A Grade-by-Grade Math Practice Roadmap

How to use this roadmap

This roadmap follows the six MathGem levels from the four operations to Pre-Calculus. The grade ranges are approximate: schools, provinces and states introduce topics at different times, and many students need to revisit an earlier stage before moving on. Treat the grades as a guide to the order, not as a deadline.

The roadmap has two phases that call for different kinds of practice. In the first, arithmetic, the goal is fluency: fast, accurate recall that comes from a lot of daily practice. In the second, from fractions onward, the goal is understanding: knowing why a method works, so that it can be used in new problems.

Phase 1: arithmetic fluency (grades 1–5)

In practice, that routine looks like this on the Basic Math worksheets, which have 20 problems per page and print up to 10 pages at a time:

• Start small and daily. One page (20 problems) at a time, every day. A short daily session builds the habit better than a long one once a week.
• Grow the amount gradually. Add a page when the current amount feels easy, up to five pages (100 problems) a day.
• Grow the numbers one step at a time. Each worksheet lets you choose the digits of each number (1 to 5). Begin with one digit and one digit, then two digits and one digit, and so on.

A typical order through the four operations:

1. Addition and subtraction facts (grades 1–2), then two- and three-digit numbers with carrying and borrowing (grades 2–3).
2. Multiplication facts, the times tables from $2 \times 2$ to $9 \times 9$ (grades 2–4), then multi-digit multiplication (grades 4–5).
3. Division facts and division with remainders (grades 3–4), then long division (grades 4–5).

Phase 2: understanding each concept (grade 4 onward)

After the four operations, more problems are no longer the main goal. Each new topic rests on an idea (a common denominator, a negative sign, a variable) that has to be understood before practice helps. A good routine for each new topic:

1. Read the explanation and worked examples on the topic page together.
2. Do one worksheet page at the easiest setting and check it with the answer sheet right away.
3. Look at the mistakes: the "common mistakes" list on each topic page usually names the misunderstanding.
4. Move to the next difficulty only when a page comes back mostly correct.

Daily practice still matters, but a single page done carefully is worth more at this stage than several pages done quickly.

The roadmap, level by level

Grades 4–6: fractions, decimals and percentages

Fractions come first, then decimals (fractions with denominators of 10 and 100), then percentages, which use both. See the Basic Math 2 overview.

Grades 6–7: Pre-Algebra

Integers (the sign rules for negative numbers) come before the order of operations, because some answers are negative. Ratios and proportions build on equivalent fractions. See the Pre-Algebra overview.

Grades 7–9: Algebra

Two order-of-operations topics lead into variables: combining like terms, the distributive property, and finally solving equations, which uses all of them. See the Algebra overview.

Grades 9–11: Algebra 2

Multiplying polynomials before factoring, and factoring before quadratic equations. Systems of equations, radicals and exponential equations complete the level. See the Algebra 2 overview.

Grades 11–12: Pre-Calculus

Functions first, since composition and inverses appear everywhere; then logarithms, sequences and series, trigonometry and circles. See the Pre-Calculus overview.

Signs that it is time to go back a step

• Slow arithmetic inside a harder topic. If a student understands fractions but is slowed down by multiplication facts, a week of daily times-table pages usually helps more than more fraction worksheets.
• The same mistake on every page. Reread the topic page's explanation, or go back to the topic it builds on: factoring trouble often comes from polynomial multiplication, and equation trouble from combining like terms.
• Frustration. Dropping to an easier setting for a few days rebuilds confidence without losing the daily habit.

The full list of levels and topics is on the Curriculum page.