Proportions & Percent: 7th grade math in The Namib Desert

Unit rates with fractions, proportional relationships, the constant of proportionality, and percent problems: discounts, tax, tips, interest and percent error.

Scout the oldest desert on Earth, where red dunes meet a foggy ocean and elephants walk dry riverbeds. Characters here greet you with “Moro!” (hello in Otjiherero), and eggs hatch into hybrids of animals like gemsbok, springbok, Hartmann’s mountain zebra and klipspringer.

What your child practices

Follows Ratios & Proportional Relationships (7.RP).

• Unit rates with fractions

  Find how much for one whole unit when both amounts are fractions, by dividing one fraction by the other.

  7.RP.A.1

• Proportional relationships

  Use a unit rate to scale a proportional relationship, and write it as an equation y = kx.

  7.RP.A.2, 7.RP.A.2c

• The constant of proportionality in tables, graphs and equations

  Find k = y ÷ x from a table or a graph, tell whether a table is proportional, and read the point (1, k).

  7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2d

• Percent of a quantity

  Find a percent of an amount, the whole from a part, and what percent one amount is of another.

  7.RP.A.3

• Discounts, markups, tax and tips

  Find sale prices, marked-up prices, prices with tax, and tips, by taking a percent of a price.

  7.RP.A.3

• Simple interest and commission

  Simple interest is a percent of the savings each year; a commission is a percent of the sales.

  7.RP.A.3

• Percent increase, decrease and error

  Compare a change, or the error of an estimate, to the starting or real amount, as a percent.

  7.RP.A.3

Try a problem from The Namib Desert

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.

• 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: multiplied the two fractions and went the wrong way.

  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.

• 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: divided the wrong way, found x ÷ y instead of y ÷ x and divided the whole by the part.

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

• 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: flipped the wrong fraction and used the percent as the amount.

  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.

• 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: added instead of scaling the ratio, used the unit rate upside down, used a total as the constant, used the change between two rows, subtracted instead of dividing, thought x must go up in equal steps, thought "both go up" means proportional, divided by the percent, took the percent of the part, used the percent as dollars, combined the two percents into one, found only one year of interest, gave the change, not the percent, divided by the new amount, gave the new amount as a percent and divided by the estimate.

  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%.

• 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: stopped at the unit rate, found the other part, stopped at the amount of change, gave the total instead of the part, forgot the second step, gave only the interest and found the part that is left.

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

More Grade 7 worlds: Rational Numbers · Expressions & Equations · Scale, Angles & Solids · Sampling & Comparing Data · Probability