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The objectives for this unit fall into the following clusters:
Cluster A: Create a base two table and identify whether a given number is
written in base 10 or base 2 (objectives 1 and 2),
Cluster B: Convert a base ten number to base two, and check the solution
using a different method of calculation (objectives 3-9),
Cluster C: Convert a base two number to base ten (objectives 10 and 11).
Each cluster is divided into steps according to Gagne's Nine Events of
Instruction and the ARCS model.
Cluster A
1) Gaining Attention.
Attention can be gained by introducing a manipulative. I will use M&Ms,
but seeds or Cuisenaire rods also work well.
2) Informing the learner of the objectives.
Inform them of objectives 1 and 2. Tell them that they cannot convert numbers
to and from base two, without first learning how to draw up a table. Explain the
accepted written format.
Relevance
Explain the use of binary numbers in computers and the importance of this.
3) Stimulating recall of prerequisite learning. Confidence.
Assess prerequisite knowledge of decimal system of digits and place values.
Link this to similarity of base 2.
4) Presenting stimulus material
Show them how the number of M&Ms in the piles are doubled, then relate
this to the base 2 table. Explain the table with text and graphics.
5) Providing learner guidance
Allow them to complete a base 2 table by providing the table only partly
completed.
Explain and test ability to identify base 2 numbers
6) Elicit performance
Allow them to draw up their own base 2 table.
7) Provide feedback
Allow them to check their table and correct any mistakes. Provide an example
of a completed table, later in the instruction.
8) Assess the performance
They will assess that the table is correctly drawn when they go onto the next
unit, and are presented with the completed table. Any errors will have to be
corrected before they can continue with the instruction.
9) Enhance retention and transfer, and satisfaction,
By proceeding with Cluster B, they are going to use and practice the skill
they have just learned.
Cluster B
1) Gaining Attention.
Show them magic cards that use base two to determine a number.
2) Informing the learner of the objectives. Relevance.
Inform them of first terminal objective 1.
3) Stimulating recall of prerequisite learning. Confidence.
Show them that we are adding base 2 numbers. Remind them that we always start
by drawing a base 2 table.
4) Presenting stimulus material.
Give the rules for converting numbers from base 10 to base 2.
5) Providing learner guidance
Provide a detailed example of converting a number from base 10 to base 2.
Using a different method of calculation, demonstrate how to check the answer.
6) Elicit performance
Begin a demonstration of a second example, leaving blanks for the student to
complete the problem.
7) Provide feedback
Demonstrate a step-by-step solution of the problem and the method used to
check the solution, so that the student can analyze their own errors, and
correct them if necessary.
8) Assess the performance
Provide three problems for the students to solve without assistance.
9) Enhance retention and transfer.
After they have completed cluster C, review the information learned by
providing the assessment problems. This time the problems can be written in a
different way, linking them to both cluster B and C. Transfer of knowledge is
facilitated in cluster C because the students are using the skills gained in
converting numbers from base 10 to base 2, in order to convert numbers from base
2 to base 10. The same concepts of base 2 values and place values apply.
Satisfaction
Give a progress report, i.e., now they are able to convert numbers from base
10 to base 2.
Cluster C
1) Gaining Attention.
Write five base 2 numbers and inform the students that it is a coded message
in ASCII and they will have to convert the numbers to base 10 to crack the code.
2) Informing the learner of the objectives.
Inform them of the second part of the terminal objective. Explain that it is
equally important to convert numbers from base two to base ten.
Relevance.
Explain how computers code information in the form of binary numbers with
ASCII.
3) Stimulating recall of prerequisite learning. Confidence.
Remind them of the previously discussed importance of binary numbers.
Reiterate the necessity of always writing the base 2 table, a skill with which
they are now familiar.
4) Presenting stimulus material
Present the base 2 numbers to be converted to base 10 and the ASCII codes in
decimal numbers.
5) Providing learner guidance
Provide a detailed example of the solution of the first problem, and thus the
answer to the first letter of the code to be solved.
6) Elicit performance
Start the next example and leave blank spaces in the solution for them to
complete the problem.
7) Provide feedback
The students will immediately recognize if they have made any errors because
their answers will not make sense. Provide solutions to the problems so that the
students can analyze their errors.
8) Assess the performance
The students will complete the three remaining problems without referring to
the examples or solutions.
9) Enhance retention and transfer, and satisfaction
After the students have completed cluster C, the assessment problems from
cluster B are answered. This also serves to transfer the skills learned from
cluster C to the required skills from cluster B.
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