NSW Curriculum and Learning Innovation Centre Exploring Place value Building capacity with the new syllabuses

NSW Curriculum and Learning Innovation Centre Multi-unit place value This aspect deals with more than just knowing the positional name of numbers. E.g The 3 is in the hundreds column in the number 347. The Place value levels focus on the structure of numbers, the relationships between numbers and the strategies that students use when solving two- and three-digit addition and subtraction questions. Multi-unit place value is evident when students can flexibly regroup hundreds, tens and ones. Having an understanding of ten as a countable unit (composite unit) is central to place value concepts.

NSW Curriculum and Learning Innovation Centre Pre-place value understanding Not all students will be able to be placed on the Place value aspect. A student must be at least at the counting-on-and-back stage on the EAS aspect before being considered to be placed on the Place value aspect. At level 0 of the Place value aspect, Pre-place value, students have an abstract understanding of a number being a completed count and are able to count on or back from the number by ones.

NSW Curriculum and Learning Innovation Centre Level 0: Ten as a count (pre-place value) Level description VideoSyllabus outcomes Key ideas in the syllabus Sample related content The student can count-on by ones and can count by tens on the decade 10,20,30… The student treats ‘ten’ as ten ones but cannot treat ten as a unit of ten at the same time as thinking of it as ten ones. Typically the student reconstructs the units of ten by counting them by ones. Click on the image to view the video This video and following work sample show evidence of students counting on by ones work sample MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers Use a range of mental strategies for addition and subtraction of two-digit numbers Solve word problems involving addition and subtraction Use and record a range of mental strategies to solve addition and subtraction problems, including: -counting-on from the larger number to find the total of two numbers -counting-back from a number to find the number remaining -counting-on or counting-back to find the difference between two numbers.

NSW Curriculum and Learning Innovation Centre Level 1: Ten as a unit Level descriptionVideoSyllabus outcomes Key ideas in the syllabus Sample related content The student can solve two-digit addition and subtraction problems by counting by tens and ones both on the decade and off the decade. The student uses materials to represent one of the numbers and to support the counting when adding or finding the difference. The student treats ten as a single unit while recognising that it contains ten ones. Click on the image to view the video This video shows a student counting on by tens and ones with the support of material. MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers Use a range of mental strategies for addition and subtraction of two-digit numbers Solve word problems involving addition and subtraction Use and record a range of mental strategies to solve addition and subtraction problems involving two- digit numbers.

NSW Curriculum and Learning Innovation Centre Level 2: Tens and ones Level description VideoSyllabus outcomes Key ideas in the syllabus Sample related content The student can solve two-digit addition and subtraction problems mentally using a range of strategies. Two important methods are the jump strategy and the split strategy. Click on the image to view the video This video shows a student mentally solving a two- digit addition question by using the jump method. MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers MA2-5NA Uses mental and informal written strategies for addition and subtraction involving two-, three- and four- digit numbers Solve word problems involving addition and subtraction Use and record a range of mental strategies for the addition and subtraction of two-, three- and four-digit numbers Use and record a range of mental strategies to solve addition and subtraction problems involving two-digit numbers, including: -the jump strategy on an empty number line -the split strategy

NSW Curriculum and Learning Innovation Centre Level 3: Hundreds, tens and ones Level descriptionWork sample Syllabus outcomes Key ideas in the syllabus Sample related content The student can mentally solve addition and subtraction of two three-digit numbers using two key methods (a)partitioning numbers into hundreds, tens and ones and increment or decrement by hundreds and tens (jump method) (b)flexibly regroup hundreds, tens and ones (split method). The student has a part- whole knowledge of numbers to 1000 The following work sample suggests that the student is able to partition the 15 into 5 and 10 before finding the corresponding multiples of 20. Work sample MA2-5NA Uses mental and informal written strategies for addition and subtraction involving two-, three- and four-digit numbers Use and record a range of mental strategies for addition and subtraction of two-, three- and four-digit numbers Apply single-digit number facts to mental strategies including -The jump strategy on a number line -The split strategy -Bridging the decades -Using place value to partition numbers Solve problems involving purchases and the calculation of change to the nearest five cents

NSW Curriculum and Learning Innovation Centre Level 4: Decimal place value Level description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student understands the positional value of decimals and can compare the value of one decimal place to numbers with two or three decimal places The student can multiply or divide decimals by ten or one hundred. Click on the image to view the video This video shows a common misconception about decimals. MA2-7NA Represents, models and compares commonly used fractions and decimals Apply the place value system to represent tenths and hundreds as decimals Model, compare and represent decimals with up to two decimal places. State the place value of digits in decimal numbers up to two decimal places Use place value to partition decimals of up to two decimal places Apply knowledge of decimals to record measurements Interpret zero digit(s) at the end of a decimal Use a calculator to create patterns involving decimal numbers eg 1÷10, 2÷10, 3÷10

NSW Curriculum and Learning Innovation Centre Level 5: System place value Level descriptionSyllabus outcomes Key ideas in the syllabus Sample related content The student understands that the place value system can be extended indefinitely left or right of the decimal point and can explain what happens when a number is multiplied or divided by a given power of ten. The student has an understanding of -multiplying and dividing decimals by decimal. -the relationship between the adjacent units in a numeral -repeating decimals. MA3-4NA Orders, reads and represents integers of any size and describes properties MA3-7NA Compares, orders and calculates with fractions, decimals and percentages MA4-5NA Operates with fractions, decimals and percentages State the place value of digits in numbers of any size Use mental, written and calculator strategies to: - multiply decimals by one- and two-digit whole numbers - divide decimals by one- digit whole numbers, 10, 100 and 1000 Apply the four operations with fractions, including decimals Record numbers of any size using expanded notation Recognise that the place value system can be extended beyond hundredths – express thousandths as decimals Use mental strategies to multiply simple decimals by single-digit numbers Divide decimals by a one-digit whole number where the result is a terminating decimal Use the notation for recurring decimals Multiply and divide decimals using efficient written strategies

NSW Curriculum and Learning Innovation Centre Where to next? Consider assessing each student to determine where he or she is on the Place value aspect. Look at the associated syllabus outcomes as indicated on the numeracy continuum. The syllabus content associated with each outcome will help you to plan a teaching program aimed at progressing each student to the next level along the continuum. Look Plan