: Number Topic: Addition and subtraction Foundation Level: Level statement Students are developing a notion of counting and an awareness of number and money. Number names are becoming more meaningful. Example learning outcomes: Students show an awareness of ‘more’, ‘less’ and ‘same’ in life situations. Elaborations — To support investigations that emphasise thinking, reasoning and working mathematically Students know: ‘more’ means adding some to a collection ‘same’ means collections match everyday language that relates to ‘more’ (adding on) and ‘taking away’ (items covered or removed from a collection). Students may: participate in familiar songs and games that involve adding more to a collection and taking away one or some notice/request ‘more’ in familiar situations (e.g. serving food or drinks, sharing toys or stickers) notice when one person is given ‘more’ of something than another person indicate that one collection has ‘more’ when two collections have significantly different quantities notice/request ‘same’ in familiar situations (e.g. serving food or drinks, sharing toys or stickers) indicate that two collections have the ‘same’ quantity by matching items one to one notice that when two collections are significantly different in quantity they are ‘not the same’ indicate ‘take away’ by covering or removing objects from a collection in familiar situations.
Level 1: Level statement Students are developing a sense of number by knowing number names and counting in sequence. They recognise, compare, order and represent small whole numbers and use concrete materials to explore the concept of parts of a whole. They are developing an awareness of the cost of goods and recognise and represent notes and coins. Students identify and distinguish between situations that require them to add or subtract, to share equally or to create equal groups. Core learning outcome: N 1.2 Students identify and solve addition and subtraction problems involving small whole numbers. Elaborations — To support investigations that emphasise thinking, reasoning and working mathematically Core content Students know: addition involves joining two or more numbers to find a total subtraction involves taking one quantity away from another how to distinguish between situations that require addition or subtraction of whole numbers addition and subtraction are the inverse of each other mental computation strategies and computation methods for solving addition and subtraction problems how to solve addition and subtraction problems involving small whole numbers. Students may: identify ways to solve problems explain the reasons for choosing an operation to solve a problem calculate solutions mentally calculate solutions using written methods identify the number that results when numbers are joined together or identify what is left after items are covered up explain the addition or subtraction strategy used to solve a problem describe what is happening to the numbers when adding or subtracting explain that subtraction undoes addition and vice versa check the reasonableness of answers using different computation strategies check answers using alternative computation methods or using the inverse operation use and explain different combinations of numbers that make the same total pose problems involving addition and subtraction using everyday language identify the number patterns or the skip counting sequence (e.g. counting in 2s, 3s) relate patterns to the counting sequence to 100 explore the use of known strategies and computation methods for extensions to larger numbers. Addition totals to 10 joining model language of joining two or more addends Subtraction whole numbers to 10 take away model language of take away Connections inverse addition undoes subtraction subtraction undoes addition Mental computation strategies count on (in 1s, 2s) count back (in 1s, 2s) Computation methods mental computations written recordings words for addition (add) words for subtraction (cover up, take away, left) calculators, computers symbols addition (+) subtraction (–)
Level 6: Level statement Students compare and order rational numbers and use scientific notation as a short-hand method of representing very large or very small numbers. They develop personal plans, consider financial options and monitor financial situations using available information. Students use a range of computation methods and strategies to solve problems that involve rational numbers, rates, ratios and direct and inverse proportions. Core learning outcome: N 6.2 Students identify and solve addition and subtraction problems involving rational numbers using a range of computation methods and strategies. Elaborations — To support investigations that emphasise thinking, reasoning and working mathematically Core content Students know: how to identify situations involving rational numbers that require addition or subtraction, or both mental computation strategies and computation methods for solving addition and subtraction problems involving rational numbers how to solve addition and subtraction problems involving rational numbers. Students may: explain whether an exact or approximate answer is required select and justify computation methods and strategies used to solve problems check reasonableness of solutions check solutions using alternative computation methods for solving problems pose and solve real-life problems involving addition and subtraction of rational numbers. Addition and subtraction rational numbers Connections inverse (backtracking) Mental computation strategies relevant to integers and whole numbers, common fractions and decimal fractions generalisations about addition and subtraction Computation methods mental computations exact approximate written recordings student-generated traditional methods calculators, computers At each level, investigations should occur in a range of contexts. For example, students could investigate: weather patterns such as the Southern Oscillation Index financial transactions involving profit and loss bank balances temperatures in outer space exploration of outer space water usage in domestic and commercial situations mass of electrons.