Number+&+Algebra+Overview+Foundation-Yr+3

ACARA Number and Algebra Overview Foundation to Year 3 **//Analysis of ACARA Year Levels and Descriptors://**

**//EARLY YEARS//** **Foundation Year;** As early as five years old students will now be expected to have proficient understandings of basic Number and Algebra, Measurement and Geometry and Statistics and Probability. Educators will establish language used to work mathematically and explore the three strands using lots of materials and visual aids to help student problem solve and make connections.

//At this year level//:
 * //Understanding// includes connecting names, numerals and quantities
 * //Fluency// includes readily counting numbers in sequences, continuing patterns, and comparing the lengths of objects
 * //Problem Solving// includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer
 * //Reasoning// includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of length


 * Year 1;**

As the result of the ‘foundation year’ students in year 1 should have already developed many of the skills they would’ve usually been learning in the year to come and will now be practising skills that would usually be addressed in year 2 and so on for the grades ahead. In the ‘Number and Algebra’ strand specifically students will already be modelling, writing, ordering and reading number sentences up to 100. As well as partitioning numbers and solving basic addition and subtraction algorithms for single digits problems.

//At this year level://
 * //Understanding// includes connecting names, numerals and quantities, and partitioning numbers in various way.
 * //Fluency//includes counting number in sequences readily forward and backwards, locating numbers on a line, and naming the days of the week.
 * //Problem Solving//includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer.
 * //Reasoning//includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data, and explaining patterns that have been created.


 * Year 2;**

At this stage students are still working within the three sub strands however the expected knowledge and understanding standards for ‘Number and Algebra’ have increased significantly. Students will now be exposed to fractions and decimals, money and financial mathematics and patterns and algebra. Students will be presented with many real life contexts to enhance these understanding, such as, “if I bought a sausage roll that cost $2 and a juice that cost $3.50 from the Tuckshop how much money would I need to buy my lunch?” Students will begin writing number sentences and explore the idea of halving and quartering figures.

//At this year level://


 * //Understanding// includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly, identifying and describing the relationship between addition and subtraction and between multiplication and division
 * //Fluency// includes counting numbers in sequences readily, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time duration
 * //Problem Solving// includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape.
 * //Reasoning// includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations, and creating and interpreting simple representations of data


 * Year 3;**

In year 3 students build on concepts developed in earlier years with a key focus on their ability to apply knowledge to problem solving questions. Students are expected to draw on higher order thinking and more emphasis is on their own understandings and ability to communicate responses verbally or formally. Unfortunately year 3 and 4 are when many students are differentiated into lower, intermediate and higher level ability groups because many students may understand maths concepts however fail to transfer that knowledge to new problems.

//At this year level://
 * //Understanding// includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry.
 * //Fluency//includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions.
 * //Problem Solving//includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns.
 * //Reasoning//includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays.

**References**
Australian Curriculum Assessment and Reporting Authority. (2010). //The Australian Curriculum: Mathematics.// Retrieved April 5, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: [|http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=2&y=6&y=7&y=8&y=9&s=NA#level=8]


 * Regards Talia :) **