Third Grade Math: What Should My Child Know?

This overview shows what the curricula provide for third grade math and what the topics feel like when your child practices them at home. For each topic you will find an example problem, a possible stumbling block and a sentence you can use to explain it. It continues the series after What does my child learn in first grade? Last comes a "What I can already do" checklist.

We built the example problems and sample mistakes ourselves. They do not come from real worksheets and say nothing about how common a mistake is.

Third grade math: what the curricula provide

What your child learns in third grade is set on three levels:

1. The Standing Conference of the Ministers of Education and Cultural Affairs (Kultusministerkonferenz, KMK) sets the goal for the end of fourth grade. The Bildungsstandards (national education standards) describe the skills that children "should have acquired by the end of grade 4" (in German). They do not contain a list for third grade alone.
2. The states write the curricula. Saxony describes third grade in a section of its own. Bavaria combines grades 3 and 4.
3. The school spreads the material across the school years. What is covered by the midyear point or report card is known by your child's teacher.

The table is our own compilation from the curricula of Saxony and Bavaria. It shows examples, not the curriculum of your state.

Curricula name goals, not minimum points for the parent-teacher meeting. How far your child is on each point is best shown by their notebooks and the teacher's feedback.

Numbers up to 1,000: place value and rounding

From first grade and second grade, your child brings along the number range up to 100. In third grade the hundreds are added. The Saxon curriculum gives the example 348 = 3 H 4 Z 8 E (hundreds, tens, ones), plus a separate point, "meaning of zero". For rounding, the curriculum prescribes a "rounding rule" and the sign ≈ for "is approximately".

Example problem (our own): Write "five hundred seven" as digits and enter the number in a place value chart. Then round 348 to the nearest ten.

Solution: 507 is 5 H, 0 Z, 7 E. 348 ≈ 350.

Possible stumbling block: The number word contains no "ten", so some children write 57 or 5007.

How you can explain it: "The zero keeps the place of the tens free: 507 is 5 hundreds, 0 tens and 7 ones." When rounding to tens, the ones digit decides: with 0 to 4 the tens digit stays, from 5 on it goes up to the next ten.

Calculating with written intermediate steps (halbschriftlich)

When calculating with written intermediate steps (halbschriftliches Rechnen), your child records partial steps, for example as partial calculations, intermediate results or on a number line, without fixed columns. The Bavarian curriculum lists as notes "number line, intermediate results, partial calculations" and expects children to decide, depending on the problem, whether they calculate "in their head, with written intermediate steps, in writing". The KMK education standards list oral calculation strategies and strategies with written intermediate steps for the four basic operations, which children should use "flexibly", as a goal for the end of fourth grade.

Example problem (our own): 346 + 278 and 524 − 187. Both can be solved in steps:

Possible stumbling block: In place-by-place subtraction the direction flips: the child calculates 500 − 100 = 400, but 80 − 20 and 7 − 4 instead of 20 − 80 and 4 − 7. That gives 463 instead of 337.

How you can explain it: "We subtract the whole 187, step by step: first 100, then 80, then 7."

Your child may choose their own way. The Saxon curriculum explicitly mentions "avoiding any premature standardization of solution paths and notations". PIKAS (TU Dortmund) advises parents in its info paper "Mathe in den Kopf?!" (in German): "Stick with your child's way of calculating and ask what they were thinking!" Why children today learn several ways is explained in the article Math in Elementary School: Why It Is Taught Differently Than It Used to Be.

Written addition, subtraction and multiplication

In the Saxon curriculum, three written methods appear in third grade: adding "up to three addends, also with carrying", subtracting "with one subtrahend, also with carrying" and multiplying "with a three-digit first and a one-digit second factor". There, children should be able to explain the methods with materials and the place value chart, that is, show what happens to the hundreds, tens and ones when you carry. Written division only comes in fourth grade in Saxony. The Bavarian curriculum combines all four methods for grades 3 and 4: there, children should apply them "automatically", and for subtraction it names the take-away method (Abziehverfahren).

Which method the class uses for written subtraction may differ from yours. PIKAS explains on its parent info page (in German) which different methods of written subtraction exist. So look in the notebook first.

In the Saxon curriculum, estimating belongs to the "estimation and checking methods for written calculation methods". A good habit is therefore to ask "Can that roughly be right?" after every calculation.

Times tables, dividing and remainders

The basic multiplication tables ("das kleine Einmaleins") should be solid in third grade. The Saxon curriculum lists "mastering the basic facts of multiplication and division" for this, with the keyword "solving automatically". The Bavarian one expects children to apply the number sentences of the basic multiplication tables and their inverses "automatically and flexibly", and gives the step into larger number ranges as an example: 6 · 4 = 24, so 60 · 4 = 240. For dividing, Saxony adds division with remainder, in the curriculum with the example 14 : 3 = 4 remainder 2 and the task of clarifying the remainder "in the concrete situation".

Example problem (our own): 29 children form teams of 5 children each. How many full teams are there, and how many children are left over?

Solution: 29 : 5 = 5 remainder 4. There are 5 full teams, 4 children are left over. Check: 5 · 5 + 4 = 29.

Possible stumbling block: The child stops dividing too early: 29 : 5 = 4 remainder 9.

How you can explain it: "The remainder must be smaller than the number you divide by. If 9 are left, another 5 still fits in."

Divisibility in Saxony includes the digit sum and the rules for 2, 3, 5, 9, 10 and 100. An example (our own): The digit sum of 348 is 3 + 4 + 8 = 15. Because 15 is divisible by 3, 348 is also divisible by 3 (348 : 3 = 116).

Measures, word problems and shapes

Besides calculating with numbers, the Saxon curriculum provides for third grade real-life situations with money, lengths, time spans and masses, plus reading values from a timetable. In geometry, it covers parallelograms, perimeter and area as well as cube and cuboid nets.

Time (our own): A train leaves at 2:35 p.m. and arrives at 3:20 p.m. How long does the trip take?

Solution: 45 minutes (25 minutes until 3:00 p.m., then 20 minutes).

Possible stumbling block: The child calculates 20 − 35, notices it does not work, and turns it around: 35 − 20 = 15 minutes.

How you can explain it: "First go to the full hour and then keep going: from 2:35 to 3:00 p.m., and then 20 more minutes."

Money (our own): A notebook costs 1 euro 35 cents, a pen 85 cents. You pay with 5 euros. How much change do you get?

Solution: 135 cents + 85 cents = 220 cents. 500 cents − 220 cents = 280 cents, so 2 euros 80 cents.

Possible stumbling block: The child subtracts 220 directly from 5 because euros and cents are mixed.

How you can explain it: "Calculate everything in cents: 5 euros is 500 cents."

Lengths (our own): A path is 1 km 50 m long. How many meters is that?

Solution: 1 km is 1,000 m, plus 50 m: 1,050 m.

Possible stumbling block: The child writes 1,50 m or 150 m because a zero is missing in the middle.

How you can explain it: "1,000 and 50 make 1,050: that is 1 thousand, 0 hundreds, 5 tens and 0 ones. The zero in the middle keeps the place of the hundreds free."

Masses (our own): You need 1 kg of flour and have 750 g. How much is missing?

Solution: 1 kg is 1,000 g. 1,000 g − 750 g = 250 g.

Possible stumbling block: The child calculates 750 − 1 = 749 because the units are different.

How you can explain it: "Write both amounts in grams, then you calculate in the same unit."

Shapes (our own): A parallelogram has sides of 6 cm and 4 cm (two of each, equal in length). What is the perimeter?

Solution: 6 + 4 + 6 + 4 = 20 cm.

Possible stumbling block: The child adds only two sides and gets 10 cm.

How you can explain it: "Go once around the whole shape: every side counts, including the opposite one."

If your child can do the calculation but fails on the text, Child Does Not Understand Word Problems helps with a method in five steps.

Checklist: What I can already do

The list is our own compilation from the curricula of Saxony and Bavaria. Bavaria sets the goals for grades 3 and 4 together, so empty boxes are to be expected in third grade. The last two rows are our suggestions for everyday life, not a curriculum goal.

How to use it: go through the list together every few weeks and check off what your child can newly do. Do not turn it into a test: your child says or shows what they can already do.

If your child is not keeping up in math

Not every child is secure on every topic at the same time. These steps can help:

1. Narrow down the topic: For one to two weeks, note which problems your child gets stuck on, for example "minus with zero" or "remainder when dividing". That helps more than "math is not working".
2. Practice with the math book: PIKAS advises that everyone who practices with the child should use the same representations that are used in class and in the math book. According to PIKAS, ways of calculating explained "completely differently" at home can lead to "great confusion".
3. Talk to the teacher: Ask which method the class is currently practicing and how the teacher sees your child's progress.
4. Get it assessed by specialists if it persists: According to the guideline on arithmetic disorder (in German), individual calculation mistakes are not decisive, but "their variety, stability and frequency". The guideline puts arithmetic disorders at 3 to 7 percent of children, adolescents and adults and also lists other reasons for weak math performance, such as undetected vision or hearing problems. Whether there is more behind it can only be clarified by professional diagnostics. This article does not replace advice from a teacher, pediatrician or learning therapist.

You can find more on stumbling blocks from first to fourth grade and on the 5-minute check in Child Does Not Understand Math. All articles on reading, math and understanding tasks are in the guide Understanding tasks. How long homework may take in third grade is regulated differently by the states: the article How Long Can Homework Take in Elementary School? gives an overview. A fixed frame for homework time is shown in Homework Routine for Elementary School.

If your child is stuck on a worksheet, you can photograph the sheet with Gennady. Gennady explains the method step by step and checks your child's answer. If the answer is wrong, there are hints first; Gennady shows the correct solution for comparison only on the third try. A question typed in freely without a worksheet gets a direct answer from Gennady.

Frequently asked questions

Sources on homework time: the North Rhine-Westphalia education ministry (Schulministerium NRW) (in German) and the Rhineland-Palatinate regulations for public elementary schools (Schulordnung für die öffentlichen Grundschulen) (in German).

Math Problems Step by Step

Gennady reads the task aloud, explains the method step by step and checks your child's answer. If the answer is wrong, there are hints first; the correct solution for comparison comes only on the third try. Try it free for 7 days.

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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 3/4 (accessed October 2026). lehrplanplus.bayern.de
• Freistaat Sachsen: Lehrplan Grundschule Mathematik (curriculum in force since 08/01/2025). schulportal.sachsen.de (PDF)
• PIKAS, TU Dortmund: Info paper for parents "Mathe in den Kopf?!" (2012). PDF at pikas.dzlm.de
• PIKAS, TU Dortmund: Elterninfos, overview (accessed September 2026). pikas.dzlm.de
• Deutsches Ärzteblatt: Haberstroh, S., Schulte-Körne, G.: Diagnostik und Behandlung der Rechenstörung, clinical guideline (2019). PDF at aerzteblatt.de
• Ministerium für Schule und Bildung NRW: Hausaufgaben (accessed September 2026). schulministerium.nrw
• Rheinland-Pfalz: Schulordnung für die öffentlichen Grundschulen (of 10/10/2008, version 2024). bildung.rlp.de (PDF)