Welcome, parents
This guide shows up to which expertise level is covered for each age or school year, across the four core skills: Addition, Subtraction, Multiplication, and Division. Use the Find your child's level tool below: pick your child's school year (or age) to instantly see the level covered in each skill, with examples.
About decimals: the worksheets in the app currently generate whole-number problems. Decimals are part of the full level guide and are shown here too, because they begin appearing at the appropriate ages (typically around Grade 4 / age 9–10) and are needed for later levels. That way you know the complete picture as your child progresses.
Find your child's level
Select a school year (or age) below:
—
What the levels mean
Every skill is scored from Level 0 (just starting) to Level 8 (mastery). A child is considered at a level only when they answer accurately and comfortably (fluently).
| Level | Name | Typical age | Typical year | What the child can do |
|---|---|---|---|---|
| 0 | Pre-Arithmetic | 3–4 | Pre-K | Counts objects; recognises numerals 1–10. No formal computation yet. |
| 1 | Introductory | 4–5 | Pre-K–K | Joins and separates groups with fingers/objects; adds & subtracts within 5–10. |
| 2 | Foundation | 5–6 | K–1 | Recalls basic facts within 10; uses count-on, make-ten, doubles within 20. |
| 3 | Developing | 6–8 | 1–2 | Fluent within 20; adds/subtracts 2-digit numbers; understands × as repeated addition and ÷ as sharing. |
| 4 | Proficient | 8–10 | 2–4 | Fluently computes within 100/1000; knows × and ÷ facts within 100; multi-digit × 1-digit; long division basics; first decimals. |
| 5 | Intermediate | 9–11 | 4–5 | Multi-digit × and ÷; decimals to hundredths/thousandths; decimal × / ÷ by whole numbers. |
| 6 | Advanced | 10–12 | 5–6 | Fluent with all four operations on decimals; decimal ÷ decimal; fraction ↔ decimal conversion. |
| 7 | Fluent | 11–14 | 6–8 | Extends all four operations to negative numbers and signed decimals; ratios and percent. |
| 8 | Mastery | 13+ | 7+ | Full rational-number arithmetic; exponents and scientific notation; fluent multi-step problem solving. |
Decimals — when they appear
Decimals start after a child is fluent with whole numbers, and build up year by year:
| Age | School year | Decimal milestone | Examples |
|---|---|---|---|
| 8–9 | Grade 3 | Fractions foundation — tenths as parts of a whole | 1/10, 7/10 |
| 9–10 | Grade 4 | Decimal notation (tenths, hundredths); compare & order; add/subtract decimals | 0.5, 1.25; 3.4 + 2.1 |
| 10–11 | Grade 5 | Decimals to thousandths; all four operations on decimals; rounding | 2.345; 12.345 − 6.7; 2.5 × 4; 5.6 ÷ 2 |
| 11–12 | Grade 6 | Decimal fluency; decimal ÷ decimal; fraction ↔ decimal; negative decimals | 2.4 ÷ 0.6; ⅓ = 0.333…; (−2.5) + 3.75 |
| 12–13 | Grade 7 | Signed decimals across all four operations; percent ↔ decimal | (−3.2) × (−1.5); 25% = 0.25 |
| 13–14 | Grade 8 | Exponents & scientific notation with very large/small decimals | 4.5 × 10⁻² = 0.045 |
| 14+ | Grade 9+ | Applied decimal fluency in real-world contexts | means, rates, unit price, finance |
Detailed progression by skill
For a closer look, expand each skill below. 🧮 green rows show where decimals appear.
➕ Addition ▸
| Level | Age | Year | Skills covered | Decimal skills 🧮 | Examples |
|---|---|---|---|---|---|
| 0–2 | 4–6 | Pre-K–K | Count all; join groups; facts within 10 | — | 2 + 1, 7 + 3 |
| 2–3 | 6–7 | Grade 1 | Facts within 20; make-ten; 2-digit addition with regrouping | — | 34 + 8, 27 + 45 |
| 3–4 | 7–8 | Grade 2 | Add within 100 fluently; within 1000 with strategies | — | 148 + 236 |
| 4 | 8–10 | Grades 3–4 | Multi-digit addition (up to 4 digits); estimation | 🧮 add tenths & hundredths | 2,345 + 6,708; 3.4 + 2.1 |
| 5 | 10–11 | Grade 5 | Add decimals to thousandths; multiple addends | 🧮 thousandths; mixed lengths | 12.345 + 6.7 |
| 6–7 | 11–14 | Grades 6–8 | Signed decimals; scientific notation sums | 🧮 negative decimals | (−3.5) + 8.2 |
| 8 | 13+ | Grade 7+ | Instant recall; applied & multi-step addition | 🧮 embedded decimals | 0.25 + 1.75 + 0.5 |
➖ Subtraction ▸
| Level | Age | Year | Skills covered | Decimal skills 🧮 | Examples |
|---|---|---|---|---|---|
| 0–2 | 4–6 | Pre-K–K | Take away objects; facts within 10 | — | 5 − 2, 9 − 4 |
| 2–3 | 6–7 | Grade 1 | Subtract within 20; 2-digit with borrowing | — | 15 − 8, 42 − 27 |
| 3–4 | 7–8 | Grade 2 | Subtract within 100 fluently; within 1000 with regrouping | — | 100 − 37 |
| 4 | 8–10 | Grades 3–4 | Multi-digit subtraction; estimation | 🧮 subtract tenths & hundredths | 5.6 − 2.3, 8.40 − 3.25 |
| 5 | 10–11 | Grade 5 | Subtract decimals to thousandths; borrow across whole numbers | 🧮 thousandths | 12.500 − 7.86, 3 − 1.75 |
| 6–7 | 11–14 | Grades 6–8 | Signed decimals; subtract a negative | 🧮 negative decimals | 7.5 − (−3.2) |
| 8 | 13+ | Grade 7+ | Flexible strategies; applied subtraction | 🧮 embedded decimals | 9.99 − 4.50 − 2.25 |
✖️ Multiplication ▸
| Level | Age | Year | Skills covered | Decimal skills 🧮 | Examples |
|---|---|---|---|---|---|
| 2 | 6–7 | Grades 1–2 | Repeated addition; arrays; skip-count by 2s, 5s, 10s | — | 2 × 3 = 3 + 3 |
| 3 | 7–8 | Grades 2–3 | Begin × facts; multiply multiples of 10 | — | 3 × 4, 40 × 6 |
| 4 | 8–9 | Grade 3 | All × facts within 100 fluent; 2-digit × 1-digit | — | 7 × 8, 23 × 4 |
| 4–5 | 9–10 | Grade 4 | 2-digit × 2-digit; area model; estimate products | 🧮 decimal × whole number; ×10, ×100 | 45 × 23; 2.5 × 4; 1.2 × 100 |
| 5 | 10–11 | Grade 5 | Multi-digit × multi-digit; powers of 10 | 🧮 decimal × decimal | 3.2 × 1.5, 0.6 × 0.4 |
| 6–7 | 11–14 | Grades 6–8 | Signed decimals; exponents & scientific notation | 🧮 negative decimals; × 10ⁿ | (−2.5) × 1.6; 4.5 × 10⁻² |
| 8 | 13+ | Grade 7+ | Instant facts; applied (area, scaling, percent) | 🧮 embedded decimals | 1.15 × 3.5 (tax) |
➗ Division ▸
| Level | Age | Year | Skills covered | Decimal skills 🧮 | Examples |
|---|---|---|---|---|---|
| 2 | 6–7 | Grades 1–2 | Equal sharing & grouping | — | 6 ÷ 2 (fair share) |
| 3 | 7–8 | Grades 2–3 | ÷ facts within 100 (inverse of ×); divide by 2, 5, 10 | — | 12 ÷ 3, 42 ÷ 7 |
| 4 | 8–9 | Grades 3–4 | All ÷ facts fluent; division with remainders; short division | — | 84 ÷ 4, 17 ÷ 5 R2 |
| 4–5 | 9–10 | Grades 4–5 | Long division (1-digit then 2-digit divisors) | 🧮 decimal ÷ whole; remainder as decimal | 952 ÷ 7; 5.6 ÷ 2, 7 ÷ 2 = 3.5 |
| 5 | 10–11 | Grade 5 | Long division (multi-digit divisors); remainders interpreted | 🧮 decimal ÷ decimal; terminating/repeating | 448 ÷ 16; 2.4 ÷ 0.6, 22 ÷ 7 ≈ 3.142857… |
| 6–7 | 11–14 | Grades 6–8 | Signed decimals; fraction ↔ decimal; scientific notation | 🧮 signed; ⅓ = 0.333… | (−3.6) ÷ 1.2; (6.0 × 10⁶) ÷ (2.0 × 10²) |
| 8 | 13+ | Grade 7+ | Instant facts; applied (rates, unit price, averages) | 🧮 embedded decimals | $45.00 ÷ 12 = $3.75 |
How the overall level is decided
Your child's overall level is the average of the four skill levels, with one important rule: it can never be more than one level above their weakest skill. This is the "cap rule" — a strong Addition score cannot hide a weak Division score.