| < Learner/Context Analysis |
Instructional Goal |
Terminal Objective |
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The student will be able to convert any given positive integer less than 25510 from base ten to base two, and any positive integer less than 111111112 from base two to base ten, without the use of a calculator. |
Given a positive integer less than 25510 the student will correctly convert the number from base 10 to base 2 using a self-created table and pencil-and-paper.
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| Given a positive base 2 number less than 111111112
the student will correctly convert the number from base 2 to base 10 using a
self-created table and pencil-and-paper.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step |
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1. Use base ten numbers to create a table indicating place values of base two. |
1.1 Given a blank sheet of paper and pencil the student will draw columns and write in the correct base two values above each column.
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Subordinate Skills1.1 Beginning from the right, assign a value of one to first place to the left of the decimal point. 1.1.1 Identify place values. |
Subordinate Objectives1.1.1 When requested to start drawing a base 2 table, the student will place a one in the column on the right. 1.1.1.1 Given a 4-digit positive integer, the student will correctly identify the numbers in the ones place, tens place and hundreds place respectively. The student will indicate where the decimal point belongs. |
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1.2 Multiply number on the right by two to obtain value of next place to the left of decimal point.
1.2.1 Multiply a 2-digit positive integer by two.
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1.2.1 When given an incomplete base 2 table, the student will correctly determine the number to be multiplied by 2, perform the operation and write the solution in the next column to the left. 1.2.1.1 Given a 2-digit positive integer the student will correctly multiply the number by 2 using pencil-and-paper, or by mental arithmetic. |
| 1.2.2 Define positive integer. | 1.2.2.1 When given the definitions of integers the student will identify the definition of a positive integer. |
| 1.2.3 Identify positive integers. | 1.2.3.1 When given a choice of numbers the student will select the positive integers. |
| 1.3 Repeat step 1.2 until place value of 128 is reached | 1.3.1 When given an incomplete base 2 table and
asked to complete the table, the student will continue to correctly
multiply the number on the right of the table by two, and fill the product
in the correct column, until the number 128 has been written down.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step
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| 2. Decision: Is given number in base ten or base two? | 2.1 Given a number, with the base indicated in subscript, the student will
correctly identify the number as either a base 10 number or a base 2 number.
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Subordinate Skills |
Subordinate Objectives |
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2.1 State form of base ten number.
2.2 Identify base ten number.
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2.1.1 When asked which digits appear in a base 10 number the student will correctly state the digits 0 - 9. 2.2.1 When given a choice of numbers with the base written in subscript the student will correctly identify a base ten number. |
| 2.3 State form of base two number. | 2.3.1 When asked which digits appear in a base two number the student will correctly state the digits 0 and 1. |
| 2.4 Identify base two number. | 2.4.1 When given a choice of numbers with the base written in subscript the
student will correctly identify a base two number.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step
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| 3. Select highest number from base two table that is equal to, or less than given base ten number. | 3.1 Using the table drawn, the student will correctly identify the number on
the table that has a value more than the given number, and the number on the
table that has a value less than the given number.
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Subordinate Skills |
Subordinate Objectives |
| 3.1 Identify number order for numbers to hundreds place value. | 3.1.1 Given a selection of 3-digit numbers the student will correctly place the numbers in order from least to greatest. |
| Main Step in Instructional Goal | Subordinate Objective for Main Step |
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4. Place a one in column under that table number |
4.1 When asked to fill in the base 2 values of a given base 10 number, the student will place a one in the column under the highest table number which has a value less than the given number.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step
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5. Subtract table number from base ten number. |
5.1 Using paper-and-pencil if necessary the student will correctly subtract
the previously selected table number from the base ten number.
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Subordinate Skills |
Subordinate Objectives |
| 5.1 Subtract 3-digit numbers | 5.1.1 Given two numbers less than 129 the student will correctly subtract the
lesser number from the greater number.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step
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6. Decision: Is this the last column on the right? |
6.1 When given a completed base 2 table the student will correctly identify the last column. |
| 7. Decision: Is this difference (new base ten number) greater than or equal to the next number to the right in base two table? | 7.1 When given a new base 10 number the student will correctly identify the highest number on the table that is less than the given number. |
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8. Place a 0 in the next column. |
8.1 When the given number is less than the next number on the base 2 table, the student should place a 0 under that table number. |
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9. Check work. |
9.1 When given the base 2 solution of a base 10 number, the student should
check the solution by applying the division method of calculation.
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Subordinate Skills |
Subordinate Objectives |
| 9.1 Divide base ten number by two. |
9.1.1 Using paper and pencil or by mental arithmetic the student will correctly divide a given base 10 number by 2. |
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9.1.1 Divide 3-digit positive integer by two. |
9.1.1.1 Given a 3-digit positive integer the student will correctly divide the number by two and clearly indicate whether there is a remainder of one. |
| 9.3 Check there is a 0 in the column on the right. | 9.3.1 When solving the given division problem and obtaining a remainder of 0, the student should check that there is a 0 in the column on the right. |
| 9.4 Check there is a 1 in the column on the right. | 9.4.1 When solving a given division problem and obtaining a remainder of 1, the student should check that there is a 1 in the column on the right. |
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9.6 Check there is a 1 in next column to the left. |
9.6.1 When calculating a quotient of 1 the student will check that there is a 1 in the corresponding column. |
| 9.7 Divide quotient by two. | 9.7.1 When given a division problem, the student will correctly demonstrate the division of a quotient by two using paper-and-pencil or by mental arithmetic. |
| 9.7.1 Define quotient. | 9.7.1.1 When asked to define a quotient the student will state that it is an answer to a division problem. |
| 9.7.2 Identify a quotient. | 9.7.2.1 Given a solved written division problem the student will identify
which number is the quotient.
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Main Step in Instructional Goal |
Subordinate Objective for Main Step
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| 10. Write base two number in columns beneath base two table. |
10.1 Given a base two number, the student will write the number in the correct columns beneath the numbers of a self-created base two table. |
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11. Add all numbers on table that have a 1 in columns beneath them. |
11.1 Given a base two number, written on a base 2 table, the student will
correctly identify which numbers on the table are to be added together.
11.2 Given the numbers to be added together, the student will find the correct sum of these numbers.
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Subordinate Skills |
Subordinate Objectives |
| 11.1 Add 3-digit numbers. | 11.1.1 Given two 3-digit numbers, the student will add the numbers together correctly. |
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