Order, Order!
Key words: decimal number, decimal fraction, less than,
greater than, between, order, compare, digit, most/least
significant digit. <, >, ≤, ≥, =, ≠
Objectives
• Compare and order decimals
Instructions for the teacher:
The purpose of this activity is to generate sets of decimal
numbers for pupils to put in order.
Lists of random numbers can be generated automatically. They
can be stored and viewed. Pupils can then attempt to order the
lists. When they are ready the calculator can sort the list to
validate the student’s attempt.
KS3 Framework
page ref: 40
Press STAT
Choose 1:Edit to show the list editor.
Use the up cursor to highlight the L1 header
Now enter the command to generate the sequence of random
numbers.
Press MATH
Press ► to select the NUM menu
Choose 5:int
Press MATH
Press ► ► ► to select the PRB menu
Choose 1:rand
Type ( 7 ) × 100 ) ÷ 100
Use the left and right cursor to check that you have entered
this:
L1 = int(rand(7)*100)/100
Press ENTER
At this stage it is helpful to notice that we did rand(7) because
the screen can show 7 numbers in the list editor. You could
choose to have more (or fewer) numbers in the list if you wish.
The trick of multiplying the integer value by 100 and then
dividing by 100 generates numbers to a maximum of 2
decimals places. We could vary this e.g. use 1000 to generate
numbers to at most 3 decimal places.
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Pupils can now work on their list.
When they are ready the calculator can order the list for you.
Press 2nd STAT to show the LIST menu
Press ► to select the OPS menu
Choose 1:SortA meaning sort in ascending order
Press 2nd 1 to sort list L1
Press ENTER
Press STAT
Choose 1:Edit to display the sorted list.
Once you feel confident with the procedure, it is possible to
vary the sequence in lots of different ways. Notably you can
change the range of the sequence by using a scaling factor:
e.g. L1 = int(rand(7)*500)/100
This generates a sequence between 0 and 5 to at most 2
decimal places.
e.g. L1 = int((1+rand(7))*500)/100
This generates a sequence between 1 and 6 to at most 2
decimal places.
The random number generator needs a seed to start the
sequence it generates. To make sure that different sequences
are generated you can change the seed. To do this, enter any
number into rand. (For example: change the seed to 0.5)
Press 2nd MODE (for QUIT) to get the main screen
Press 0.5
Press STO→
Press MATH
Press ► ► ► to select the PRB menu
Choose 1 (rand)
Press ENTER
Answers to student activity sheet.
1. 0.04, 0.14, 0.4, 0.51, 0.73, 0.8, 0.94
2. 0.02, 0.2, 0.3, 0.61, 0.83, 0.97, 0.98
3. 0.42, 0.99, 1.56, 3.16, 3.48, 4.92, 4.98
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Order, order!
First: Reset your TI 83-Plus
• Press 2nd + to get MEM
• Choose 7 (Reset…)
• Choose 1 (All Ram…)
• Choose 2 (Reset)
This activity will give you a list of decimals.
Your job is to put them in order.
You can use your calculator to check if you have got it right.
The first three questions will help you practice without the calculator.
1.
Look at the list of decimals in the list L1.
Write them in order of size, smallest first.
2.
Now write this list in order of size:
3.
Now write this list in order of size:
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4.
Now you can make lists of your own.
Press STAT
Choose 1:Edit to show the list editor
Press ▲ Use the up cursor to highlight the L1
Press MATH
Press ► to select the NUM menu
Choose 5:int
Press MATH
Press ► ► ► to select the PRB menu
Choose 1:rand
Type ( 7 ) × 100 ) ÷ 100
Press ENTER
Write down the list in order of size, smallest first.
5.
Now sort the list on the calculator
Press 2nd STAT to show the LIST menu
Press ► to select the OPS menu
Choose 1:SortA
Press 2nd 1 to sort list L1
Press ENTER
Press STAT
Choose 1:Edit to display the sorted list
Check that your answers are the same.
6.
Now repeat steps 4 and 5 at least 4 times. You will keep getting different lists
because the calculator uses a random number generator to make the lists.
Challenge
7. Repeat steps 4 and 5 again, but change this line:
Type ( 7 ) × 100 ) ÷ 100 , to:
(a)
(b)
(c)
(d)
Type
Type
Type
Type
(
(
(
(
7
7
7
7
)
)
)
)
×
×
×
×
300
500
1000
2000
) ÷ 100
) ÷ 100
) ÷ 1000
) ÷ 1000
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