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Fraction skills using the calculator. (b) How many bundles of 4 in 9? 9  4 = 2.25 There are two whole bundles of 4 plus another quarter of a bundle (i.e. 2.25 bars). What concrete real-world situations are modelled for example, by the fraction ? Two possible situations:.

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interpreting fractions
(b) How many bundles of 4 in 9? 9  4 = 2.25

There are two whole bundles of 4 plus another quarter of a bundle (i.e. 2.25 bars)

What concrete real-world situations are modelled for example, by the fraction ? Two possible situations:

Interpreting fractions
  • 9 ‘Lion Bars’ are divided between 4 students.
  • 9  4 = 2.25
  • Each student receives two bars as well as an extra quarter bar (i.e. 2.25 bars)
pen and paper vs calculator
‘Pen and Paper vs. Calculator

When introducing the concept of a fraction as division and the resultant ‘answer’ as a decimal, students should be encouraged to carry out pen and paper calculations before using the calculator, for example:

‘Pen and Paper: = 9.00  4 = 2.25

‘Calculator’: key in 9 [] 4 to get 2.25

use of and a b c keys
Use of [] and [a b/c] keys
  • As already shown, can be keyed in using the [] key and the answer is given in decimal format. 9  4 = 2.25
  • can also be keyed in using the [a b/c] key and here the answer is given in mixed-number or ‘fraction format’.
  • 9[a b/c]4 = 2  1  4

Note that 2  1  4 is a calculator output meaning 2¼

changing fractions to decimals and back again
Changing fractions to decimals and back again

The calculator has been programmed to perform ‘fraction to decimal’ or ‘decimal to fraction’ conversions automatically.

We already had:

9[a b/c]4 = 2  1  4

2  1  4

Pressing the [a b/c] key coverts this output to 2.25

Pressing the [a b/c] key again and it is coverted back to

2  1  4

mixed numbers top heavy fraction
Mixed numbers Top heavy fraction
  • 2  1  4 is a mixed number
  • To convert it to a top heavy fraction, usethe[d/c] button which is [shift] [a b/c]

i.e.2  1  4 [shift] [a b/c] produces 9 4

  • Use [shift] [a b/c] repeatedly to alternate between mixed number output and top-heavy fraction output
adding fractions
Adding fractions
  • ‘Pen and paper’ approach is essential for:

(a) mathematical understanding and

(b) developing approaches to operating on algebraic fractions.

  • Have a look at the next slide 
operating on fractions using a calculator
Operating on fractions using a calculator
  • Use calculator to add: +Key sequence 1 [a b/c] 2 [+] 2 [a b/c] 3 produces output 1  1  6
  • Use calculator to subtract: - Key sequence 2 [a b/c] 3 [-] 1 [a b/c] 2 produces output 1  6
operating on fractions using a calculator10
Operating on fractions using a calculator
  • Use calculator to multiply: xKey sequence 1 [a b/c] 2 [x] 2 [a b/c] 3 produces output 1  3
  • Use calculator to divide:Key sequence 1 [a b/c] 2 [] 2 [a b/c] 3 produces output 3  4
fractions and the x 2 key
Fractions and the x2key
  • Evaluate:
  • ‘Key as you see’ approach incorrectly produces 20
  • ‘Separate approach’ (separate top, separate bottom) is safer at this level of complexity as you will see on the next slide
the separate approach
The ‘Separate’ approach!

Evaluate:

Top:

Key sequence 4 [(] 1 [+] 2 [)] [x2]

Numerator output is: 36

Bottom:

Key sequence 3 [x2] [+] 4 [x2]

Denominator output is: 25

the separate approach cont d
The ‘Separate’ approach! (cont’d)

Once numerator and denominator have been calculated, a student has the choice of using [] key or [a b/c] key i.e.

36  25 = 1.44decimal format

36 [a b/c] 25 = 1  11  25fraction format