades 1 and 2. What matters in a maths app for grade 1 is covered in the article on logging in without reading, short practice phases and materials first. You can create a teacher account by registering for free and look through the content at your own pace. Using it with a class is currently available to schools in Germany. If your school is in another country, registration records your interest.
Frequently asked questions
Is Mazio Math available for grade 1?
Yes. There are units for grade 1 too. With “Open & play” you can check in advance which ones fit, seeing them the way a child sees them.
How do I find out where the children in grade 1 stand?
The most informative approach is a short conversation with materials in the first weeks. Ask the child to lay out, count and partition quantities, and ask how they went about it. Keep brief written notes of your observations.
Should children in grade 1 already practise on a tablet?
In the first months, working with materials comes first, because children build up their ideas of number through hands-on activity. Short digital exercises can be added later. You decide when that fits, based on where your class stands.