Students represent finite sample spaces with organized lists and tree diagrams, determine theoretical probabilities from equally likely outcomes and experimental probabilities from relative frequencies, and express, compare, and interpret probabilities as fractions, decimals, and percents, including complements and expected variation across repeated trials. They calculate sale prices by applying a discount percentage, calculate taxes and tips as percentage increases to a stated base or recover an original amount when appropriate, and compare values using unit prices with equivalent units and monetary amounts rounded to cents. They create and evaluate simple budgets by organizing income, savings, and fixed or variable expenses, calculating spending percentages, and determining whether allocations produce a surplus or deficit without using compound interest, credit charges, taxes, or investment decisions.
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These adaptive units introduce, teach, or reinforce skills in this group (Probability and Financial Literacy) through scaffolded problems that grow in difficulty as concepts are understood.