Fractions: 2nd grade math in Patagonia

Halves, thirds and fourths, naming fractions, comparing fractions, and adding like fractions.

Ride with gauchos across the windy steppe, past blue glaciers and the granite towers of Torres del Paine. Characters here greet you with “Mari mari!” (hello in Mapudungun, the Mapuche language), and eggs hatch into hybrids of animals like guanaco, huemul, southern pudú and puma.

What your child practices

Follows Geometry — Equal Shares (2.G.A.3), plus fractions of a whole (Singapore P2).

• Halves, thirds and fourths

  Cut a loaf into 3 equal pieces: each piece is one third. The pieces must be the same size.

  2.G.A.3

• Naming fractions

  A blanket has 5 equal stripes and 2 are red: 2/5 of the blanket is red. The bottom number counts all the parts.

  3.NF.A.1

• Fractions that make a whole

  All the pieces make one whole: 6/6 = 1. If 2/6 of a pie is eaten, 4/6 is left to make the whole.

  3.NF.A.3c

• Comparing unit fractions

  1/3 of a pie is more than 1/8 of it: the fewer the pieces, the bigger each piece.

  3.NF.A.3d

• Comparing like fractions

  5/8 of a blanket is more than 3/8 of it: the pieces are the same size, so more pieces is more.

  3.NF.A.3d

• Adding and subtracting like fractions

  2/6 + 3/6 = 5/6: the pieces are the same size, so add the top numbers and keep the bottom number.

  4.NF.B.3a

Try a problem from Patagonia

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.

• Counting and sequences

  Losing track while counting: off by one, skipping or double-counting, or counting the wrong things (fence posts instead of gaps).

  Mistakes we catch: counted the cuts, not the pieces.

  Try at home: Count objects by touching or moving each one into a pile. Count on from a number other than 1 (“start at 8 and count 5 more”), and count back too.

• 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: gave how many parts, not the name of one part, forgot the parts must be equal, thought equal parts must look the same, swapped the top and bottom numbers, put the other parts on the bottom, counted the wrong parts, thought one piece is the whole, counted pieces, not wholes, gave the part already there, left out the bottom number, thought a bigger bottom number means a bigger fraction, thought the same top number means equal, thought fewer pieces is more, thought the same bottom number means equal and added the bottom numbers too.

  Try at home: Fold paper or cut a sandwich into 2 and 4 equal parts. Ask which is bigger, a half or a quarter, and why the parts must be equal.

• 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 when it should take away (or the other way round).

  Try at home: Act out word problems with toys: “3 birds, 2 fly away.” Ask “are we putting together or taking away?” before any numbers.

• 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 away from the whole.

  Try at home: Read the question aloud together and ask “what are we trying to find?” before solving. Point at the question part of the sentence.

More Grade 2 worlds: Numbers to 1,000 · Adding & Subtracting to 1,000 · Multiplication & Division · Measuring & Graphs · Time, Money & Shapes