3rd Grade Math: Skills & Worked Examples

Third-grade math connects facts to meaning: multiplication describes equal groups, division finds a missing group size or number of groups, and fractions describe equal parts of a whole. At home, a drawing can help you see which connection your child understands.

For US families, the Common Core Grade 3 overview is a useful reference for multiplication and division, fractions, area, and shapes. It also includes multi-digit arithmetic and measurement. Check your child’s current classroom topic before choosing practice; state standards and school sequences vary. This guide samples important ideas rather than providing a complete curriculum.

Multiplication: draw the groups before recalling the fact

Draw four plates with six dots on each. There are twenty-four dots, so four groups of six give 4 × 6 = 24. Ask your child to circle one group, then explain what each number in the equation represents.

Arrange the same dots into four rows of six. Turn the paper to see six rows of four. Both arrangements contain twenty-four dots. This gives a reason that 4 × 6 and 6 × 4 have the same product.

For a harder fact such as 7 × 6, split seven rows into five rows and two rows. That gives 30 + 12 = 42. Our 6 times table page supplies focused practice, and the times tables chart lets your child check a result. Keep the drawing available until the fact makes sense.

Division: two stories can use the same equation

Start with twenty-four dots. In one story, share them equally among four plates: each plate gets six. In another, put four dots on each plate: you need six plates. Both stories use 24 ÷ 4 = 6, but the six means different things.

Ask your child to finish the sentence “The answer is six…” with either “dots on each plate” or “plates.” Labeling the result helps distinguish a calculation error from a misunderstanding of the situation.

Try eighteen crayons shared among three boxes. Each box gets six, checked by 3 × 6 = 18. If your child counts uneven groups, move one crayon at a time into each box until the groups are equal. Then record the equation beside the picture.

Fractions: equal parts and the same whole matter

Draw two equally long strips. Divide one into four equal parts and shade three; divide the other into four equal parts and shade one. Compare 3/4 and 1/4. Three of the same-sized parts cover more than one.

Now compare 1/3 and 1/6 using equal-length strips. One third is larger because dividing the same whole into fewer equal pieces makes each piece larger. If a child says one sixth is larger because six is larger than three, point to the pieces before discussing a rule.

Place 0 and 1 on a number line and mark four equal intervals. The third mark after zero represents 3/4. Fractions are numbers with positions, not just shaded pizza slices. For more on common stumbling points, read why fractions can be difficult.

Area and perimeter: count different things

Draw a rectangle four squares long and three squares wide on grid paper. Its area is twelve square units, found by counting squares or calculating 4 × 3. Its perimeter is fourteen units: 4 + 3 + 4 + 3 around the outside.

Ask your child to shade the area and trace the perimeter. A 2-by-6 rectangle also has area twelve, but its perimeter is sixteen. Comparing the two helps show why area and perimeter are separate measurements.

Try a three-question practice check

Five bags contain four marbles each. How many marbles? 20, because 5 × 4 = 20.
Twenty marbles are shared equally among five bags. How many per bag? 4, because 20 ÷ 5 = 4.
A rectangle is five units long and two units wide. What are its area and perimeter? 10 square units and 14 units.

Ask for one explanation before adding more questions. These are practice prompts, not a validated readiness test. The manipulatives research review supports a bounded discussion of objects in math instruction; our specific examples and sequence are editorial suggestions.

Tiger Math can supplement arithmetic practice with topic-based adaptive difficulty, hints, and a parent report. It is not a complete third-grade course or a guarantee of school performance. Try our free multiplication game, or explore the app for ongoing practice. When these ideas feel comfortable, our 4th grade guide shows how the numbers and fraction work develop.