INVESTIGATION MATHEMATICS Level 4 The top places to live Strands Topics Number Number concepts Chance and Data Data Space Location, direction and movement Outcomes N 4.1, CD 4.2, S 4.2 Investigation The editor of a travel magazine wants to include an article about the best countries to live in. Your job is to present information that compares the standard of living in with that of three other countries on three different continents. Use a variety of methods including data displays, data analyses and maps to support your conclusions. Overview The following table shows how this investigation is organised in phases associated with thinking, reasoning and working mathematically. Thinking, reasoning and working mathematically 7 1. Identifying and describing 2. Understanding and applying 3. Communicating and justifying Discussing standards of living Students: discuss and define ‘standard of living’ discuss the standard of living in and compare it to other countries. Unpacking the investigation Students: discuss and clarify the requirements of the investigation identify prior mathematical knowledge about number, collecting data and using maps that may assist in carrying out the investigation choose countries to investigate and identify features of the standards of living about which they intend to collect statistical information. Understanding data collection Students: revise data-collection methods, and data displays Understanding number concepts Students: revise relevant number concepts Gathering information from maps Students: revise how to use conventions of maps to extract information Conducting the investigation Students: research, gather and record relevant data about the standards of living in three countries use maps to identify relevant information draw conclusions about the standards of living in their chosen countries compared to that of . Presenting conclusions Students: present their conclusions and describe the procedures and strategies used compare their findings with other students’ findings about the same countries and review their conclusions. Creating the ‘top countries’ list Students: compare statistical information of all countries researched and order countries according to agreed criteria identify the top countries according to the ordering of the data. Reflecting on the learning Students: consider the new learning that has occurred and relate their findings to their own situation.
new learning and look for opportunities to apply the learning. Core content Core content in black text only is included in this investigation. Number — Number concepts: Level 4 Chance and Data — Data: Level 4 Space — Location, direction and movement: Level 4 Numeration whole numbers decimal fractions key percentages (100%, 50%, 25%, 20%, 10%, 1%) fractions common fraction format terms (vinculum, numerator, denominator) decimal fraction format percentage format equivalence square and cubic notation Number sense position and order of numbers relationships between numbers sensible adjustments of numbers connections between key percentages, unit fractions and decimal fractions everyday representations of numbers (e.g. 20K/20 000, $1.5m/$1.5 million, $3b/$3 billion subsets of numbers prime and composite square triangular Money financial decisions purchases (best buys, discounts) advertising (for purchases) methods of payment budgets for specific events key percentages simple interest discounts cashless transactions (e.g. cheques, money orders, EFTPOS, store cards) Collecting and handling data plans and methods for data collection design of data record templates data entry into spreadsheets extraction of data from existing data sources classify data check data discrete data categorical data count data continuous data Exploring and presenting data displays pie charts bar graphs dot-plots line graphs two-way tables lists Identifying and interpreting variation features of data measures of location (central tendency) mean median mode (for discrete data) limitations of measures of location Location and movement conventions simple scale on maps (linear form or 1 cm:1 km) coordinates grid references movement between grid reference points latitude and longitude key lines of reference (prime meridian, equator) polar limits maps flat maps globes maps plans (e.g. shopping centre) Direction and angle eight compass points (N, NE, E, SE, S, SW, W, NW) connection between the eight compass points and the amount of turn angle as a difference in direction estimation and measurement of angles in degrees Resources internet (e.g. Australian Bureau of Statistics)