Handling Data 8
Number 15
All should be able to
Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts.
Collect data from a simple experiment and record in a frequency table; estimate probabilities based on this data.
Most should be able to
Use the vocabulary of probability when interpreting the results of an experiment; appreciate that random processes are unpredictable.
Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 p; find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way, using diagrams and tables.
Estimate probabilities from experimental data; understand that:
if an experiment is repeated there may be, and usually will be, different outcomes;
increasing the number of times an experiment is repeated generally leads to better estimates of probability.
Some should be able to
Identify all the mutually exclusive outcomes of an experiment; know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems.
Compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence.
Use fraction notation to express a smaller whole number as a fraction of a larger one; simplify fractions by cancelling all common factors and identify equivalent fractions; convert terminating decimals to fractions. Add and subtract fractions with common denominators; calculate fractions of quantities (whole-number answers); multiply a fraction by an integer. Understand percentage as the number of parts per 100; calculate simple percentages. Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10 10, and quickly derive associated division facts.
Know that a recurring decimal is a fraction; use division to convert a fraction to a decimal; order fractions by writing them with a common denominator or by converting them to decimals. Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction. Interpret percentage as the operator so many hundredths of and express one given number as a percentage of another; use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease. Understand addition and subtraction of fractions; use the laws of arithmetic and inverse operations. Recall known facts, including fraction to decimal conversions; use known facts to derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8. Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages; solve word problems mentally.
Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing. Solve problems involving percentage changes. Use known facts to derive unknown facts. Extend mental methods of calculation, working with factors, powers and roots.
