First half
- Numbers to 10,000 and place value
- Number lines, patterns, and rounding
- Flexible addition/subtraction
- Multiplication and division
- Word problems, graphs, and tables
Second half
- Multiplication/division facts 6–9
- Fractions: meaning, equivalence, operations
- Measurement and metric units
- Geometry, area and perimeter
- Time and money
3A · Place value to 10,000
Every digit's position is worth ten times the position immediately to the right.
| Skill | Model / example |
|---|---|
| Compare | 4,095 < 4,509 |
| Round to nearest ten | 3,476 → 3,480 |
| Round to nearest hundred | 3,476 → 3,500 |
| Round to nearest thousand | 3,476 → 3,000 |
| Number line | Order benchmark values before estimating intermediate locations |
Ask students why rounding works. The nearest hundred to 3,476 is 3,500 because the distance is 24, compared with 76 to 3,400.
3A · Mental and written arithmetic
| Method | Worked example |
|---|---|
| Compensation | 398 + 257 = (400 + 257) − 2 = 655 |
| Equal adjustment in subtraction | 503 − 198 = 505 − 200 = 305 |
| Multiply by place value | 236 × 4 = 800 + 120 + 24 = 944 |
| Divide into multiples | 156 ÷ 6 = (120 ÷ 6) + (36 ÷ 6) = 26 |
| Remainder check | 158 = 6 × 26 + 2; remainder 2 is less than 6 |
A tutoring move that pays off
Ask for two valid methods, then have the student explain why both give the same result. Flexible methods are useful, but the standard written algorithm remains perfectly acceptable when accurate and understood.
3B · Fractions: equal parts of the same whole
The denominator determines the size of each equal part; the numerator counts how many of these parts are taken. Fractions can also represent positions on a number line.
| Concept | Rule / example |
|---|---|
| Same denominator | 5/8 > 3/8 |
| Same numerator, positive fractions | 3/5 > 3/7 because fifths are larger than sevenths |
| Equivalent fractions | 2/3 = 4/6 = 6/9 |
| Simplest form | 6/10 = 3/5 |
| Addition of like denominators | 2/8 + 3/8 = 5/8 |
| Subtraction of like denominators | 7/8 − 3/8 = 4/8 = 1/2 |
| Compare unlike denominators | 2/3 = 8/12 < 9/12 = 3/4 |
Why 1/2 + 1/4 = 3/4
Rename half a whole into two fourths of the same-sized whole. Then combine parts of equal size.
Diagnostic issue: A response of 6/10 to 1/10 + 5/10 shows correct addition but is incomplete if the question explicitly requires simplest form. Diagnose simplification separately from addition.
3B · Measurement and unit conversion
| Quantity | Relationship |
|---|---|
| Length | 1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm |
| Mass | 1 kg = 1,000 g |
| Liquid capacity | 1 L = 1,000 mL |
| Time | 1 hour = 60 minutes; 1 minute = 60 seconds |
| Calendar | 1 day = 24 hours; 1 week = 7 days |
Mixed-unit subtraction
Subtract 1 km 750 m from 3 km 40 m. Regroup one kilometer as 1,000 meters.
Time does not work in base ten. A timeline is often clearer than ordinary written subtraction.
Elapsed time
7:45 a.m. to 10:20 a.m.
3B · Area versus perimeter
Area
The amount of a surface covered, measured in square units.
4 by 3 rectangle → area = 12 square units.
Perimeter
The length of the boundary around a shape, measured in linear units.
4 by 3 rectangle → perimeter = 14 units.
Composite shapes
A large 8 × 6 rectangle has a 3 × 2 rectangular corner removed:
Students should also identify right angles, circles, radius and diameter, common quadrilaterals, and geometric properties of simple shapes. For circles, diameter = 2 × radius.
3B · Money and word problems
Use equivalent money notation, combinations of coins/bills, making change, and sums/differences of amounts. Emphasize the choice of operation in a story rather than keyword matching.
A simple comparison model
Emma and Noah have 68 marbles. Emma has 12 more. How many does each have?
Noah has **28** and Emma has **40**. See the labeled bar model →
Grade 3 exit checklist
- Accurate computation, including 1-digit division and remainders.
- Fractions: equal parts, comparison, equivalence, simplification, and the taught operations.
- Metric conversions and mixed-unit arithmetic.
- Area/perimeter distinction and simple composite areas.
- Elapsed-time and money situations solved independently.
- Two-step story problems interpreted through equations or models.
Ready to connect ideas? Continue when these skills are secure.
Grade 4 →