First half
- Numbers through 1 million
- Addition/subtraction and mental methods
- Multiples and factors
- Multiplication and division
- Fractions, mixed numbers, unlike fractions
- Fraction multiplied by a whole number
- Line graphs and line plots
Second half
- Measurements involving fractions
- Area and perimeter
- Decimal place value and decimal arithmetic
- Angles, parallel and perpendicular lines
- Shapes, cuboids and nets
4A · Numbers through 1,000,000
Understand the relationships between ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and millions. Use expanded form, benchmarks, number lines and rounding. Do not let correct rounding conceal a lack of place-value understanding.
4A · Factors and multiples
| Concept | Example / definition |
|---|---|
| Factor | 12 has factors 1, 2, 3, 4, 6, 12 |
| Multiple | Multiples of 6 include 6, 12, 18, 24, … |
| Prime | Exactly two distinct positive factors, e.g. 2, 3, 5, 7 |
| Composite | More than two positive factors, e.g. 4, 6, 8, 9 |
| Common factors | Of 12 and 18: 1, 2, 3, 6 |
| Common multiples | Of 4 and 6: 12, 24, 36, … |
Useful divisibility patterns: multiples of 2 end in an even digit; multiples of 5 end in 0 or 5; multiples of 3 have digit sums divisible by 3; multiples of 9 have digit sums divisible by 9.
4A · Multidigit multiplication and division
The area model for 34 × 26
Write 34 as 30 + 4 and 26 as 20 + 6. The four rectangular regions are four partial products.
| 30 | 4 | |
|---|---|---|
| 20 | 600 | 80 |
| 6 | 180 | 24 |
Place-value division
Check: 234 × 4 = 936. Students may use the standard algorithm after understanding its place-value meaning.
4A · Mixed numbers and fraction operations
A proper fraction is less than one; an improper fraction is at least one. A mixed number combines a whole number and a proper fraction.
| Skill | Method |
|---|---|
| Improper to mixed | 11/4 = 2 3/4 |
| Mixed to improper | 3 2/5 = (3 × 5 + 2)/5 = 17/5 |
| Unlike-denominator addition | 3/4 + 2/5 = 15/20 + 8/20 = 1 3/20 |
| Regroup a whole | 3 1/4 = 2 5/4 = 2 10/8 |
| Mixed-number subtraction | 3 1/4 − 1 5/8 = 2 10/8 − 1 5/8 = 1 5/8 |
| Fraction × whole number | 3/4 of 28 = (28 ÷ 4) × 3 = 21 |
Teaching connection: Renaming a fraction or mixed number must preserve its value. This is why common denominators work and why the extra eighths in a regrouping step are not “created.”
4B · Decimals as fractions of ten and one hundred
| Decimal | Meaning |
|---|---|
| 0.7 | 7/10 |
| 0.35 | 35/100 |
| 4.73 | 4 + 7/10 + 3/100 |
| 0.4 and 0.35 | 0.40 > 0.35 |
Add & subtract
Align place values, not just decimal punctuation.
Multiply/divide by wholes
Think in hundredths or tenths to justify the computation.
4B · Measurement, geometry, and angles
| Angle | Measurement |
|---|---|
| Acute | Between 0° and 90° |
| Right | Exactly 90° |
| Obtuse | Between 90° and 180° |
| Straight | 180° |
| Reflex | Between 180° and 360° |
| Full rotation | 360° |
An angle on a straight line is 180°; angles around a point sum to 360°. Also practice parallel/perpendicular lines, quadrilaterals, symmetry, and spatial reasoning about cuboids and nets. A cuboid has 6 faces, 12 edges, 8 vertices.
4B · Extended bar models
Multiplicative comparison
Sarah has three times John's stickers; together they have 72.
John has 18, Sarah has 54. The diagram and the equation x + 3x = 72 express the same relationship.
Grade 4 exit checklist
- Accurate multidigit multiplication/division with explanations and estimates.
- Factors, multiples, and common relationships.
- Mixed numbers and unlike-denominator fraction operations.
- Fractions of whole-number quantities.
- Decimal comparison, hundredths, and the operations taught in Grade 4.
- Area/perimeter, angles, and cuboid geometry.
- Independent multistep bar-model or algebraic reasoning.
Next level: fractions, percentages, and proportional reasoning.
Grade 5 →