Week 8: Number and Place Value part 2.

The Big Idea: 

Following on from last week, this weeks main focus was on numbers. Specifically, number sense and numeration. Number sense includes the fluidity and flexibility of numbers whereas numeration is the process of reading, writing and building numbers. In the Foundation Year students learn single digit numbers, numbers consisting of 0 to 10. As they progress through to Year One they have more knowledge on double digits this include 10-99. When they reach Year 2 it becomes more complex as students are learning triple digit numbers, numbers consisting of 100 to 199. In Year 6 students mainly operate in Base 10 using the place value houses,

Concepts, Skills and Strategy:

Concept- Place Value can be defined as the mother of all concepts. Where the number is situated informs us about the value of that number. Large number concept need to be taught at an early age as it is the basis to algebra which all students will learn as they proceed through school, if they are unable to comprehend the concept it will be difficult for them to grasp further content. It is important for students to understand that the numbers in the place value system are group differently according to their base system. The base number is the largest digit which is one less than the base number. For example:

Base 10 = 9
Base 5 = 4


Skill- A high level of number knowledge and understanding, knowledge of basic number facts and a general knowledge of operations: addition, subtraction, multiplication and division are the basic skills needed in order to understand place value and number.

Strategy- Mental computation can be used when teaching place value. Knowledge of order of operations and estimation as well as rounding are useful when trying to visual numbers. Other strategies includes: using a calculator with numbers beyond 10, the count on strategy, double up and back and build up and down.

Misconceptions: 

Misconceptions generally occur when double digits are taught. If the student has not understood the concept properly they may begin to build misconceptions when it comes to larger numbers. A common misconception is that the number 10,11, 12 is not known to be a " teen" number when in fact teen numbers start immediately when there is a double digit. Furthermore, although the number eleven and twelve may be written as 11 (one - one)  and 12 (one two ) it is important for the student not to pronounce it as it is written. It is crucial for students to understand and recognise the consistency with number names such as thirteen, fourteen, fifteen all the way to  nineteen. Reading back to front can assist students who might have difficulty reading number to understand and learn better a number such as 18 for example is read back to front the number eight comes before the one (also known as teen). Lastly, a numeral expander can help easily overcome misconceptions when a number such as 304 is written it is said to be three hundred and four, children commonly mistake it and write 3004 as they know how the number 300 and the number 4 so they combine both numbers together assuming they are correct in doing so. Hence why the numeral expander is a useful tool as it spreads out the numbers into place value houses making it easier for children to understand. 

Resources: 

Similar to last week The Australian Curriculum ( ACARA) under the heading Patterns and Algebra students are to " investigate and describe number patterns formed by skip counting and patterns with objects". Moreover, they are to use place value patterns beyond the teen numbers to help generalise the number sequence and predict the upcoming number. In the numeracy strand it is crucial for the students to recognise and use the patterns and relationship. 

Sourced Teaching Strategy: 

(Blogger.com:  http://www.promotingsuccessprintablesblog.com/2014/10/place-value.html)

Textbook, Concepts, Skills and Strategy: 

The C/S/S this week is similar to the C/S/S mentioned in last weeks blog post in that the position of the digit represents its value and that the two main ideas for promoting number sense includes : Explicit grouping or trading rules are defined and consistently followed and The position of the digit determines the number being represented. All prior knowledge of all operations are needed in order to gain a deeper understanding of number and place value.  

References

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406579&chapterid=190019

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 219,220,227,237). Milton, Qld: Wiley.

Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA001

Week 7: Number and Place Value

The Big Idea:

Students in Year Six should be able to understand decimal numbers and numbers up to one million. There are two sections in which number knowledge is broken into these include Formal and Informal. Formal is taught in primary school it combines reading, writing and understanding of numbers. Informal is when no mathematics skills are required, most informal math skills are based on everyday activities and requires no mental computation or basic calculations. Mental computation refers to ones understanding of operations the process surrounding the operation, it requires estimation and basic knowledge of number facts. Place value is the value of the number that is represented based on the position. 

Concepts, Skills and Strategy:

Concept-  The concepts in Place Value is that the place holder is always zero. It is multiplicative meaning it is associated with the mathematical operation of multiplication. The lines of symmetry pass through the ones house, the decimal point separates a whole number from a fraction.

Skill- The skills needed to place numbers correctly into Place Value columns are the ability to understand number, know basic number facts and have well rounded knowledge of the concept of operations.

Strategy- Obtain information and process accurately and efficiently. Use the 7 thinking strategies (count back, double/ half, use 10) : addition and subtraction as well as ( double 2x, 4x, 8x, counting x5 and x10, build up x3 and x6 and build down x9): multiplication and division.

Misconceptions:

The common misconception when it comes to Place Value is the inability to understand the value of the number when numbers are regrouped or renamed in an addition or subtraction problem. A misconception regarding place value in addition is that when students are given the number 35 + 26 their answers may equal 511, as they understand that 5+6= 11 and 3+2=5 therefore they add both columns separately and combine both numbers together getting the incorrect total of 511. This can happen when students do not yet understand the concept of Place Value. 

Resources:

The Australian Curriculum ( ACARA) under the heading Number and Algebra subheading Number and Place value it states that they have to " Establish an understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20." Furthermore, it is critical in estimating and calculating whole numbers, recognising and using patterns and relationships,  understanding use of number context. It develops their fluency with forwards and backwards counting and their understanding that numbers are said in a particular order and the pattern in which it is said. 

Sourced Teaching Strategy: 

 

( Blogger.com: http://twocandoit.blogspot.com/2012/05/place-value-and-telling-time.html ) 

Textbook Concept, Skills and Strategy: 

The position of the digit represents its value the understanding of Place Value develops through counting and mental computation. Promoting number sense and resting on 2 main ideas which include: Explicit grouping or trading rules define and consistently followed and The position of a digit determines the number being represented. Prior knowledge of number and basic addition and subtraction, the ability to focus on the leading number is an important to number sense and estimation ( Reys. R, 2012).

References

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406579&chapterid=190017

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406579&chapterid=190018

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 219,220, 227). Milton, Qld: Wiley.

Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA001

Week 6: Pre-number

The Big Idea:

Pre-number begins at a very young age. It combines both the symbolic and children's language stage. It requires the students to know how to sort, order and recognise patterns. The more significant attributes students associate with learning numbers is by the shape, size and number. Pre-number refers to the beginning processes of a child's understanding to numbers. The order in which it occurs are as follows: Pre-number, early number, subitising ( remembering patterns), cardinal ( eg. how many people are there on the desk), ordinal ( 1st,2nd,3rd place) and nominal ( Maning something eg. student number).

Concepts, Skills and Strategies:

Concept- Pre-number concepts are referred as the foundation to mathematics and may not include numbers. The concepts include: Matching, Sorting, Comparing and Patterning. Matching may be as simple as recognising mum and dad, children are able to do this from a very early age as they match them based on their attributes therefore being able to distinctly recognise their parents from other parents. The Caldwell pattern was designed to teach children how to visualise numbers and patterns to develop their understanding of early number. This pattern helps children recognise number patterns quickly and effectively introducing the concept of subtising. Creative activities such as role playing (Mrs. Tens and Mrs. Ones) can also be useful in introducing the concept of place value further developing their understanding.

Skills-  The basic skills children will need in order to understand Pre-number will be: Learning to count ( numbers 0-10), sequencing, shape, size as well as matching, sorting, comparing and ordering mentioned above.

Strategy-  Useful strategies when introducing Pre-number are one to one correspondence where the children point to the object as they count, stable order ( getting the number order correct), order irrelevance ( no matter which way the order or pattern is the number of objects are still the same).By far the most common strategy used is by finger counting.

Misconceptions:

Students' might not fully understand that counting is a strategy to determine " how many" and the last number counted determines " how many". They may also avoid counting objects which have already been counted. 

Resources: 

In the Australian Curriculum, ACARA under the heading Foundation Year in subheading Number and Algebra it states that students will learn how to " connect number names, numerals and quantities, including zero, initially up to 10 and then beyond.

Sourced Teaching Strategy: 

  

( Caldwell Pattern, YouTube: https://www.youtube.com/watch?v=Xaxy8ylxuzo)

Textbook Concepts, Skills and Strategy:

Developing early number concepts in children is vital in ensuring that they are learning both ordinal, nominal and cardinal numbers. Number cards would be useful for children when learning about ordinal numbers as it can help students solve a problem and clarifying the notion. Nominal numbers are used when providing a label or classifying something such as postcode or license plate, these numbers provide information but does not use the cardinal or ordinal aspects ( Reys.R, 2012). Cardinal numbers are the natural numbers used to identify the cardinality ( size) of a set.  

References

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406574&chapterid=190012

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406574&chapterid=190011

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 181,195,196,207). Milton, Qld: Wiley.

Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA001

Week 5: Division

The Big Idea:

The Big Ideas taken from this week is that both division and multiplication both stem from the concept of equal groups. Multiplication requires two equal groups added together to find the total. Whereas, division is the opposite as it requires separating the total into equal groups. Finally, both multiplication and subtraction are linked to division through the use of quotation stories.

Concepts, Skills and Strategy: 

Concept- To teach children how to distribute a certain number of items or objects equally and fairly among them. In order for children to understand the concept of division they have to know how to share. The separation process consist of two processes being Partition and Quotition. Partition is the idea of sharing a large number to see how many there are in each group. Quotition is the process of repeated subtraction where small quantities are subtracted from a larger amount.

Examples 

Partition - Lucy has 6 lollies to share with his 3 friends. How many lollies can each of Lucy's friends receive?

Answer: 6 divided by 3 equal 2

Quotition - There are 12 goody bags and I want to give 1 bag each to my friends. How many friends can I give goody bags to?

Answer: 12 divided by 1 equals 12


Skills- The skills required in order to do division are Multiplication and Subtraction.


Strategy- The strategy needed in division are knowing the multiples very well, being able to do multiplication. Other strategies that can be used in division include Use doubles, Properties to zeros, Counting strategy, Build up or down strategy and using real-life scenarios can also help when demonstrating division.

Misconceptions: 

The misconceptions when it comes to division are that children don't often use the language of division to describe the process. They do not understand that groups and sets need to be subtracted in order to solve the problem. Another misconception is that when dividing the number 0 does not need to be added, this is false as the number should always be recorded.  The language " Goes into" changes what we want students to know about division, where the total is shared out into equal groups. Unlike the other operations, there are several symbols to represent division including: ÷ / - .


Resources:

The Australian Curriculum ( ACARA), states under Minimum Standards-Numeracy that students in years 3 and onwards should be able to apply the appropriate strategies to solve problems which require multiple steps. Using mental multiplication demonstrating by using the skills of doubling and halving as well as simple multiplication and division.

Sourced Teaching Strategy:

(https://www.pinterest.com/mariehdutoit/long-division/)

Textbook Concepts, Skills and Strategy:

Similar to multiplication, the concept of division is developed through concrete, pictorial and symbolic representations. There are two situations that are considered these include: Measurement (Repeated Subtraction) and Partition (Sharing). Fluency in basic skills such as addition, subtraction and multiplication are needed for years 3, 5 and 7. Some strategies used are concrete materials or counting specifically finger counting ( Reys. R, 2012).

References

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406570&chapterid=190005

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406570&chapterid=190004

NAP - Minimum standards - numeracy. (2016). Retrieved from https://www.nap.edu.au/naplan/numeracy/minimum-standards

Numeracy Learning Continuum. Retrieved from https://www.australiancurriculum.edu.au/media/1077/general-capabilities-numeracy-learning-continuum.pdf

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 267,276). Milton, Qld: Wiley.