DK+&+PK+for+fractions+and+decimals+-+Year+6


 * **Year Level** || **Content Descriptor** || **Declarative Knowledge & Prodcedural Knowledge** || **Progression from the Previous Year Level** ||
 * Year 6 || - //Compare// fractions with related denominators and locate and represent them on a number line.

Elaborations: • demonstrating equivalence between fractions using drawings and models

- //Solve// problems involving addition and subtraction of fractions with the same or related denominators.

Elaborations: denominators and fractions as an operator, in preparation for calculating with all fractions develop understanding of equivalent fractions and the use of fractions as operators
 * understanding the processes for adding and subtracting fractions with related
 * solving realistic additive (addition and subtraction) problems involving fractions to
 * modelling and solving additive problems involving fractions by using methods such as jumps on a number line, or by making diagrams of fractions as parts of shapes

- //Add and subtract// decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers.

Elaborations: strategies for addition and subtraction of decimal numbers to thousandths decimals, to gain fluency with calculating with decimals and with recognising appropriate operations
 * extending whole-number strategies to explore and develop meaningful written
 * exploring and practising efficient methods for solving problems requiring operations on

- //Multiply// decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies.

Elaborations: remainders, appropriate to the context (for example understanding that the result of 6.5 ÷ 4 is sensibly expressed as 1.625km if the context involves dividing a 6.5km running course into four equal legs; $1.63 if it represents the price of one item where four sell for $6.50)
 * interpreting and representing the remainder in division calculations, including nonintegral

- //Multiply and divide// decimals by powers of 10.

Elaborations:
 * understanding and using the fact that equivalent division calculations result if both numbers are multiplied or divided by the same amount (for example 34.87 ÷ 7 is equivalent to 3487 ÷ 700)
 * using and explaining the use of multiplication and division by powers of 10 to multiply decimal numbers mentally (for example 1.4 × 0.6 can be calculated by multiplying 14 by 6 and dividing the result by 100)

- //Make connections// between equivalent fractions, decimals and percentages.

Elaborations:
 * connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solved || Compare -
 * denominators.
 * related denominators
 * comparing fractions
 * locate and represent on a number line.

Solve
 * Addition of fractions.
 * Subtraction of fractions.
 * related denominators.

Add and subtract.
 * Addition and subtraction of fractions.
 * Using digital technologies.
 * Estimation and rounding.

Mulitply
 * Multiplication of decimals.
 * Terminating decimals.
 * Division of decimals.
 * Using digital technology.

Multiply and Divide
 * Multiplication and division of decimals.
 * powers of ten.

Make Connections
 * Equivalent fractions.
 * Decimals.
 * Percentages.
 * relationship between fractions, decimals and percentages. || - Students are engaging with a greater range of concepts.

- Exploration and investigation of algorithms with decimals and fractions. Knowledge on addition, subtraction, multiplication and division of these concepts.

- The concept of related denominators has been introduced to students.

- Decimals become a focus for this year level.

- Students being to investigate technology and its use within mathematics.

- Whole numbers and terminating decimals are examined.

- Powers of 10 are used in complex algorithms.

- Introduction of the mathematical concept of percentages in connection with fractions and decimals.

- Making connections between three key concepts, fractions, decimals and percentages. || __Content Descriptor/s __
 * __Year Six __**
 * Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
 * Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)
 * Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)
 * Multiply decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies (ACMNA129)
 * Multiply and divide decimals by powers of 10 (ACMNA130)
 * Make connections between equivalent fractions, decimals and percentages (ACMNA131)

__Analysis of Declarative and Procedural Knowledge __ During Year Six students continue to build on their prior knowledge of fractions and decimals, however they are also exposed to new concepts within this sub-strand. The Year Six mathematics curriculum focuses on students gaining a proficiency of understanding, fluency, problem solving and reasoning (ACARA, 2012). Students will consolidate their knowledge of fractions with related denominators, additions of simple fractions and their work with number lines that was undertaken during Year Five. They will then engage their problem solving skills to solve realistic additive problem to develop an understanding of equivalent fractions (ACARA, 2012). Both concrete and abstract methods will be used to model and solve additive problems involving fractions. The concept of decimals will be extended and explored during Year Six. Through extensive work with decimals students will develop their knowledge and understanding of the base-10 system for whole numbers (Booker et. al., 2010). Students will being with addition and subtraction algorithms when working with decimals and include estimation to check the reasonableness of answers. They will soon increase their knowledge and understanding of decimal points by investigating and applying multiplication and division algorithms to decimals. Students will need to interpret and represent the remainder in division calculations (ACARA, 2012). A clear understanding of the concept of 'powers of ten' will also need to be ascertained and explained by students. Comparing fractions, decimals and percentages is a concept that is introduced during Year Six. As outlined by ACARA (2012), by the end of Year Six students will need to make connections between "fractions, decimals and percentages as different representations of the same number and solve associated problems". Students will also use their knowledge of fraction, decimals and percentages to predict and communicate probabilities as well as designing and investigating a range of data (ACARA, 2012).