Ratios, Rates & Percent: 6th grade math in Mongolia and the Gobi

Ratios, ratio tables, unit rates and speed, sharing in a ratio, and percents.

Ride across the Land of the Blue Sky, where camels cross singing dunes and wild horses run free. Characters here greet you with “Sain baina uu!” (hello in Mongolian), and eggs hatch into hybrids of animals like Bactrian camel, Przewalski’s horse, khulan and goitered gazelle.

What your child practices

Follows Ratios & Proportional Relationships (6.RP), plus speed (Singapore P6).

• Ratios and ratio language

  Write ratios in simplest form, turn a ratio into a fraction, and say how many times as large one amount is.

  6.RP.A.1

• Equivalent ratios and ratio tables

  Fill in ratio tables by multiplying or dividing both quantities by the same number.

  6.RP.A.3a

• Ratio and rate reasoning

  Scale a ratio rule up, find a unit rate, and write one quantity as a fraction of another.

  6.RP.A.3, 6.RP.A.3b

• Sharing in a ratio

  Use units to share a total in a ratio, find the whole from one part, and combine two ratios.

  6.RP.A.3

• Unit rates and speed

  Find unit rates, use distance = speed × time, and change speeds between km/h, m/min, m/s and cm/s.

  6.RP.A.2, 6.RP.A.3b

• Speed word problems

  Solve trips in up to 3 steps: average speed is the total distance ÷ the total time.

  6.RP.A.3b

• Percent of a number and finding the whole

  Find a percent of a number, the percent one number is of another, and the whole from a part and its percent.

  6.RP.A.3c

• Percentage increase and decrease

  Find the percent a quantity went up or down by, and the new amount after a percent change.

  7.RP.A.3

Try a problem from Mongolia and the Gobi

Every problem is a short story set in the world. These are real problems from the game. Kids get endless new ones with different numbers.

Common mistakes, and how to help

Every wrong answer in Mixmonde is planned: it points to a named mistake, and the tip after a miss explains it with that problem’s numbers. These are the mistakes this world watches for, grouped the way the grown-ups’ dashboard shows them.

• Order and direction

  The right idea done the wrong way round: taking the smaller digit from the bigger one, dividing backwards, swapping x and y, or flipping more and less.

  Mistakes we catch: wrote the ratio in the wrong order, wrote the fraction upside down, swapped the two quantities, used the ratio upside down, divided the wrong way and changed in the wrong direction.

  Try at home: For ratios and coordinates, write labels on the numbers (“birds : eggs”, “across, then up”) and check the order matches the question.

• Ratio and scaling

  Adding when the situation multiplies: doubling a recipe by adding 2 to each amount, or taking a percent of the wrong total.

  Mistakes we catch: did not fully simplify, compared a part to the whole, added the same amount to both, multiplied only one term, added instead of scaling the ratio, skipped the unit rate, treated one part as the whole, joined two ratios without matching them, averaged the two speeds, divided by the percent, took the percent of the part, used the change as the percent, compared to the new amount and gave the new amount as a percent of the old.

  Try at home: Compare prices at the shop per item or per 100 g. For percents, always ask “percent of what?” and start from 10% and 1%.

• Choosing the operation

  The arithmetic is fine, but the wrong operation was picked: adding when the story takes away, or multiplying when it shares out.

  Mistakes we catch: found the difference instead of how many times and used the wrong operation.

  Try at home: Have them say the plan in words first (“share 48 into groups of 6, so divide”). Swap in easy numbers to see which operation makes sense, then use the real ones.

• Reading the question

  The math works, but the answer is to a different question: a number already given, a halfway step, or only part of a two-step problem.

  Mistakes we catch: gave the number of groups as the answer, stopped at the number of groups, found the other part, stopped at one unit, left out a step, found the rest instead of the part, stopped at 1%, mixed up the two parts and stopped at the change.

  Try at home: Underline what the question asks for and list the steps (“first find …, then …”). Tick each step off before giving the answer.

• Fractions and decimals

  Treating the top and bottom of a fraction as two separate whole numbers (so 1/2 + 1/3 = 2/5), thinking a bigger bottom number means a bigger piece, or reading 0.25 as bigger than 0.3.

  Mistakes we catch: compared to the total instead and used the part as the percent.

  Try at home: Put fractions and decimals on one number line from 0 to 1 (0.3, 1/4, 0.25, 1/2). For adding, cut both into the same size pieces first.

• Units and measuring

  The number is fine but the unit is off: a missing conversion (cm and m), the ruler not started at zero, or area mixed up with perimeter.

  Mistakes we catch: changed only one of the units, converted the wrong way and used minutes as if they were hours.

  Try at home: Before converting, ask whether the answer should be a bigger or smaller number. Fill a box with cubes to feel why volume uses cubic units.

More Grade 6 worlds: Fractions, Decimals & Factors · Negative Numbers & Coordinates · Expressions & Equations · Area, Volume & Circles · Statistics