Factors & Patterns: 4th grade math in The Andes and Patagonia

Times-as-many comparisons, multi-step word problems, factors, multiples and patterns.

Herd alpacas past Machu Picchu, sail reed boats on Lake Titicaca and watch condors soar over Patagonia. Characters here greet you with “Allillanchu!” (hello in Quechua), and eggs hatch into hybrids of animals like llama, alpaca, vicuña and guanaco.

What your child practices

Follows Operations & Algebraic Thinking (4.OA).

• Times as Many

  Compare amounts with "times as many": find the bigger amount, the smaller amount, or how many times.

  4.OA.A.1, 4.OA.A.2

• Multi-Step Word Problems

  Solve story problems with up to three steps, decide what a remainder means, and check answers make sense.

  4.OA.A.3

• Factors

  Check if a number is a factor, list all the factors of a number up to 100, and find common factors.

  4.OA.B.4

• Multiples

  See how factors and multiples go together, list multiples, and find common multiples.

  4.OA.B.4

• Prime and Composite

  Decide whether a whole number from 1 to 100 is prime, composite, or neither.

  4.OA.B.4

• Number Patterns

  Follow a rule to continue number and shape patterns, and spot features like odd and even.

  4.OA.C.5

Try a problem from The Andes and 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.

• 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: times as many read as more, subtracted to compare, wrong operation and added instead of multiplied.

  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?”

• 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: multiplied the wrong way.

  Try at home: For subtraction, read the top number first every time (“52 take away 37”). For division, say “how many 4s fit in 20?” so the order is clear.

• 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: found the total instead, stopped too early, dropped the remainder and counted a part group as full.

  Try at home: Before solving, ask them to finish the sentence “The answer will be the number of …”. After solving, check that the answer fits that sentence.

• Place value

  The digits are right but their places are not: a 3 in the tens is worth 30, not 3. This shows up when carrying, borrowing, lining up numbers or placing a decimal point.

  Mistakes we catch: did not check the size and stepped in the wrong place.

  Try at home: Write a number on paper with a column for thousands, hundreds, tens and ones. Take turns saying what each digit is worth, then add or subtract by trading between columns out loud ("ten ones make a ten").

• 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: did not check the division, mixed up factor and multiple, forgot 1 and the number itself, counted pairs, not factors, factor of only one number, judged by the last digit, multiple of only one number, odd means prime, 2 is not prime, 1 is prime or composite, missed a factor, saw a factor that is not there and forgot the starting amount.

  Try at home: Write puzzles like 7 + ? = 12 and ? × 4 = 20. Talk about the equals sign as a balance, not “the answer is”.

• 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: off by one multiple, went the wrong way, one step too many and missed the odd and even pattern.

  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.

More Grade 4 worlds: Big Numbers · Fractions · Measurement & Data · Lines, Angles & Shapes · Decimals