DK+&+PK+for+fractions+and+decimals+-+Year+4+&+5

4 || **//Investigate// equivalent fractions used in contexts** __Elaboration:__ - exploring the relationships between families of fractions (halves, quarters and eights or thirds and sixths) by folding a series of paper strips to construct a fraction wall. __Elaboration:__ - converting mixed numbers to improper fractions and vice versa - investigating the use of fractions and sharing as a way of managing Country __Elaboration: __ - using divsion by 10 to extend the place-value system - using knowledge of fractions to establish equivalences between fractions and decimal notation || **//__Investigate: __//** - Explore equivalent fractions e.g. ¼, ½ - Construct a fraction wall **//__Count, Locate & Represent:__//** - Convert mixed numbers to improper fractions e.g 2 ½ to 5/2 - Fractions and the notion of 'sharing' e.g taking no more than //half// the eggs from a nest to protect future bird populations //__**Make Connections:**__// - use division by 10 - use fractions to identify equivalences between fractions and decimals || - The mathematical concept of decimals have been introduced <span style="font-family: Arial,sans-serif;">- Language has changed from ‘model and represent’ to ‘investigate’, ‘explore’ and ‘make connections’ <span style="font-family: Arial,sans-serif;">- Improper fractions has been included as a focus <span style="font-family: Arial,sans-serif;">- Comparisons are made between fractions and decimals, rather than focusing on multiples || __<span style="font-family: Arial,sans-serif;">Elaboration: __ <span style="font-family: Arial,sans-serif;">- recognising the connection between the order of unit fractions and their denominators __<span style="font-family: Arial,sans-serif;">Elaboration: __ <span style="font-family: Arial,sans-serif;">- modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes __<span style="font-family: Arial,sans-serif;">Elaboration: __ <span style="font-family: Arial,sans-serif;">- using knowledge of place value and division by 10 to extend the number system to thousandths and beyond <span style="font-family: Arial,sans-serif;">- recognising the equivalence of one thousandths and 0.001 __<span style="font-family: Arial,sans-serif;">Elaboration: __ <span style="font-family: Arial,sans-serif;">- locating decimals on a number line || <span style="font-family: Arial,sans-serif;">**__//Compare & Order://__** <span style="font-family: Arial,sans-serif;">- Order of fractions <span style="font-family: Arial,sans-serif;">- Denominators <span style="font-family: Arial,sans-serif;">**//__Investigate:__//** <span style="font-family: Arial,sans-serif;">- Addition using fractions <span style="font-family: Arial,sans-serif;">- Subtraction using fractions <span style="font-family: Arial,sans-serif;">both with the use of number lines & shapes <span style="font-family: Arial,sans-serif;">//__**Recognise:**__// <span style="font-family: Arial,sans-serif;">- Using the place value system <span style="font-family: Arial,sans-serif;">- Decimals to thousandths <span style="font-family: Arial,sans-serif;">- Division by 10 <span style="font-family: Arial,sans-serif;">**__//Compare, Order & Represent://__** <span style="font-family: Arial,sans-serif;">- Use a number line to find a range of decimals <span style="font-family: Arial,sans-serif;">e.g. 0.01, 0.5, 1.0 || <span style="font-family: Arial,sans-serif;">- The concept of denominator has been introduced <span style="font-family: Arial,sans-serif;">- Using addition and subtraction to work with fractions is now a focus <span style="font-family: Arial,sans-serif;">- Language still involves ‘investigating’, but more comparisons are made in this year level <span style="font-family: Arial,sans-serif;">- More direct focus on decimals as a whole (not in relation to fractions), and the place value system || //__<span style="font-family: Arial,sans-serif;">Content Descriptors: __//
 * **Year Level** || **Content Descriptor** || **Declarative Knowledge & Procedural Knowledge** || **Progression from previous year level** ||
 * Year
 * //Count// by quarters, halves and thirds, including with mixed numerals. //Locate// and //represent// these fractions on a number line**
 * <span style="font-family: Arial,sans-serif;">//Make connections// between fractions and decimals **
 * Year 5 || **<span style="font-family: Arial,sans-serif;">//Compare and order// common unit fractions and //locate// and //represent// these on a number line **
 * <span style="font-family: Arial,sans-serif;">//Investigate// strategies to solve problems involving addition and subtraction of fractions with the same denominator **
 * <span style="font-family: Arial,sans-serif;">//Recognise// that the place value system can be extended beyond hundredths **
 * <span style="font-family: Arial,sans-serif;">//Compare, order and represent// decimals **
 * __<span style="font-family: Arial,sans-serif;">Year Four: __**
 * Investigate equivalent fractions used in contexts (ACMNA077)
 * Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)
 * Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

//__<span style="font-family: Arial,sans-serif;">Analysis of Declarative and Procedural Knowledge: __// In year 4 students continue to model and represent the notion of equivalent fractions, however a much more **investigative** focus is introduced. Building upon their prior knowledge of equivalent fractions, students begin to convert mixed numbers to **improper fractions**, and vice versa (ACARA, 2012). They explore the concept of **'sharing**' and start to make connections to the prior knowledge of fractions which was gained in earlier years. These year 4 students make significant connections between fractions and decimals, particularly focusing on using their knowledge of fractions to establish equivalences between fractions and **decimal notation** (ACARA, 2012). This is supported through the use of concrete materials such as a **number line**. ACARA (2012) states that in year 4 it is imperative for the students to develop their critical and creative thinking skills, which is highlighted throughout the fractions and decimals substrand. Ultimately, this develops the students declarative and procedural knowledge for this substrand, as they first need to **understand** the relevent connections between fractions and decimals, and then **solve problems** relating to these concepts. The Year Four Achievement Standards - Maths Portfolio suggests that the students work closely and constructively with a number line to identify common equivalent fractions, and then locate and order these fractions on a number line accordingly (ACARA, 2012).

//__<span style="font-family: Arial,sans-serif;">Content Descriptors: __//
 * __<span style="font-family: Arial,sans-serif;">Year Five: __**
 * Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)
 * Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)
 * Recognise that the place value system can be extended beyond hundredths (ACMNA104)
 * Compare, order and represent decimals (ACMNA105)

//__<span style="font-family: Arial,sans-serif;">Analysis of Declarative and Procedural Knowledge: __// <span style="font-family: Arial,sans-serif;">In year 5 the fractions and decimals substrand introduces a more problem solving focus, as the students are challenged to investigate strategies to solve problems involving **addition and subtraction of fractions** with the same denominator (ACARA, 2012). The students also begin to **compare, order and represent decimals** rather than just simply recognise these numbers, as they further explore this concept in relation to the **place value system** (ACARA, 2012). In addition, the emphasis ACARA (2012) places on the place value system allows the students to further develop and extend their understanding beyond hundreths, and eventually focus on decimals to thousandths. Similiar to the concepts developed in year 4, the students are still using a number line to locate and represent common unit fractions, however they are required to **make comparisions** between these common fractions (ACARA, 2012). This can be indentified in the following work sample from t he Year Five Achievement Standards - Maths Portfolio, which focuses on the students abilities to demonstrate the skills they use to compare common unit fractions, and then to justify this accordingly.