2nd Grade Math: What Should My Child Know? With Checklist

This article is part 2 of our series on where children stand in elementary school. Part 1 describes grade 1. Here you will find, for each topic in grade 2, what the curricula expect, a sample problem, a stumbling block and a sentence you can use to explain it to your child. At the end there is a checklist to go through. How it continues in grade 3 is in part 3: Third Grade Math.

What should my child know in math in grade 2? Who decides

There is no nationwide list of "what a second grader must know." The Kultusministerkonferenz (KMK, the standing conference of the state education ministers) describes the competencies that children "should have acquired by the end of grade 4" (in German). These educational standards are standard expectations: they state "what level of competence students should reach on average in a subject". How the path there is spread across the school years is set by the states (Länder) in their curricula.

We use the curricula of Bavaria (LehrplanPLUS) and Saxony (Lehrplan 2025) as examples. Both combine the goals for grades 1 and 2. The goals mentioned refer to grades 1 and 2 together and serve as a guide up to the end of this phase. In other states the breakdown may differ. The Deutscher Bildungsserver (in German) gives an overview of all states.

Grade 2 at a glance

The table is our own compilation from the two curricula. We made up the problems in the middle column ourselves; they do not come from a curriculum.

The Bavarian curriculum divides grades 1 and 2 into four learning areas: numbers and operations, space and shape, quantities and measuring, and data and chance. This article focuses on numbers, calculating and quantities.

Numbers to 100: ordering, decomposing, place value

The Bavarian curriculum describes how children find their way around the number range up to one hundred "through flexible counting (forward, backward, in steps)", and how they order and compare numbers, also on the number line and the hundred chart. This includes neighboring numbers, even and odd numbers, and decomposing, for example 32 = 30 + 2. Saxony also names bundling: children represent numbers with base-ten material and use the place value chart with hundreds, tens and ones.

Stumbling block: The North Rhine-Westphalia (NRW) guide to learning arithmetic lists a weak understanding of place value as a sign of difficulties: children need to understand "that the 3 in 35 means something different from the 3 in 307 or 43" (in German). While practicing, watch whether your child mixes up 34 and 43. With numbers like "vierunddreißig" (literally "four-and-thirty"), German speakers say the ones first but write the tens first, which can be confusing.

How to explain it: "The left digit tells you how many base-ten rods you have, the right one how many single cubes."

Adding and subtracting to 100, crossing a multiple of ten

Crossing a multiple of ten (Zehnerübergang) means: while calculating, you go past a full ten or below it, for example in 38 + 7 or 52 − 6. The Bavarian curriculum names as calculation strategies "calculating in steps, inverse problems, problems with the numbers switched, analogous problems, related problems using neighboring numbers", in the number range up to 20 and up to 100. As an example of calculating step by step, Saxony gives 7 + 9 = 7 + 3 + 6 and names missing-number problems like 11 − 7 = ___ and 7 + ___ = 11. According to Bavaria, the addition facts up to 20 should be applied "automatically and flexibly", and that is for grades 1 and 2 together.

Stumbling block: The NRW guide shows a case study of a child who calculates 81 − 34 like this: 80 − 30 = 50, then 50 − 4 = 46 and 46 − 1 = 45. Our interpretation: the 1 from the 81 is subtracted again at the end instead of being added back, and the correct answer would be 47. Try the question: "Did you leave out the 1 at the start? Where does it need to go back?" According to the guide, counting to calculate is normal in early phases. If it becomes fixed "well beyond the beginning of the 2nd school year", the guide treats it as a clear sign of special difficulties. In that case, talk to the teacher.

How to explain it: "First to the next ten, then the rest."

If your child's ways of calculating seem unfamiliar to you, our article on why children calculate differently today than their parents did explains what is behind the number line method and the like.

Times tables and division

For the times tables, the curricula focus on core problems from which the rest can be derived. Bavaria names the "times table facts with 1, 2, 5, 10 and the square facts", including their inverses (14 : 7 = 2 belongs with 2 · 7 = 14) and multiplication problems with 0. From these, a child can derive further problems, such as 9 · 8 as 10 · 8 − 1 · 8. Saxony lists the core problems of 2, 5 and 10, problems with the numbers switched and inverse problems, and deriving, such as 7 · 8 = 5 · 8 + 2 · 8. Children learn division as sharing out or grouping, and in Bavaria also with a remainder.

The states differ noticeably here. How much of the times tables is expected already in grade 2 can look different depending on the state and the textbook. The KMK standard sets the goal only for grade 4: children "master the basic mental arithmetic problems (including number decompositions, addition facts, times tables) from memory".

Stumbling block: The NRW guide gives the example of a child who solves 5 · 7 by counting in steps of seven (7, 14, 21, then 26, 31) and loses count along the way. Anyone who only recites or counts out multiplication problems easily loses the thread. Try having your child derive a multiplication problem from a known core problem.

How to explain it: "Dividing is multiplying backward: 14 : 2 asks what times 2 makes fourteen." Division with remainder is added in third grade: Third Grade Math: What Should My Child Know?.

Quantities: clock, money and lengths

For grades 1 and 2, the Bavarian curriculum says that children read times and determine simple time spans from start and end time, tell coins and bills apart, and determine and compare amounts of money in euros and cents. They measure lengths with a ruler and a tape measure in meters and centimeters. They also write amounts of money and lengths in mixed notation, such as 9 € 30 ct or 2 m 15 cm. For the time of day, Saxony names an accuracy of 5 minutes, and for time spans, problems where the start and end are full hours or fall within the same hour.

Stumbling block: With money, euros and cents can get mixed into one number, for example 2 € 50 ct wrongly read as 250 €. Watch whether your child knows which number belongs to which unit. With the clock, first ask: "Which hand shows the hours?"

How to explain it: "Euros and cents are like meters and centimeters: two units that you calculate separately."

Everyday life is good for practicing: read the time when getting up, add up the price of two things in the supermarket, measure the kids' room with a tape measure. These are our own suggestions, not curriculum requirements.

Checklist: I can already do this (grade 2)

The list is our own compilation from the curricula of Bavaria and Saxony. It describes goals up to the end of grade 2, not a must for today. Empty boxes in the middle of the school year are therefore to be expected. Go through the list together every few weeks, without a test: your child says or shows what they can already do. The curricula differ, so if in doubt, ask the teacher what is on the schedule in your child's class. This page can be printed.

If your child is not keeping up

Not every child is at the same point at the same time. According to the NRW guide: "Calculation problems are normal, and mistakes are part of learning." Only when such problems pile up and children seem overwhelmed throughout do they turn into special, lasting difficulties with calculating.

What you can do:

1. Look closely: Try noting down specific difficult problems for one to two weeks, for example "subtracting across the 10" or "6 · 7".
2. Ask instead of correcting: Ask your child: "How did you calculate?" That way you can follow their way of calculating.
3. Talk to the teacher: Ask how they see your child's level compared with the goals of the class and what you can practice at home.
4. Practice briefly: Try five minutes on several days instead of one long session on the weekend.
5. Get it assessed by experts if it continues: If the difficulties continue, discuss with the teacher what further assessment makes sense.

This article does not replace advice from a teacher, pediatrician or learning therapist.

If your child gets stuck on tasks from the worksheet, Gennady explains the method step by step and checks the answer. Gennady is our own product. Why math can be hard for children and what parents can do is covered in Child does not understand math, and for word problems, Child does not understand word problems helps. You will find more on reading, math and understanding tasks in the guide Understanding tasks. How to stay calm during homework is shown in Homework without stress.

Frequently asked questions

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Math problems step by step

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Sources

• Kultusministerkonferenz: Bildungsstandards für das Fach Mathematik, Primarbereich (version of 06/23/2022). kmk.org (PDF)
• Staatsinstitut für Schulqualität und Bildungsforschung Bayern: LehrplanPLUS Grundschule, Fachlehrplan Mathematik 1/2 (accessed October 2026). lehrplanplus.bayern.de
• Freistaat Sachsen: Lehrplan Grundschule Mathematik (subject curriculum in force since 08/01/2025). schulportal.sachsen.de (PDF)
• Deutscher Bildungsserver: Lehrpläne für die Grundschule (accessed September 2026). bildungsserver.de
• Ministerium für Schule und Bildung NRW: Rechenschwierigkeiten vermeiden. Hintergrundwissen und Unterrichtsanregungen für die Schuleingangsphase (2020). schulministerium.nrw (PDF)