ED2652 Lecture Notes - Lecture 9: No Introduction, Decimal Mark, 24 Minutes
Mathematics 2: Number and Algebra
Lecture Nine – Week Nine
Review
• Besides what the student brings to the table
o The biggest difference in effecting achievement in the classroom is the teacher by a considerable margin
o The western Australian curriculum doesn’t know your students
• Constructivism (Summary)
o Constructivism is:
▪ Active
▪ Reflective
• In our practice
▪ Social
• Most memorable teaching methods (Souza, 2005 & Fuller, 2003)
o Lecture - 5%
o Reading – 10%
o Audiovisual – 20%
o Demonstration – 30%
o Discussion Group – 50%
o Practice by doing 75%
o Teaching others – 90%
• Numeracy
o Numeracy encompasses the knowledge and skills required to effectively manage mathematical demands in
personal, societal and work situations, in combination with the ability to accommodate and adjust flexibly
to new demands in a continuously rapidly changing society that is highly dominated by quantitative
information and technology.
▪ Van Groenestijn 2002, p.37
• Partitioning Numbers
o Breaking the number into parts
o 10 = 1 + 9 or 2 + 8 or 3 + 7 etc
o 10 is also = 1 + 1 + 8, or 1 + 2 + 7 etc
o 10 is also = 1 + 1 + 1 + 7 or 1 + 2 + 4 + 3 etc
o 1 760 = 1 000 + 700 + 60
• Understanding Operations
o We need to understand the meaning, use and connections between addition, multiplication, subtraction and
division
o Multiplication and Division
o Closely tied to addition and subtraction but conceptually VERY different.
• First Steps in Mathematics – Number (Key Understanding 7)
o We can extend the patterns in the way we write whole numbers to the way we write decimals.
▪ There are numbers between consecutive whole numbers.
▪ The place value system can be extended to the right of the ones place to show numbers between
find more resources at oneclass.com
find more resources at oneclass.com
2
two whole numbers.
▪ To represent a number between two consecutive whole numbers, record the smaller whole
followed by the part, separated by a decimal point (e.g. a number between 14 and 15 is 14.64)
▪ The digits to the right of the unit have decreasingvalues in powers of ten...and can represent
infinitely small numbers.
▪ Decimal fractions can be partitioned just as whole numbers can.
• In a number written as a whole number and a decimal fraction:
o Everything to the left-hand side of the decimal point is a whole number.
o Everything to the right-hand side of the decimal point refers to parts of a whole, a fraction.
o So when we write 14.647, 14 is a whole number and .647 is a fraction of one.
▪ (it’s 647, 1000ths or 647/1000 of 1).
• Progress of Decimal Understanding – FsiM
o A decimal point is like punctuation or a decoration.
o A decimal point separates two whole numbers.
▪ (using money or measurement as a context can promote this!)
o In decimals numbers on the right are different in some way.
o Some misconceptions which may arise before understanding develops
▪ Longer is larger: 0.217 > 0.37 because two hundred and seventeen is greater than thirty-seven.
▪ Shorter is larger: 0.3 is larger than 0.567 because tenths are larger than thousandths
▪ The place value columns reverse after the decimal point – may use “oneths”
▪ Decimal point separates the whole numbers from negative numbers
o In decimals the numbers on the right are about parts or fractions Some misconceptions which may arise
before understanding develops
▪ may see them as common fractions e.g. .5 = 1/5
▪ may learn that 0.5 is a half so 0.05 is half of a half (1/4)
▪ May think that 0.3 is larger than 0.4 because one third is bigger than one quarter
o Decimal numbers extend whole number place relationships to represent numbers between whole numbers.
Developing the idea that the size of the unit/whole determines what the fraction “looks” like is essential
• The different models of fractions
o Region models
▪ 2D and 3D
o Area models
▪ Same areas but not the same shape
o Length Models
▪ String, paper, strips
o Set Models
▪ Counters etc.
• Six Important Messages about fractions
o What we need to remember
▪ Fractions are an important part of the Australian Curriculum Mathematics
▪ Fractions are a challenge to teach and learn
o What our students need to learn
▪ Developing the idea that the size of the unit/whole determines what the fraction looks like
▪ Multiple representations of fractions are required
▪ Equal parts
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The place value system can be extended to the right of the ones place to show numbers between two whole numbers. To represent a number between two consecutive whole numbers, record the smaller whole followed by the part, separated by a decimal point (e. g. a number between 14 and 15 is 14. 64) The digits to the right of the unit have decreasing values in powers of tenand can represent infinitely small numbers: decimal fractions can be partitioned just as whole numbers can. In decimals numbers on the right are different in some way: some misconceptions which may arise before understanding develops. Longer is larger: 0. 217 > 0. 37 because two hundred and seventeen is greater than thirty-seven: shorter is larger: 0. 3 is larger than 0. 567 because tenths are larger than thousandths, decimal point separates the whole numbers from negative numbers. The place value columns reverse after the decimal point may use oneths .
