How to Prepare for Continental Math League (CML)

If your child is sitting the Continental Math League this year, you may be wondering how to prepare for Continental Math League meets without turning every week into homework. The good news is that CML prep is small and steady. Each meet is six problems in thirty minutes, and your child writes every answer in an answer column; there are no choices to pick from. Grades 2 and 3 sit three meets a season, and grades 4 through 9 sit five. So preparing well means three things: reading each problem carefully, writing a clean final answer, and pacing practice across the whole season.

Below you’ll find a meet-by-meet plan for both grade bands, what to practice between meets, the mistakes that cost points, and five original problems with worked solutions. For what CML is and how scoring works, see our parent’s guide to Continental Math League.

What makes CML prep different

Three features of the contest shape the whole plan.

Every answer is written. Every official CML sample paper we checked has the same directions: “Place your answer to each question below in the answer column.” Your child produces the number, day, or pair of values asked for, with no options to check against or work backward from.

The clock is tight but fair. Six problems in 30 minutes is five minutes each: enough to read twice and check, too little to wrestle with one problem for ten minutes and still finish.

It is a season. Grades 2–3 have three meets, running January to March. Grades 4–9 have five, starting in November. Scores add up across the season, so one rough morning decides nothing, and prep can be spread over months.

One more thing is worth knowing before you plan. CML describes its two upper divisions by reading level first: the Euclidean division calls on “average reading comprehension and analytical reasoning,” and the Pythagorean division on “above-average reading comprehension and analytical reasoning.” The official sample papers underline key words such as sum, difference, and only. Reading is part of the test, and it deserves a place in the prep.

Which CML paper will your child sit?

Grades 2 and 3 have no divisions: each grade has one paper, on the same three-meet schedule. CML posts a free sample for each grade, so your child can try the one for their own grade.

Grades 4 through 9 choose between the Euclidean and Pythagorean divisions. The division is chosen at registration, by the school or, for a home-school entry, by you. From the official samples, our read is that Euclidean problems are more direct, while Pythagorean problems pack more steps and more reading into each question. A child who is new to contests, or who reads slowly, will usually have a better first season in Euclidean. Our Euclidean vs Pythagorean guide walks through the choice in more detail.

Our grade-by-grade shortlists explain where CML fits alongside other options: 2nd grade, 3rd grade, 4th grade, 5th grade, and 6th grade.

Start with an official sample meet

Before you plan anything, find out where your child is. CML posts a free sample test “for every grade of every Contest,” linked from the grade pages on cmleague.com. The samples we checked are real past meets, with CML’s step-by-step solutions on the second page.

1. Print the sample for your child’s grade (and division, for grades 4 and up).
2. Set a timer for 30 minutes. Pencil and scratch paper only.
3. Ask your child to write each final answer in the answer column, as they will on meet day.
4. Mark it with the solutions page.
5. For every miss, write one of four labels next to it: misread, slip (a calculation error), didn’t know how, or ran out of time.

The labels matter more than the score. In our experience, children new to CML lose more points to “misread” and “slip” than to “didn’t know how,” and those two are the cheapest to fix. As a rough guide (ours, not an official scale): two or fewer correct, focus the fall on reading and basic problem types; three or four, follow the plan below as written; five or six, add more timed meets and harder problems.

A meet-by-meet season plan

Exact dates for this season are in the dates and deadlines table. The shape of the plan is the same every year. Meets fall roughly a month apart, and each month follows the same four-week cycle:

• Week 1: review the last meet. Go through every problem your child missed using the step-by-step solutions. This is the most useful half hour of the month.
• Weeks 2 and 3: skills. Two or three short sessions a week (15 to 20 minutes, three or four problems each), focused on the problem types from the mistake log.
• Week 4: one practice meet. Six problems, 30 minutes, timed, then marked together. Keep the rest of the week light.

When a school runs the team, CML provides the answer keys and step-by-step solutions to the school, which proctors and grades the meet. It’s reasonable to ask the teacher whether you can see the solutions or your child’s paper afterward.

Grades 4–9: five meets, November to March

September and October (before Meet 1). Run the diagnostic, then three 20-minute sessions a week. Spend the first few weeks on reading habits (see below) and on the problem types from the sample paper. In late October, do one full practice meet.

Meet 1 to Meet 2 (November). Use the four-week cycle. This is the most important month of the season: your child has seen a real meet, and its mistakes show you what to work on.

Meet 2 to Meet 3 (December). Winter break falls in this gap. Two short sessions a week is plenty, plus one timed practice meet before school starts again.

Meet 3 to Meet 5 (January to March). Keep the cycle. By now the mistake log usually shows one or two repeat patterns, often the same reading slip, so give those the skill weeks. Before Meet 5, add a second practice meet if your child is enjoying them. After Meet 5, talk about what went well and put the log away until next fall.

Grades 2–3: three meets, January to March

October to December. Start gently: two 15-minute sessions a week, two or three problems each, untimed and talked through out loud. The goal is getting used to problems that take more reading than classwork does, such as made-up symbols, digit puzzles, and money problems. In December, try one timed practice meet so the 30 minutes isn’t a surprise.

Meet 1 (January) to Meet 2 (February). Use the four-week cycle with shorter sessions. For a 7- or 8-year-old, three problems in 15 minutes is a good session.

Meet 2 (February) to Meet 3 (March). Keep it the same, and resist adding more before the last meet. A child who finishes still liking the problems is set up for five meets in grade 4.

How much time is enough?

For most children in grades 2 to 6, 45 to 60 minutes a week is enough: three 15- to 20-minute sessions. If practice starts to feel like a chore, shorten sessions before you drop any.

What to practice between meets

CML’s official sample papers for grade 2, grade 3, and grade 5, together with the kinds of problems we see in contests at this level, fall into a handful of types. Here is how we group them (the grouping is ours):

1. Made-up rules. A symbol is defined (“a @ b means…”) with an example, and your child applies it. The skill is following the rule exactly.
2. Digit puzzles. Letters stand for digits in an addition or subtraction, or a number is described by clues about its digits.
3. Money and coins. Combinations of coins that make a total, often with a condition like “at least one of each.”
4. Remainders and calendars. What day of the week it will be in 50 days, or which numbers leave a remainder of 2.
5. Measurement and units. Chains of conversions (tablespoons to cups to quarts) and map scales.
6. Sum and difference. Two numbers with a known total and a known gap.
7. Counting. Organized lists, “in how many ways,” and seating positions.
8. Working backward. A story that ends with a known amount, and a question about the start.

In a skill week, pick one or two types from the mistake log, do three or four problems of each, and finish with one mixed problem so your child practices spotting the type as well as solving it.

Keep a mistake log. One page in a notebook. For every missed problem, write the date, the type (from the list above), and the label (misread, slip, didn’t know how, ran out of time). After two meets you’ll see patterns that no score report shows.

Writing it down: the habits CML rewards

The answer column is what gets checked against CML’s answer key, and scratch work is how your child catches their own mistakes before it does. Build these habits one at a time.

Read the question twice, and the last sentence three times. The last sentence says what to write in the column. Have your child underline or circle what it asks for: the sum, the larger number, how many more. CML often underlines these words itself, a sign of how much they matter.

Write something for every problem. A short list, a small table, a sketch of a number line. Written steps are easier to check than mental math, and they make “slip” mistakes visible when you review the paper together afterward.

Answer the question that was asked. Before writing in the column, ask: “Is this the number they wanted, or a number I found on the way?” In our experience, this one question saves a lot of lost points.

Follow the answer instructions. Some official problems say “express in simplest form,” so 12/16 would need to become 3/4. Some ask for two answers; on the official grade 5 Pythagorean sample, the solutions note “Both answers must be correct to receive credit.” If a blank has a unit printed next to it, the answer is in that unit.

Copy carefully into the column. It sounds too obvious to practice, but children do copy 38 as 83 under time pressure. At home, have your child point at the scratch-paper answer, then at the column, and say the number out loud.

Common mistakes on written-answer contests

• Stopping at a middle step. The problem asks for the total, and the child writes one part. On a multiple-choice paper, the missing answer choice might have caught it. On CML, nothing does.
• Skipping the small words. Only, each, at least, different, altogether. One skipped word changes the problem.
• Ignoring the answer instructions: an unsimplified fraction, one answer where two were asked for, or cups when the question wanted tablespoons.
• Spending ten minutes on one problem. With five minutes each, one stubborn problem can cost two others.

How to use practice meets

A practice meet is six problems in 30 minutes, run like the real thing. Use one a month, and always follow it with a review.

Where to find practice meets:

• Official CML sample tests (free). One for every grade and division, with CML’s own solutions. Use one for the diagnostic and save another for later in the season.
• Our free CML practice problems. Two full practice meets (one for grades 2–3 and one for grades 4–6), each six problems with worked solutions. All original.
• Best of CML books (paid). CML’s own books (price in the table below).
• Our CML prep guide for grades 2–6 (paid). Strategies by topic, original practice problems, full practice meets, and step-by-step solutions. There’s a free sample if you want to look first.

How to run one at home: quiet table, visible timer, answer column on the right. Say nothing for 30 minutes. Afterward, let your child explain each answer before you reveal whether it’s right; the explaining is where the learning happens.

What to do with the result: add every miss to the mistake log, with its label. Then pick one problem your child almost got and redo it together the next day. Near misses teach more than problems that were far out of reach.

Five original CML-style practice problems

These are our own problems, written in the style of CML meets. Have your child try each one with a pencil and write a final answer before reading the solution.

Problem 1 (Grades 2–3): The sticker count

Sam has 12 stickers. Leo has 4 fewer stickers than Sam. Maya has 3 more stickers than Leo. How many stickers do Maya and Leo have altogether?

Answer: 19.

Solution. Leo has 12 − 4 = 8 stickers. Maya has 8 + 3 = 11 stickers. Together they have 8 + 11 = 19.

What it teaches: stopping at a middle step. Many children find Maya’s 11 stickers and write 11. The word altogether asks for one more step.

Problem 2 (Grades 2–3): The mystery number

I am a two-digit number. My tens digit is 3 more than my ones digit. My two digits add up to 11. What number am I?

Answer: 74.

Solution. Try ones digits in order and check both clues. If the ones digit is 1, the tens digit is 4, and 4 + 1 = 5, too small. Each step up adds 2 to the digit sum: ones digit 2 gives 52 (sum 7), 3 gives 63 (sum 9), 4 gives 74 (sum 11). The number is 74.

What it teaches: an organized list beats guessing, and it shows the pattern (the sum grows by 2 each time), so a child can see there is only one answer.

Problem 3 (Grades 4–6): Two answers

Find all the whole numbers greater than 20 and less than 50 that leave a remainder of 2 when divided by 4 and also leave a remainder of 2 when divided by 6.

Answer: 26 and 38.

Solution. If a number leaves a remainder of 2 when divided by both 4 and 6, then subtracting 2 gives a number divisible by both 4 and 6, which means a multiple of 12. Multiples of 12 are 12, 24, 36, 48, and adding 2 gives 14, 26, 38, 50. Greater than 20 and less than 50, that leaves 26 and 38. Check: 26 = 4 × 6 + 2 = 6 × 4 + 2, and 38 = 4 × 9 + 2 = 6 × 6 + 2.

What it teaches: the word all. A child who finds 26 and stops has half an answer. It also rewards reading the range carefully: 50 fits the remainders but is not less than 50.

Problem 4 (Grades 4–6): Working backward

Jada spent half of her money on a book. Then she spent $4 on lunch. Then she spent half of what was left on a gift. She had $7 left. How much money did Jada start with?

Answer: $36.

Solution. Undo each step, starting from the end. Before the gift, she had twice $7, which is $14. Before lunch, she had $14 + $4 = $18. Before the book, she had twice $18, which is $36. Check forward: $36, half is $18, minus $4 is $14, half is $7.

What it teaches: working backward, and checking forward. Writing the four amounts in a row ($36, $18, $14, $7) takes ten seconds and catches almost every slip.

Problem 5 (Grades 5–6): The water tank

A water tank is 2/3 full. After 12 liters are used, the tank is 1/2 full. How many liters does the tank hold when it is completely full?

Answer: 72 liters.

Solution. The 12 liters used are the difference between 2/3 of the tank and 1/2 of the tank. In sixths, that is 4/6 − 3/6 = 1/6. So 12 liters is one sixth of the tank, and the full tank holds 6 × 12 = 72 liters. Check: 2/3 of 72 is 48, and 48 − 12 = 36, which is half of 72.

What it teaches: answering the question that was asked. A child who finds that the tank ends with 36 liters, or that it started with 48, has done good work and written the wrong number.

Pacing on meet day

Five minutes a problem is only an average. A simple plan that works for most children:

1. First pass (about 20 minutes). Go through all six problems in order. If one hasn’t started to make sense after about three minutes, circle it and move on.
2. Second pass (about 7 minutes). Go back to the circled problems.
3. Last 3 minutes. Stop solving. Check that every answer in the column matches the scratch work, is in the form the question asked for, and has both parts where two were asked for.

Rehearse this routine in the monthly practice meets. The school runs the meet itself, so ask the teacher about details like scratch paper.

Supporting your child through a season

• Review each meet within a week, while your child still remembers the problems. Scores are entered on CML’s website after each meet, and results can be viewed online.
• Notice progress on the labels. Fewer “misread” marks from November to February is real progress, even if the score stays flat because the problems got harder.
• Keep the stakes low. Every child can sit every meet, and only a school team’s top six scores make up the team score, so no single child carries the team.
• Accommodations apply. CML asks schools to allow the accommodations in a student’s plan, as for other standardized tests. If your child has an IEP or 504 plan, mention it to the teacher.

Dates and deadlines

As of September 2026, from the official Continental Mathematics League site. Confirm on cmleague.com before you rely on a date or price.

Schools are asked to give each meet as close to the scheduled date as possible, so your child’s meet may fall a few days either side. To enter as a home-school student, create an account on cmleague.com without buying anything, then email support@cmleague.com to have the reduced pricing added before you purchase. Our parent’s guide walks through those steps.

Frequently asked questions

How many meets are in a CML season? It depends on the grade. Grades 2 and 3 have three meets; grades 4 through 9 have five. Each meet is six problems in 30 minutes.

Is CML multiple choice? No. Students write each answer in an answer column. That’s why reading carefully and writing a clean final answer matter so much in prep.

My child’s school doesn’t do CML. Can they still take part? Yes. CML’s home-school option is for any student whose school doesn’t take part, at a reduced per-child fee. The steps are in the table notes above and in our parent’s guide.

This guide is not affiliated with or endorsed by Continental Mathematics League. “Continental Mathematics League” is a trademark of its respective owners.

Where to go from here

This week, print the official sample for your child’s grade and run it as a 30-minute diagnostic. Label the misses, start a mistake log, and set up three short sessions a week until the first meet. When you want more practice meets, our free CML practice problems have two full sets with solutions, and our CML prep guide for grades 2–6 adds strategies, full practice meets, and step-by-step solutions.