Fractions: 3rd grade math in Madagascar

Unit fractions, fractions on a number line, equivalent fractions, comparing, and adding related fractions.

Leap with lemurs on the Great Red Island, where most animals live nowhere else on Earth. Characters here greet you with “Salama!” (hello in Malagasy), and eggs hatch into hybrids of animals like ring-tailed lemur, Verreaux's sifaka, diademed sifaka and indri.

What your child practices

Follows Number & Operations — Fractions (3.NF).

• Unit fractions and parts of a whole

  Cut a rice cake into 4 equal pieces: each piece is 1/4, and 3 pieces are 3/4.

  3.NF.A.1, 3.G.A.2

• Fractions on a number line

  Split the space from 0 to 1 into equal jumps. Each jump is a unit fraction, like 1/4.

  3.NF.A.2

• Equivalent fractions

  1/2 of a field is the same as 2/4 of it: multiply the top and bottom by the same number.

  3.NF.A.3a, 3.NF.A.3b

• Simplest form

  6/8 of the eggs is 3/4 of them: divide the top and bottom by the same number until you can’t.

  3.NF.A.3b

• Whole numbers as fractions

  3 whole meters is 12 pieces of 1/4 meter, so 3 = 12/4. And 4/4 is 1 whole.

  3.NF.A.3c

• Comparing and ordering fractions

  Same top number? Bigger pieces win. Same bottom number? More pieces win. Or check against 1/2.

  3.NF.A.3d

• Adding and subtracting related fractions

  Halves and fourths are related: rename 1/2 as 2/4, then add 2/4 + 1/4 = 3/4.

  5.NF.A.1

Try a problem from Madagascar

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.

• 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: swapped the top and bottom numbers, put the other parts on the bottom, counted the wrong parts, wrote how many parts, not one part, counted the cuts, not the pieces, forgot the parts must be equal, used the whole line as one whole, added instead of multiplying, changed only one number, stopped before simplest form, divided only one number, took away instead of dividing, counted meters, not planks, counted one whole only, counted pieces, not wholes, thought a bigger bottom number means a bigger fraction, thought the same top number means equal, thought the same bottom number means equal, looked only at the top numbers, looked only at the size of the pieces, added (or took away) the tops and the bottoms and changed the bottom number but not the top.

  Try at home: Use a chocolate bar or paper strips to compare fractions: is 1/3 or 1/5 bigger? Line up fraction strips to find equal ones (2/4 = 1/2).

• 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 tick marks, not spaces and counted the 0 mark as a jump.

  Try at home: Draw a number line and hop along it in 2s, 5s or 10s. For “posts and gaps” questions, sketch 3 posts and count the gaps before doing the big number.

• 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: Read a word problem together and draw it as a quick picture or bar before choosing + − × ÷. Ask “is the answer bigger or smaller than the numbers we started with?”

More Grade 3 worlds: Numbers to 10,000 · Multiplication & Division · Area, Perimeter & Shapes · Measuring & Graphs · Time & Money