Expressions & Equations: 7th grade math in Sumatra

Combining like terms, expanding and factoring, multi-step problems, two-step equations and inequalities.

Trek into the steaming rainforest of Sumatra, the last place where tigers, rhinos, elephants and orangutans share one forest. Characters here greet you with “Horas!” (hello in Batak, around Lake Toba), and eggs hatch into hybrids of animals like Sumatran orangutan, siamang, Sunda colugo and flying dragon lizard.

What your child practices

Follows Expressions & Equations (7.EE).

• Combining like terms

  Add and subtract terms with the same letter, including negative and decimal coefficients.

  7.EE.A.1

• Expanding and factoring

  Multiply out brackets, including negative numbers outside, and take out the greatest common factor.

  7.EE.A.1

• Rewriting expressions to see the problem

  See that “grow by 20%” is 1.2x, “lose 15%” is 0.85x, and that brackets can be multiplied out.

  7.EE.A.2

• Multi-step problems with estimates

  Solve problems with fractions, decimals and percents in several steps, and check with an estimate.

  7.EE.B.3

• Two-step equations

  Solve equations like 3x + 7 = 31 and 4(x + 2) = 36 by undoing each step in reverse order.

  7.EE.B.4, 7.EE.B.4a

• Equation word problems

  Write an equation like px + q = r or p(x + q) = r for a story and solve it.

  7.EE.B.4a

• Two-step inequalities

  Solve inequalities like 3x + 5 ≤ 26, flip the sign when dividing by a negative, and read the answer in context.

  7.EE.B.4b

Try a problem from Sumatra

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.

• Expressions and equations

  Order of operations, unknowns and the equals sign: reading “=” as “the answer comes next” instead of “both sides balance”.

  Mistakes we catch: combined unlike terms, lost the minus sign, forgot x means 1x, adding made a power, multiplied only one term, sign error, divided only one term, not the greatest factor, read x/4 as 4x, multiplied instead of divided, added instead of subtracting, did the operation again, undid the steps in the wrong order, forgot the last step, undid with the wrong operation, left out the fixed part, added the fixed part, forgot to divide and included or left out the edge.

  Try at home: Write “mystery number” riddles for each other (“I double it and add 3, I get 17”). Solve by undoing the steps, last one 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: wrote only the change and went the wrong way.

  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%.

• 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: used the percent as a number and wrote 1/4 as 0.4.

  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.

• 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: took the part of the whole, not the rest, stopped after one step, answered the other part and rounded the wrong way.

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

• 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: took away only one length.

  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.

• 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: sign the wrong way.

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

• Negative numbers

  Numbers below zero: comparing them (−5 is smaller than −2), counting across zero on a number line, and sign rules.

  Mistakes we catch: forgot to flip the sign.

  Try at home: Track a bank balance or a temperature over a week with ups and downs, including below zero. Compare which day was coldest.

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