GA Milestones Math Grade 3: Primary whole numbers, equal groups, patterns and problem solving

Number Sense and Operations

These elementary number and operation foundations include place value through 10,000, reading and writing whole numbers in standard, expanded, and word form, comparing and ordering numbers, rounding to the nearest 10 or 100, and adding and subtracting multi-digit numbers. Practise multiplication and division facts, the relationship between multiplication and division, multiplying one-digit numbers by multiples of 10, and using properties such as the commutative and distributive properties.

Core rules to know

In a four-digit number, each digit has a value ten times the value of the digit to its right: in 4,507, the 5 means 5 hundreds, or 500, and the 0 means 0 tens.
To compare whole numbers, compare the greatest place value first. If those digits match, move right until the digits differ.
Expanded form breaks a number into the value of each digit: 4,507 = 4,000 + 500 + 7.
To round to the nearest 10, look at the ones digit; to round to the nearest 100, look at the tens digit. If the deciding digit is 5 or greater, round up.
Multiplication and division are inverse operations: 6 × 7 = 42 means 42 ÷ 6 = 7 and 42 ÷ 7 = 6.
Multiples of 10 use place-value patterns: 4 × 30 = 4 × 3 tens = 12 tens = 120.

Worked example

Compare 4,507 and 4,570, then round 4,570 to the nearest hundred. Both numbers have 4 thousands, so compare hundreds: both have 5 hundreds. Compare tens: 4,507 has 0 tens; 4,570 has 7 tens. Since 7 > 0, 4,570 > 4,507. To round 4,570 to the nearest hundred, look at the tens digit, 7. Because 7 is 5 or more, the hundreds digit increases from 5 to 6, and the tens and ones become zeros: 4,600.

Traps that cost marks

Writing 4,507 in expanded form as 4,000 + 500 + 7 is correct, but writing 4,000 + 50 + 7 is not; the 5 is in the hundreds place.
Forgetting to regroup across a zero when subtracting, such as in 503 − 278.
Rounding 4,570 to 4,500 by looking at the hundreds digit; the tens digit decides, so it is 4,600.
Mixing up 3 × 40 = 120 with 3 × 40 = 12 by dropping the zero.
Treating the equals sign as “the answer comes next” instead of “is the same as” when checking an equation.

Algebraic Reasoning

The Algebraic Reasoning domain tests how Grade 3 students use operations to solve problems and describe relationships. Items ask students to find unknown factors or addends, solve one- and two-step word problems with multiplication and division, apply properties such as the distributive property, complete equations, and identify or extend patterns in tables and multiplication charts.

Core rules and concepts

An equation is a statement that two expressions have the same value. The equals sign means “is the same as,” not “the answer comes next.”
Multiplication and division are inverse operations. If 7 × □ = 56, then □ = 56 ÷ 7 = 8.
The distributive property breaks a factor into friendly parts: 6 × 8 = 6 × (5 + 3) = (6 × 5) + (6 × 3) = 30 + 18 = 48.
The commutative property lets factors switch order: 4 × 9 = 9 × 4. The multiplicative identity property says any number times 1 stays that number. The zero property says any number times 0 is 0.
In patterns, find the rule that moves from one term to the next, then test it on more than one pair. Rules can be additive (add 6) or multiplicative (multiply by 3).
For two-step problems, decide what must be found first, then use that result in the second step. A model or equation can show the hidden question.

Worked example

A class has 5 tables with 6 students at each table. Three students leave. How many students remain? First find the starting number: 5 × 6 = 30 students. Then subtract the 3 who leave: 30 − 3 = 27 students. As one equation: (5 × 6) − 3 = 27. If the problem asked for an unknown factor instead, such as 5 × □ = 30, the inverse operation gives □ = 30 ÷ 5 = 6.

Traps that cost marks

Solving only the first step of a two-step problem, such as reporting 30 instead of 27.
Treating the equals sign as an instruction to compute only the right side; 8 + 4 = □ + 6 requires balancing both sides, so □ = 6.
Assuming every pattern adds the same number; check whether the rule multiplies.
Breaking apart a factor incorrectly in the distributive property, such as 6 × 8 = 6 × 5 + 3 instead of 6 × 5 + 6 × 3.
Finding an unknown factor by adding instead of using the inverse operation.