What is grade 1 “thinking math”? Should your child learn it, common problem types and how to teach it at home
Grade 1 “thinking math” (what Vietnamese parents call “toan tu duy”) is the phrase parents search for most when their child starts primary school – yet every center uses the name for something different. This article explains what grade 1 thinking math really is, how it differs from school math, the 6 common problem types (with examples), whether your child should learn it, and how parents can teach it at home in 15 minutes a day with free worksheets.
Grade 1 thinking math is a way of learning math that focuses on understanding and thinking – recognizing quantities, splitting and combining numbers, finding patterns, comparing, reasoning from pictures and situations – rather than only getting sums right by following a model. It supports school math; it does not replace it. Start once your child is comfortable counting and recognizing numbers, for 10–15 minutes a day, through games and worksheets at the right level. The “mental math and place value” part of thinking math is what the soroban does best; the logic, reasoning and geometry parts need other problems and games.
What is grade 1 thinking math? How is it different from school math?
In Vietnam, “thinking math” is not one fixed program but a common name for many ways of teaching math outside the textbook: Singapore-style logic math, soroban math, Finger Math, franchised abacus programs, Kumon math… What they share is a focus on how the child thinks: why 7 + 5 = 12, which number comes next in 2, 4, 6, which shape is different from the others.
| Grade 1 math at school | Grade 1 thinking math | |
|---|---|---|
| Goal | Standard knowledge: numbers to 100, addition and subtraction without carrying, shapes, measurement, telling the time | Understanding what numbers really are, ways of thinking, the habit of working things out |
| Problem types | Following the model in the textbook, skill practice | Missing numbers, comparing, patterns, reasoning, putting shapes together, mental math |
| How children learn | The teacher explains – the whole class works | Games, hands-on materials (beads, cards, the abacus), questions and discussion, open problems |
| Assessment | Right/wrong, marks | How the child works it out, progress compared with themselves |
The two are not opposites. Vietnam’s 2018 general education curriculum also stresses “mathematical thinking and reasoning” from grade 1. Thinking math is simply a more thorough way of doing that, with time and materials that a class of 40 pupils rarely has.
6 common types of grade 1 thinking math problems (with examples)
1. Recognizing quantities and how numbers are made
Example: look at 7 dots arranged in a row of 5 and a row of 2 and say “seven” straight away without counting; “7 is 5 and how many?”; “How many tens and how many ones make 12?”. This is the foundation for all the other types. On the soroban each number has exactly one shape (7 is one 5-bead and two 1-beads), so children who learn soroban become very secure at this type – see the pictures of the numbers 0–9 on the page What is a soroban?.
2. Missing numbers
Example: 3 + ☐ = 7; ☐ − 2 = 5; 6 = 4 + ☐. This type teaches children to see a sum as a relationship (“3 plus what makes 7?”) instead of an instruction to carry out. It is also a stepping stone to subtraction: 7 − 3 is exactly the question “3 plus what makes 7?”.
3. Comparing and writing >, <, =
Example: 7 + 2 ○ 10; 2 + 6 ○ 3 + 5; 15 ○ 9 + 6. The child has to work out both sides and then compare – two steps in one problem. A common mistake: comparing straight away using the first number they see.
4. Finding patterns
Example: 2, 4, 6, __, __; 20, 18, 16, __; circle – square – circle – square – __. “Spot the pattern” problems are the closest thing to “thinking” and also the type children enjoy most once they can do them.
5. Reasoning and word problems
Example: “An has 5 sweets and gives Binh 2. How many does An have left?”; “There are 3 children and each has 2 cakes. How many cakes are there?” (counting in twos); “Minh is taller than Lan, and Lan is taller than Ha. Who is the shortest?”. The child has to read (or listen), picture the situation and only then choose the operation.
6. Shapes and space
Example: putting two triangles together to make a square; counting the triangles inside a large figure; finding the shape that is different from the others; imagining a shape seen from above. This type trains spatial imagination – the same ability children use when they picture an abacus in their head for mental math.
Besides these 6 types, almost every grade 1 thinking math program includes mental math (addition and subtraction within 10, 20, then 100), because slow calculation holds a child back in every other type. We wrote a separate article, How to teach a grade 1 child fast mental math, for this part.
Should your child learn grade 1 thinking math?
Yes, if three conditions are met – and no, if any one of them is missing:
- Your child is already comfortable counting and recognizing numbers to 20. Thinking math is not a way of “getting ahead of the curriculum”; it needs a foundation in counting. If your child does not have that yet, play counting and number games for a few more weeks.
- A reasonable amount of time: 10–15 minutes a day, or 1 class a week. A 6-year-old is at school all day; adding 2 hours of “thinking math” in the evening will make a child hate math faster than anything else.
- Problems at the right level, 80% correct. This is the standard we use at Kodomo Soroban Center for every test: 80% correct within the set time means moving on to the next step. Easier than that is boring; harder than that is frightening.
Benefits you can see after 2–3 months: your child counts on their fingers less, can explain how they worked something out, enjoys setting “puzzles” for their parents, and school math becomes easy. What thinking math cannot do: turn a child into a “prodigy” after one course, or replace reading, writing and physical activity. If you are still deciding between methods, the article Soroban or Finger Math? compares 4 popular approaches.
Where to learn grade 1 thinking math: at home, online or in a class?
| At home with parents | Online (apps, videos) | In a class | |
|---|---|---|---|
| Suits you when | Parents have 15 minutes a day and patience; the child is happy to sit with them | Extra practice after understanding; the child is self-motivated | You need someone to teach the right technique (especially mental math and soroban), and the child needs classmates and the rhythm of a class |
| Strengths | Cheap, flexible, brings you closer | Lots of problems, instant feedback | The teacher spots mistakes; study habits; regularity |
| Weaknesses | Parents lose patience easily; hard to see where the child goes wrong | Screens; the child “taps to get it over with” | Travel time; you need to choose the class carefully |
The best combination we see in our students’ families: 1 class a week + 10 minutes of worksheets at home every day, with online used only for mental math practice (such as our Flash Anzan tool). When choosing a class, ask: how many children are in the class, which curriculum it follows, what the children do with their hands, and what parents receive to use at home. The article Is learning soroban good for children? has a list of 6 questions to take with you to a trial lesson.
How to teach grade 1 thinking math at home: 15 minutes a day
- 3 minutes: warm up with quantities.
Hold up fingers, dot cards or beans laid out in rows of 5 – your child says the number straight away. Then “7 is 5 and how many?”, “How many tens and ones make 12?”.
- 7 minutes: one problem type, one week.
This week missing numbers, next week comparing, the week after patterns. Each day 8–10 problems on a worksheet, with gentle timing. Repeating one type for 5 days is how a 6-year-old moves from “knowing” to “doing it without thinking”.
- 3 minutes: one open “puzzle”.
“How many ways can you make 10 from two numbers?”, “How can you arrange 6 sticks to make 2 triangles?”. There is no single answer – let your child talk while you listen.
- 2 minutes: the child marks their own work and records it.
Use the answer page of the worksheet. Your child ticks right and wrong and writes down the time. Seeing their own progress is the biggest motivation at this age.
Where does the soroban fit in “grade 1 thinking math”?
We are a soroban center, so let us be clear about the boundaries. The Japanese soroban does three things in grade 1 thinking math very well: how numbers are made and place value (each rod is one place, each bead stands for a number), splitting and combining with 5 and 10 (the 5-friend rule and the 10-friend rule), and mental math (the abacus in the head). The soroban also trains concentration and the habit of sitting down to study – which every problem type needs.
The soroban does not teach reasoning in word problems, geometry or shape patterns. That is why every lesson in our classes always includes “grid calculation” and number games alongside the abacus, and we recommend that parents also use thinking math worksheets (types 2–6) at home. See the level pathway to find out what your child learns in each module.
Grade 1 thinking math worksheets (PDF with answers)
The free worksheets that go with this article are on the Free worksheets page: worksheet 19 (missing numbers), 20 (comparing with > < =), 21 (number patterns), 22 (100-square grid calculation – subtraction), plus 6 mental math worksheets within 10 – 20 – 100 (13–18). Each worksheet is 2 A4 pages: problems and answers.
Frequently asked questions
What is grade 1 thinking math?
It is a way of learning math that focuses on understanding and thinking: recognizing quantities, splitting and combining numbers, filling in missing numbers, comparing, finding patterns, and reasoning from situations and pictures. Thinking math supports school math; it does not replace it.
How is thinking math different from ordinary math?
School math focuses on standard knowledge and skills that follow a model; thinking math focuses on how the child thinks and works things out, through games, hands-on materials and open problems. Each needs the other: understanding the basics helps children do their schoolwork faster and more securely.
At what age should children start thinking math?
Once your child counts confidently and recognizes numbers to 20 – usually at 5–6 years old. Before that, counting and number games are enough. For soroban, Kodomo Soroban Center accepts children from 5 years old.
Is grade 1 thinking math good for children, and can it do any harm?
It is good when the level is right (about 80% correct), the time is reasonable (10–15 minutes a day or 1 class a week) and there are games. It does harm when children are pushed to do too much, the problems are too hard, or it is only exam drilling – the child will become afraid of math.
Where can I find grade 1 thinking math worksheets?
The Free worksheets page of Kodomo Soroban Center has 10 worksheets for grades 1–2 (mental math within 10, 20 and 100; missing numbers; comparing; patterns; grid calculation), each with answers, to print at home.
Try a free soroban lesson
Classes of 3–5 children at Vinhomes Gardenia (Hanoi), 70 minutes each, taught exactly as in Japan. Phone · Zalo 096.802.8484.
Written by the teaching team of Kodomo Soroban Center, following the method and textbooks of Kodomo School (Japan, teaching soroban since 1976). The center is licensed by the Hanoi Department of Education and Training, and our project is a 2026 EDU-Port Nippon supported project of Japan’s Ministry of Education (MEXT).
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