THE BIG IDEAS
Face value and place value are two very different things. Face value is the value of the symbol represented whilst place value is the value of the place the symbol is in, for example in 34 the face value of the 3 is 3, however the place value is 30. This is a concept that may not be fully understood by all children, leading to situations where students are unable to think abstractly to understand the quantity of a place value as the symbolic method of understanding (face value) is much more commonly use to express large numbers.
Helping children learn mathematics (2012) discusses this on page 179 where it states:
"Research reports that many children lack an understanding of the relative sizes of numbers greater than 100. This results of many factors - one of which may be the lack of opportunity to model large numbers, which helps children develop a visual awareness of the relative sizes of numbers"
This means, as a teacher I need to provide my students with many opportunities to picture and develop a conceptual understanding for large numbers to relate the face value and the place value to a physical quantity. This can be done through activities or videos.
Video: What is face value and place value?
Video: Example of a video that demonstrates the size of large numbers - This video could be used with older students when looking at space
Video: Example of a video that demonstrates the size of large numbers - This video could be used with older students when looking at space
THE CONCEPT, SKILL, STRATEGIES AND SUPPORTING RESOURCES
There are 7 concepts that fall under place value. These concepts include:
- Place holder – 0
- The base is the multiplier – 10 in a Base 10 system
- The PV system is symmetrical around the ones place
- The decimal point separates the whole from the fraction part of the number
- The number of digits required equals the base number – 10 digits in Base 10, 5 digits in Base 5, 2 digits in Base 2
- The largest digit is 1 less than the base number – 9 in Base 10, 4 in Base 5, 1 in Base 2, M-1 in Base M
- When operating on numbers, trading happens when the base number is reached – 6 + 4 = ? Need to trade 10 ones for 1 ten
For this section, only 'Place Holder' will be explored further.
Concept
For place holder, the concept is that all place values must contain a digit and if it is empty, it is filled with a 0 . This doesn't contain value, however it adds to the value of the other digits in the number. This can be introduced in a video (such schoolhouse rock - my hero, zero below) or through experimenting with a place value mat or similar resource.
Number cups is a cheap and easily constructed resource that can assist with this concept. By starting with one cup and focusing on a number (for example five) the students can watch the place value of the 5 change by adding more cups with zeros (5, 50, 500, etc)
Video: Schoolhouse rock - My hero, zero
Link: Number Cups
Video: How to make number cups
Concept
For place holder, the concept is that all place values must contain a digit and if it is empty, it is filled with a 0 . This doesn't contain value, however it adds to the value of the other digits in the number. This can be introduced in a video (such schoolhouse rock - my hero, zero below) or through experimenting with a place value mat or similar resource.
Number cups is a cheap and easily constructed resource that can assist with this concept. By starting with one cup and focusing on a number (for example five) the students can watch the place value of the 5 change by adding more cups with zeros (5, 50, 500, etc)Video: Schoolhouse rock - My hero, zero
Link: Number Cups
Video: How to make number cups
Skill
The ability to change the value of a number using place holders and read the value of a number that contains place holders. This skill can be practiced using resources such as number cups (as mentioned above), apps (such as Kids Maths Place Value), number expanders and other activities that can be done in class.
Strategies
The strategies for place value includes the 'Big 7' mental computation strategies and turn around facts explored in weeks 1 to 4. These included:
Addition and subtraction strategies:
1.Count on/back for 0,1, 2, 3
2.Doubles/halving for numbers that are the same
(4+4, 6+6, 234+234)
3.Use 10 for 8 and 9
Multiplication and Division strategies:
4.Double (x2); Double, Double (x4); Double, Double, Double (x8)
5.Counting for x5 and x10
6.Real world for x0 and x1
7.Build up for x3 and x6 and build down for x9
8. Turn around facts for x7
These strategies are important because mental computation plays a large role in the number sense we use as a part of place value.
THE LANGUAGE MODEL
The language model is used to display the relationship between the visual, verbal and symbolic elements of mathematics and forms 'stages' of learning.
Student language - During student language, all language used should be familiar to the child and accompanied with familiar objects.
Materials language - At this stage, there is still no introduction of mathematical terms. The language is very similar to student language however the visuals used have become more abstract.
Mathematics language - Moving away from 'stories', this stage introduces mathematical terms.
Symbolic language - This stage introduces symbols.
THE LANGUAGE MODEL FOR PLACE VALUE
THE MISCONCEPTION
A child may not understand the use of a place holder as you don't say the zero when saying the number. In this case, the child would write five hundred and two as 52 because the only numbers spoken is the five and the two. A child in this position does not yet understand place value (or the 'houses') and therefore needs more work with a place value mat.
THE ACARA LINK
Place value is first introduced in year one.
Strand: Number and Algebra
Substrand: Number and place value
Content descriptions: Count collections to 100 by partitioning numbers using place value
Elaborations:
- Understanding partitioning of numbers and the importance of grouping in tens
- Understanding two-digit numbers as comprised of tens and ones/units
Scootle resource ideas:
1. eChalk: Hundreds, tens and units is a virtual place value mat that can be used when introducing the use of MAB blocks at the materials language stage
2. Importance of Zero is a quick 30 second clip that has a song that explains zeros importance as a place holder, this song could be taught to the children when learning about place holders.
THE RESOURCES AND IDEAS
- The place value hop mat teachers children place value with a new 'hopscotch' like twist. This helps children learn how to say large numbers as well as provides a section for concrete materials to be involved. This mat also assists with the concept of place holders.
- This childrens' language place value activity introduces the concepts of a place value mat without entering materials language.
THE TEXTBOOK SUMMARY
- Place Value is first mention in year one of the Australian Curriculum
- The number system we use is called the Hindu-Arabic system, it was primarily invented in India by the Hindus and transmitted to Europe by the Arabs, but many countries and cultures contributed to its development
- The Hindu-Arabic system has 4 important characteristics: the position of the digit represents its value, it is a base ten system, a symbol for zero exists and allows us to represent symbolically the absence of something and numbers can be written in expanded notation and summed with respect to place value.
- Practice in skip counting helps decrease bumps in the place value road.
- Reading and writing numbers are symbolic activities and should follow much modelling and talking about numbers. This reccommendation is based on research that highlight the dangers of introducing children to symbolic numbers too soon. A sustained development of number sense should accompany reading and writing numbers. This ensures that the symbols the students are writing and reading are meaningful to them (Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al.,2012).
THE REFERENCES
ACU,. (2016). Learning Environment Online. Leo.acu.edu.au. Retrieved 3 March 2016, from http://leo.acu.edu.au/course/view.php?id=18458
Australia, E. (2016). Home - Scootle. Scootle.edu.au. Retrieved 3 April 2016, from https://www.scootle.edu.au/ec/p/home
Australian government,. (2016). Home - The Australian Curriculum v8.1.Australiancurriculum.edu.au. Retrieved 3 April 2016, from http://www.australiancurriculum.edu.au/
Reys, Lindquist, Lambdin, Smith, Rogers, & Falle, et al. (2012). Helping children learn mathematics. Milton, QLD: John Wiley & Sons.
YouTube. (2016). Youtube.com. Retrieved 3 April 2016, from https://www.youtube.com/
No comments:
Post a Comment