Probability: 7th grade math in Kruger National Park

Likelihood, experimental and theoretical probability, probability models, compound events and simulations.

Head out on game drives across South Africa’s great savanna, home to the Big Five and hundreds of kinds of birds. Characters here greet you with “Avuxeni!” (good morning in Xitsonga), and eggs hatch into hybrids of animals like lion, leopard, African elephant and African buffalo.

What your child practices

Follows Statistics & Probability — probability (7.SP.C).

• Probability from 0 to 1

  A probability is a number from 0 (impossible) to 1 (certain). Close to 0 is unlikely, 1/2 is as likely as not, close to 1 is likely.

  7.SP.C.5

• Experimental probability and predictions

  Experimental probability = times it happened ÷ number of tries. Multiply it by a number of tries to predict.

  7.SP.C.6

• Theoretical probability

  When all outcomes are equally likely, probability = outcomes that count ÷ all outcomes. Use it to find “not” and to predict.

  7.SP.C.7, 7.SP.C.7a

• Probability models from data

  Data can build a model where outcomes are not equally likely. All the probabilities in a model add up to 1.

  7.SP.C.7b

• Compound events: lists, tables and tree diagrams

  Count the outcomes of several steps by multiplying, and multiply probabilities when two separate things must both happen.

  7.SP.C.8, 7.SP.C.8a, 7.SP.C.8b

• Simulations

  Pick a tool with the same chance as the real event, run many trials, and use the results to estimate a probability.

  7.SP.C.8c

Try a problem from Kruger National Park

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.

• 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: read the scale backwards, turned the fraction upside down and simulated the opposite.

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

• 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: treated close as sure, thought 0 and 1 are not probabilities, treated each kind as equally likely and treated outcomes as equally likely.

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

• 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: compared counts, not fractions, thought decimals are not probabilities, gave a count, not a probability, compared with the misses, compared with the other outcomes and tool with the wrong chance.

  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.

• 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: reused the old count and divided but did not multiply.

  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%.

• 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: predicted the other part, ignored the “not”, predicted the other outcomes, used only one outcome, gave the known part, used only one step and counted “both”, not “at least one”.

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

• 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: multiplied for “or”, added instead of multiplied and added the probabilities.

  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.

• 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 rolls, not trials.

  Try at home: For patterns and sequences, write the first few terms in a table and say what changes each step before jumping to the 20th term.

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