Programed instructional material:Integers
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This is an initial attempt by my students of B.Ed. in creating Programmed Instructional material using the template I had provided them. Your observations and suggestions are welcome!
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How to Be Responsive if…· A student solves it one .docx
How to Be Responsive if…
·
A student solves it one way and can’t think of any other way:
· Ask if they can draw a picture that shows the answer.
· Ask if they can invent a new way to solve it.
· Show them a method that they haven’t used and ask if they can figure out how it works and why.
·
A student solves the problem multiple ways easily:
· Ask
why they did what they did. Why do their methods work? Be specific about what you want to know.
· See if they can come up with another method that isn’t as easy to find.
· Ask the interviewee how their methods are similar and different. Be as specific as possible.
·
A student solves the problem incorrectly:
· Remain neutral.
· Ask the interviewee
why they did what they did. Why do their methods work?
· See if they can solve it a different way. Compare solutions.
· Say, “I saw someone else solve it like this….and they got 90.” What would you say to that person?
General Strategies for Being Responsive
· Ask, “Why?” Why did they do …(be specific about what you want to know)? How do they know it’s mathematically correct?
· Be patient. Use lots of wait time, and don’t answer your own questions.
· Focus on understanding what they are thinking.
· Ask them to make connections.
· How is this the same as what you did in the first solution?
· How is this different then what you did in the standard algorithm?
· Ask them to generalize their strategy.
· Will it always work to …?
· What if it was … instead?
Solution
Strategies and Chart for Students
Strategy
Example
Probing Questions
Direct Modeling
Equal groups
Array
· How does this represent the problem?
· Could you represent it in a different way?
· 18 groups of 5 instead of 5 groups of 18
Traditional Algorithm
· Why did you put a little 4 on top of the 1?
· Why didn’t you put the little 4 on top of the 8?
· What does the little 4 represent?
Partial Products
· How is the 40 represented in the traditional algorithm?
· Why is it 50 instead of 5?
· How did you know how to line up the 40 and the 50?
· Can you apply this method to 32 x 9?
Box Method
· How did you know where to put the numbers and what to write in the boxes?
· Why did you add 50 and 40?
Distributive Property
a(b+c) = ab + ac
5 x ( 10 + 8)
50 + 40
90
OR
5 x (5 + 5 + 8)
25 + 25 + 40
90
OR
5 x (11 + 7)
55 + 35
90
OR
5 x (20 - 2)
100 - 10
90
· Why did you decide to break 18 into 10 and 8?
· You broke the 18 into 10 and 8. If you broke it up differently, would your method still work?
· Does the distributive property work with subtraction?
Doubling/Halving
5 x 18
Double 5 → 10
Halve 18 → 9
10 x 9 = 90
· Why does this strategy work? What is happening here?
Repeated Addition
18 + 18 + 18 + 18 + 18 = 90
OR
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 18
· Is adding 18 five times the same as adding 5 eighteen times? Why?
Associative Property
5 x 18
5 x (6 x .
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Programed instructional material:Integers
- 1. Topic : Integers Class : 6th Age : 13- 15 Medium : English Let’s start module Programmed Instructional material
- 2. Objectives At the end of this module you will be able to- know about the meaning of integers know about the types of integers know how to solve problems Let’s start module
- 3. Integers are a special group or category of numbers that: • Consist of the set of numbers:[...-3,-2,- 1,0,1,2,3...] • Integers can be positive or negative. • Integers do not have decimals . • Integers do not have fractions. Next Slide…
- 4. INTEGERS NON-INTEGERS • 5 5.9 • -9 7/5 • 67 45.2 • -68 8/2 Next Slide… Examples
- 5. TYPES OF INTEGERS POSITIVE INTEGERS • Positive integers are the set of natural numbers. • They do not have any fractional and decimal parts. • Examples : 1,2,3,4…… NEGATIVE INTEGERS • Negative integers are the set of negative numbers. • They do not have fractional and decimal parts . • Examples : -1,-2,-3,- 4………. Next Slide…
- 6. Next Slide…
- 7. On the number line points to the right of zero are positive and points to the left of zero are negative . Zero is neither negative nor positive . It is greater than negative numbers and smaller than positive numbers. Lets answer some questions
- 8. Q1: Integers can be ................. Positive Negative Both positive and negative Neither negative or positive
- 9. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 10. Oops! Wrong Answer Click Here to attempt the question again Hint! EXAMPLES INTEGERS : 7, 9, - 15, 20, - 32......... NON-INTEGERS : 4/6, 3/9, 4.8, 3.9 .....
- 11. Congratulations you have selected Right Answer! Click Here to go the next question …
- 12. Q2: Integers do not have........... Positive Fractions Decimals Both fractions and decimals
- 13. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 14. Oops! Wrong Answer Click Here to attempt the question again Hint! EXAMPLES INTEGERS : 6, 3, 9 ,-7 , -4....... NON-INTEGERS : 5.8 ,4/5, 8/7, 9.3.....
- 15. Congratulations you have selected Right Answer! Click Here to go the next question …
- 16. Q3: 33 and 4 is an example of............ Integer Non-integer Decimals Fractions
- 17. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 18. Oops! Wrong Answer Click Here to attempt the question again Hint! Integers can be positive and negative
- 19. Congratulations you have selected Right Answer! Click Here to go the next question …
- 20. Q4: Positive integers are set of ........ Decimal numbers Natural numbers Odd numbers Even numbers
- 21. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 22. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 23. Congratulations you have selected Right Answer! Click Here to go the next question …
- 24. Q5: On the number line points to the right of zero are.............. numbers Positive Negative Decimals Both decimals and negative
- 25. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 26. Oops! Wrong Answer Click Here to attempt the question again Hint!
- 27. Congratulations you have selected Right Answer! Click Here to know your score…
- 28. Congratulations you have Scored 50 marks!