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Math Skills by Age: What to Expect from Kindergarten to 4th Grade
What math should a 5- to 10-year-old know? Grade-by-grade Common Core milestones for K–4, what on track looks like, what to practice and when to ask.
Quick answer
By the end of kindergarten (ages 5–6), children count to 100 and add and subtract within 10. By the end of 1st grade they add and subtract within 20, and by the end of 2nd grade within 100, knowing all one-digit sums from memory. In 3rd grade they multiply and divide within 100 and learn all one-digit times facts; in 4th grade they work with multi-digit numbers, fractions and decimals.
Key takeaways
- Grade standards describe what children should know by the end of the school year, so gaps in the fall are normal.
- Kindergarten: count to 100 by ones and tens, and add and subtract within 10. 1st grade: within 20, plus tens and ones.
- 2nd grade: fluent within 100 and all one-digit sums from memory. 3rd grade: multiplication and division within 100 and all one-digit products from memory.
- 4th grade: multi-digit multiplication and division, equivalent fractions and decimals to hundredths.
- Talk to the teacher if your child is far from these goals late in the year, or starts to dread math.
How should I use these milestones?
The milestones below come from the Common Core State Standards for Mathematics, which most US states adopted; states may change or add to them, so ask the teacher which standards your school follows. They describe what children should do by the end of each grade, not on the first day. Children also develop at different speeds: early-years guidance from the Education Endowment Foundation notes that early math ideas take time to settle and that skills may appear in different orders.
Outside the US? In England, a US kindergartner is roughly in Year 1 (ages 5–6) and a 4th grader in Year 5 (ages 9–10). For Turkey's MEB curriculum, see the Turkish version of this guide.
Tip Use the table as a map, not a test
If your child can do most of a row, practice what's new. If they can do almost none of it late in the year, talk to the teacher.
Math milestones by grade at a glance
| Grade (age) | Numbers and place value | Operations | Also by year end |
|---|---|---|---|
| Kindergarten (5–6) | Count to 100 by ones and tens; count up to 20 objects in a row (10 if scattered); write 0–20; compare two numbers from 1 to 10 | Add and subtract within 10, fluent within 5; find the number that makes 10 (7 + 3) | 11–19 as ten ones and some more (18 = 10 + 8); name flat and solid shapes |
| 1st grade (6–7) | Count to 120; tens and ones; compare two-digit numbers with >, = and <; 10 more or 10 less in your head | Add and subtract within 20, fluent within 10; add within 100, such as 45 + 8 or 45 + 30 | Understand the equals sign; find a missing number (8 + ? = 11); time to the hour and half hour |
| 2nd grade (7–8) | Hundreds, tens and ones to 1,000; skip-count by 5s, 10s and 100s; compare three-digit numbers | Fluent within 100; add and subtract within 1,000 with models; all sums of two one-digit numbers from memory | Odd and even; arrays up to 5 by 5; time to 5 minutes; coins and bills |
| 3rd grade (8–9) | Round to the nearest 10 or 100; fractions as numbers on a number line (halves, thirds, fourths, sixths, eighths) | Multiply and divide within 100; all products of two one-digit numbers from memory; fluent adding and subtracting within 1,000 | Two-step word problems; area and perimeter; time to the minute |
| 4th grade (9–10) | Place value to 1,000,000; round to any place; compare multi-digit numbers | Standard written method for adding and subtracting; multiply up to 4 digits by 1 digit and 2 digits by 2 digits; divide up to 4 digits by 1 digit, with remainders | Factors and multiples; equivalent fractions; add and subtract fractions with like denominators; decimals to hundredths; angles |
“Fluent” means accurately and without long counting, using a strategy your child understands. It is not a race against a stopwatch.
Ages 5–7 (kindergarten and 1st grade): what does on track look like?
At this age, number sense is built with hands and voices. By the end of kindergarten, a child who is on track can count up to 10 scattered objects (or 20 in a row), touching each one once, and knows that the last number said tells how many. They can start counting from any number, not just 1, and know which pairs make 10. Our comparing numbers guide builds the “which is more?” skill.
By the end of 1st grade, look for a child who can:
- count on to add instead of counting everything: for 8 + 3, say “8… 9, 10, 11”;
- use a ten to add and subtract: 8 + 6 = 8 + 2 + 4 = 14 and 13 − 4 = 13 − 3 − 1 = 9;
- use one fact to find another: knowing 8 + 4 = 12 means 12 − 8 = 4;
- say 10 more or 10 less than a two-digit number without counting by ones: 47 → 57 and 37;
- decide whether 4 + 1 = 5 + 2 is true or false (false, because 5 is not 7).
Our guide on how to teach addition shows counting on and making ten step by step.
- Line up 14 pieces of pasta: “How many?” → touches each once and says 14
- “7 and what make 10?” → 3
- “Which is more, 9 or 6?” → 9
- “What's 10 more than 23?” → 33, without counting by ones (1st grade)
Ages 7–9 (2nd and 3rd grade): from place value to times tables
In 2nd grade, children learn that 706 means 7 hundreds, 0 tens and 6 ones, and they skip-count by 5s, 10s and 100s. They add and subtract within 100 fluently and within 1,000 with drawings or blocks, regrouping when needed (see how to teach subtraction). By the end of the year they know every sum of two one-digit numbers from memory. Multiplication thinking starts too: odd and even numbers, and arrays of up to 5 rows and 5 columns.
In 3rd grade the big new ideas are multiplication, division and fractions. Children learn that 5 × 7 means 5 groups of 7, that 56 ÷ 8 can mean sharing 56 into 8 equal groups, and by the end of the year they know all products of two one-digit numbers from memory. Fractions with denominators 2, 3, 4, 6 and 8 become numbers on a number line.
- 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56
- 32 ÷ 8 = ? → 8 × ? = 32 → 4
- 6 × 4 = 24, so 4 × 6 = 24
- 247 rounded to the nearest 10 → 250; to the nearest 100 → 200
Tip Times tables: a 3rd-grade goal
Knowing all one-digit products is an end-of-3rd-grade goal, built on understanding first (see how to learn times tables). England's national curriculum expects the 2, 5 and 10 tables in Year 2, the 3, 4 and 8 tables in Year 3 and all tables up to 12 × 12 in Year 4.
Ages 9–10 (4th grade): bigger numbers, fractions and decimals
In 4th grade, place value stretches to 1,000,000, and children see that each place is worth ten times the place to its right (700 ÷ 70 = 10). They add and subtract multi-digit numbers with the standard written method, multiply numbers of up to four digits by one digit and two-digit numbers by two-digit numbers, and divide up to four-digit numbers by one digit, interpreting remainders in word problems. They also find factor pairs for numbers up to 100 and tell whether a number is prime or composite.
Fractions grow up too: children explain why 1/2 = 2/4 = 3/6, add and subtract fractions with the same denominator, multiply a fraction by a whole number, and write fractions with denominators 10 and 100 as decimals.
- 3/8 = 1/8 + 1/8 + 1/8
- 3 × 2/5 = 6/5
- 3/10 + 4/100 = 30/100 + 4/100 = 34/100
- 0.62 = 62/100
- 25 ÷ 4 = 6 remainder 1 (because 4 × 6 = 24)
What should we practice at home at each stage?
| Grade | Practice at home | Everyday moment |
|---|---|---|
| Kindergarten | Count objects into a bowl; make 10 with fingers (6 + 4) | Count stairs; set the table for 5 people |
| 1st grade | Count on from the bigger number; make 10 to add (9 + 5 = 10 + 4) | Add two dice; read house numbers |
| 2nd grade | Bundle straws in tens to show tens and ones; add and subtract within 100 | Count coins; read a clock with hands to 5 minutes |
| 3rd grade | Build arrays with buttons (4 rows of 6); turn facts around (6 × 4 = 4 × 6) | Share snacks fairly; total up prices |
| 4th grade | Fold paper strips to compare fractions (2/4 = 1/2); multiply by 10, 100 and 1,000 | Double or halve a recipe; read prices with decimals |
Ten More, Ten Less
- Turn over two cards to make a two-digit number: a 4 and a 7 make 47.
- Your child says 10 more (57) and 10 less (37) without counting by ones.
- For 2nd graders and up, turn over three cards; your child says 100 more and 100 less: 352 → 452 and 252.
- Swap roles so your child checks you. Make one deliberate mistake and see if they catch it.
More screen-free ideas are in our math games at home guide.
Signs it's time to talk to the teacher
Every child has stronger and weaker areas, so one tricky topic is not a red flag. Talk to the teacher if you notice any of these, especially late in the school year:
- Kindergarten: can't yet count out 10 objects reliably, or say which of two numbers up to 10 is bigger.
- 1st grade: still counts every object from 1 for sums like 8 + 3, or can't add and subtract within 10 without objects.
- 2nd grade: doesn't yet see that the 5 in 52 means 5 tens, or needs fingers for most sums within 20.
- 3rd grade: doesn't connect multiplication with equal groups, or can't use a known fact to work out another.
- 4th grade: struggles with multi-digit place value, or thinks 1/8 is bigger than 1/4 because 8 is bigger than 4.
- Any age: tears, stomach aches or refusal around math (see math anxiety in kids), or a gap with classmates that keeps growing.
At the meeting, ask what your child can do, what comes next and what to practice at home. Schools can often add small-group support, which the Education Endowment Foundation finds works best when it is brief, regular and linked to classroom teaching. For the bigger picture, see how to teach math at home.
Frequently asked questions
What math should a 5-year-old know?
By the end of kindergarten, usually around age 6, children are expected to count to 100 by ones and tens, count out up to 20 objects, write numbers 0 to 20, and add and subtract within 10. Many 5-year-olds are still working toward them, which is normal.
What math should a 7-year-old know?
Most 7-year-olds are in 1st or 2nd grade. By the end of 1st grade, children add and subtract within 20 and understand tens and ones; by the end of 2nd grade, they add and subtract within 100 and know all sums of two one-digit numbers from memory.
At what age should a child know their times tables?
The Common Core expects children to know all products of two one-digit numbers from memory by the end of 3rd grade, around age 9. In England, the national curriculum expects all tables up to 12 × 12 by the end of Year 4, at ages 8–9.
When do children learn fractions?
Children split shapes into halves and fourths in 1st grade and into thirds in 2nd grade. Fractions become numbers on a number line in 3rd grade, and in 4th grade children find equivalent fractions and add fractions with like denominators.
Is my child behind in math?
Compare your child with the end-of-year goals for their grade, not with the fall. If they are far from the goals late in the year, or the gap keeps growing despite regular practice, ask the teacher about extra support.
Sources
Written by the Matobur team at Edict Digital and checked against these sources:
- Common Core State Standards for Mathematics: Kindergarten (opens in a new tab)Common Core State Standards Initiative
- Common Core State Standards for Mathematics: Grade 1 (opens in a new tab)Common Core State Standards Initiative
- Common Core State Standards for Mathematics: Grade 2 (opens in a new tab)Common Core State Standards Initiative
- Common Core State Standards for Mathematics: Grade 3 (opens in a new tab)Common Core State Standards Initiative
- Common Core State Standards for Mathematics: Grade 4 (opens in a new tab)Common Core State Standards Initiative
- Standards in Your State (opens in a new tab)Common Core State Standards Initiative
- The national curriculum: key stages and year groups (opens in a new tab)GOV.UK, Department for Education
- National curriculum in England: mathematics programmes of study (key stages 1 and 2) (opens in a new tab)GOV.UK, Department for Education
- Improving Mathematics in the Early Years and Key Stage 1 (guidance report) (opens in a new tab)Education Endowment Foundation (2020), archived copy