Rational Numbers: 7th grade math in Iceland

Adding, subtracting, multiplying and dividing positive and negative numbers, fractions as decimals, and rational number word problems.

Explore the land of fire and ice, where volcanoes rumble under glaciers and puffins nest on sea cliffs. Characters here greet you with “Góðan daginn!” (good day in Icelandic), and eggs hatch into hybrids of animals like Arctic fox, rock ptarmigan, Atlantic puffin and razorbill.

What your child practices

Follows The Number System (7.NS).

• Adding and subtracting positive and negative numbers

  Add a positive number to move up, a negative one to move down, and land at 0 when opposites meet.

  7.NS.A.1, 7.NS.A.1b

• Distance between rational numbers

  The distance between two numbers on a number line is their difference: b − (−a) = b + a across zero.

  7.NS.A.1, 7.NS.A.1c

• Multiplying and dividing positive and negative numbers

  A negative times a positive is negative, a negative times a negative is positive, and division follows the same rules.

  7.NS.A.2, 7.NS.A.2a, 7.NS.A.2b

• Fractions as terminating and repeating decimals

  Divide the top by the bottom: the decimal either ends or repeats a block of digits forever.

  7.NS.A.2d

• Order of operations with rational numbers

  Brackets first, then × and ÷, then + and −, keeping track of every minus sign.

  7.NS.A.3

• Rational number word problems

  Solve real problems with positive and negative fractions and decimals in more than one step.

  7.NS.A.3

Try a problem from Iceland

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.

• 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: moved the wrong way, ignored the minus sign, gave the answer the wrong sign, lost the minus sign, measured only one side of zero, added two numbers on the same side of zero, subtracted in the wrong order, got the sign of the product or quotient wrong, thought where the minus sign sits changes the value and lost a minus 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.

• 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: added instead of multiplying and multiplied instead of dividing.

  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 and divided the bottom by the top.

  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: wrote the top and bottom as digits, stopped dividing too soon and repeated the wrong digits.

  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.

• 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: worked left to right and ignored the brackets.

  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.

• 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: used only one step.

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

• Graphs and data

  Reading graphs: missing that one picture stands for several, misreading the scale, or mixing up mean, median and range.

  Mistakes we catch: gave the total, not the mean.

  Try at home: Collect real numbers (bedtimes, scores) and find the mean, median and range together. Ask which one best describes “a typical day”.

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