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{{MyTitle| Jim Kelly}}

{{Infobox_personal
|Name =Jim Kelly
|Photo=[[Image:jkelly.jpg|150px|center]]
|Website = www.k-12math.info
|Occupation = a catalyst and concerned parent
|Email=k-12math@sbcglobal.net
|Boxes = {{User_MathGloss}}
|WM2=Nelliemuller
}}


==Reminiscences==
Shortly after completing studies in mathematics and education, I worked on provincial and national level education and community development projects in several Asian countries. The foundation for www.k-12math.info (a non-commercial and easy to use information website) had its origins in Asian secondary school mathematics development. 


For most of my life I have been fortunate enough to have had the opportunity to apply mathematics in the world outside the classroom. Working experience has shown me that the mathematics of elementary and secondary school provides a solid basis for the majority of mathematics used in the world’s retail, manufacturing and banking businesses. Inventory tracking and reporting information in the most efficient ways are skills picked up in the business world, and used in the development of the website 
[http://www.k-12math.info k-12math.info]. <br/>

==My WE projects==
To develop or improve materials you must understand the present state of those materials. We need to know what the key ideas are, what grade level (age level) they are used on and how they are used. We need to know what has been happening to key ideas over time (is the idea something that has lasted?).  A study of those key ideas in a number of primary and secondary school student textbook series provides a good starting point. Some of that information is provided in 
[[k-12math.info (English  -  Español – Français)]]

November 2009: K-12math.info(English-Español–Français) is being reformatted so that its content is divided into 2 approaches to the information.  One side of the page looks at the content of primary and secondary school mathematics. And the other side examines primary and secondary school mathematics by age groups (grade levels). 
 
Also check out the link to "ACUTE ANGLE" as the table contained in it now contains links to cnx.org's OER mathematics series MATHEMATICS GRADE 1 (through 9). Additional links will be set up once the question of the stability of the information within the links is established.

Regretfully the trilingual nature of the page will be discontinued. Spanish and French versions of the new approach will be placed in their appropriate language Wikieducator worlds.

November 16: the page has been reformat - hope the new page will allow for quicker access to information.

{{InfoboxContributor 
|Boxes = {{User_MathGloss}}
}}

=Notes from Other Members=
* Thanks, Jim, for your kind words about my participatory approach to Literacy training.--[[User:Philbartle|Phil Bartle]] 10:25, 27 June 2009 (UTC)
*<font color=purple>Jim, I am looking forward to "seeing" your project develop. --[[User:Nelliemuller|Nellie Deutsch]] 03:53, 26 June 2009 (UTC)</font>
{{note|great page !welcome to the network of colllaborative work.}}--Hemrom 01:03, 20 October 2008 (UTC)

{{WelcomeEL4C25Workshop}}

= WikiEducator Sandbox =
<h2> Addition (decimal ) </h2>

'''Age requirements: '''

The activities and content of this module can be used with learners from '''age 9 years (U.S. grade 4) and up'''. On the average within a textbook series the term '''Addition of Decimals''' will be defined, developed, reviewed or treated as enrichment activities on 4 grade levels in United States materials. (Reminder: U.S. textbook series are often designed using a spiral approach - the content evolves in successive grade levels. So choose activities that are appropriate.) 


{{web_resources|
Most of the links provided go beyond the scope of this lesson, but are given to focus on where the ideas of this lesson are going or provide additional background information. And to serve the needs of the few learners who seem to know everything!



Decimal [http://en.wikibooks.org/wiki/Arithmetic/Reading_Decimal_Numerals Reading decimals]

Decimal [http://en.wiktionary.org/wiki/decimal Wiktionary] 

Place-value [http://en.wikiversity.org/wiki/Primary_mathematics:Numbers Wikiversity] 

Place-value [http://en.wikipedia.org/wiki/Place_value Wikipedia]

Adding decimals [http://en.wikipedia.org/wiki/Addition#Decimal_system  basic Wikipedia]

Adding decimals [http://en.wikibooks.org/wiki/Primary_Mathematics/Decimals Wikibooks - very basic]

Adding decimals [http://en.wikibooks.org/wiki/Applied_Math_Basics Wikibooks - good information]

Estimating [http://en.wiktionary.org/wiki/estimate Wiktionary]

}}


'''Special Note: No formal definition of Addition of decimals is being made within these activities. Please refer to your textbook, curriculum guide, national syllabus, etc. for the definition to be used.'''

{{Preknowledge| 

Before beginning to develop the procedure for adding decimals, make sure that students are comfortable with:

1. Being able to recognize a decimal.

2. Understanding place-value.

3. Estimating the nearest whole number to a given decimal.
}}




{{Objectives 
| Upon completion of this module:
*  The students should review what a decimal is, and the importance of the concept of place-value.
* The students should be able to explain how to add decimals. 
*  (optional)The students should be able estimate the correctness of their answers.
*  The students should be able to give examples of ratios which they come into contact with daily.

}}


{{Activity 
| Your Activity:
''If you have an original activity on Adding of Decimals which has worked for you in your classroom, and would like to share please use this space to enter it.  Please do not use activities that are copyrighted.''   }}


{{Activity 
| Activity 1:
Work with local currencies in situations that students find themselves in. If there are receipts examine them. 
}}


{{Activity 
| Activity 2:
If one litre of drinking water costs 1.5 (1,5). Is this too much? What does it cost in your town?
}}

{{Activity 
| Activity 3:
Create an assortment of objects of different lengths, some not equal to unit lengths (keep it simple a whole unit plus .5 and/or .25 in length). Measure them and add the lengths. Use decimal format to measure and add lengths.
}}

{{Activity 
| Activity 4:
Use patterns to help learners understand processes. 
(Note please use appropriate decimal notation with your learners.)

0 ,  0.0 ,  0.00 ,  0.000 ,  0.0000  are names for the ___(Same or different)__  value.


Select 6 students and have each write one of the addition problems on the chalkboard and read it to the class (allow for variations in how these problems are read). For the seventh problem put it on the chalk board and without saying a word draw a big circle where the sum should be and ask the class what should be here?        

                                         
   2.0     2.3    3.4    23.43   764.8    481.94         109.543
 + 0.0   + 0.0  + 0.0  + 00.00 + 000.0  + 000.00       + 000.000
 -----   -----  -----  ------- -------  --------       ---------
   2.0     2.3    3.4    23.43   764.8    481.94        _________



'''Therefore - Zero added to any decimal number is ___________
'''

}}


{{Activity 
| Activity 5:
Drill is a necessity in learning how to do arithmetic operations. Being able to verbalize problems and their solutions is important.  Divide the class into teams (mix the teams appropriately). Have one team put a problem on the chalkboard, and another team solve it. The first team is responsible for verbalizing the problem, and the second team verbalizing the solution (maybe a third team judging which team was the clearest in their explanation).
}}

{{Activity 
| Activity 6:
Never ignore those few open minutes at the end of the period (or at the beginning of the period when student attention needs to be focused). A couple of mental arithmetic problems should always be handy and ready to use. "Put your paper and pencil away - add .3 to .5 to get ... - adding .3 to .7 gives .... etc. " "round the addends to the nearest whole number and add 1.3 to 1.8 to get...." 
}}

<h2> Protractor </h2>

'''Age requirements: '''

The activities and content of this module can be used with learners from '''age 10 years (U.S. grade 5) and up'''. On the average within a textbook series the term '''Protractor''' will be defined, developed, reviewed or treated as enrichment activities on 4 grade levels in United States materials. (Reminder: U.S. textbook series are often designed using a spiral approach - the content evolves in successive grade levels.So choose activities that are appropriate.) 


{{web_resources|
Most of the links provided go beyond the scope of this lesson, but are given to focus on where the ideas of this lesson are going or provide additional background information. And to serve the needs of the few learners who seem to know everything!

Protractor [http://www.en.wiktionary.org/wiki/protractor  Wiktionary with translations],
[http://en.wikipedia.org/wiki/Protractor Wikipedia]

Angle [http://www.en.wiktionary.org/wiki/angle  Wiktionary with translations],[http://en.wikipedia.org/wiki/Angle Wikipedia]

Ray [http://www.en.wiktionary.org/wiki/ray  Wiktionary with translations],[http://en.wikipedia.org/wiki/Line_(mathematics)#Ray  Wikipedia]

Accuracy [http://www.en.wiktionary.org/wiki/accuracy  Wiktionary],[http://en.wikipedia.org/wiki/Accuracy Wikipedia]

Estimating [http://en.wiktionary.org/wiki/estimate Wiktionary]

Degree [http://en.wiktionary.org/wiki/degree  Wiktionary with  translations], [http://en.wikipedia.org/wiki/Degree_(angle) Wikipedia] 

}}

'''Special Note: No formal definition of PROTRACTOR is being made within these activities. Please refer to your textbook, curriculum guide, national syllabus, etc. for the definition to be used.'''

{{Objectives 
| Upon completion of this module:

1)The students should improve their ability to guess and estimate answers.

2)The students should be able to give some basic information on what  a protractor is.

3)The students should be able to give examples of where protractors may be used.

4)The students through their work the need for standard units.

}}

'''Materials needed: '''

'''Classroom needs:''' a cardboard circle large enough to be used on the chalkboard, sheets of paper  large enough to be able to fit over half the circle.

'''Students need to bring:''' three sheets of paper and notebook.

{{Activity 
| Activity:
''If you have an original activity on PROTRACTOR which has worked for you in your classroom, and would like to share please use this space to enter it.  Please do not use activities that are copyrighted.''   }}

{{Activity 
| Historic approach:

Who is Thomas Blundeville ?[http://en.wikipedia.org/wiki/Thomas_Blundeville Wikipedia] 

What is a Dividing Engine? [http://en.wikipedia.org/wiki/Dividing_engine Wikipedia] 

How is a protractor related to a compass?   [http://en.wikipedia.org/wiki/Protractor_compass#Modern_compasses wikipedia] 
 }}

{{Activity 
| Activity 1:
If the students have not worked with a protractor; or indicate by their actions that they do not have an understanding of what the purpose of a protractor is the following activity should be used.
Have several students on opposites sides of the classroom take out a piece of paper and by folding it create an angle [make sure that at least one is not huge]. After the students have completed the construction of their angle, have them color it [make sure they use different colors]. Compare the different angles.. Who has the smallest? Who has the largest? How many of the small angles make up the larger angle? … 
On the chalkboard draw horizontally a ray which will represent one side of an angle. Taking one of the small sized paper folded angles, and have one of the students go up to the chalkboard and copy the angle using the already drawn ray as one side of the angle. Have another student using the same angle  and starting from the original draw ray construct an angle that is three times the size. “How many different angles do we have?” “ Can we name them ? [Put the names on the chalkboard]”  “How big are the angles as compared to paper folded angle [On the chalkboard using the correct notation for measurement of an angle, write the number of paper folded angles after each of the identified angles]?” 
The paper folded angle has become our standard unit for measuring angles. 
“While there is nothing wrong with our paper folded angle as being the standard unit for measuring angles, the world outside our classroom has accepted another unit of measurement for an angle. The standard of unit for measuring an angle is called..... [degree]?”  

 }}


'''Questions to Consider'''

----




<h2> Ratio </h2>

'''Age requirements: '''

The activities and content of this module can be used with learners from '''age 10 years (U.S. grade 5) and up'''. On the average within a textbook series the term '''Ratio''' will be defined, developed, reviewed or treated as enrichment activities on 6 grade levels in United States materials. (Reminder: U.S. textbook series are often designed using a spiral approach - the content evolves in successive grade levels. So choose activities that are appropriate.)


{{web_resources|
Most of the links provided go beyond the scope of this lesson, but are given to focus on where the ideas of this lesson are going or provide additional background information. And to serve the needs of the few learners who seem to know everything!

Ratio [http://www.en.wiktionary.org/wiki/ratio  Wiktionary],
[http://en.wikipedia.org/wiki/Ratio Wikipedia]

Accuracy [http://www.en.wiktionary.org/wiki/accuracy  Wiktionary],[http://en.wikipedia.org/wiki/Accuracy Wikipedia]

Rectangle [http://www.en.wiktionary.org/wiki/rectangle  Wiktionary],[http://en.wikipedia.org/wiki/Rectangle Wikipedia]

Estimating [http://en.wiktionary.org/wiki/estimate Wiktionary]

English units of measurement [http://en.wikipedia.org/wiki/English_units_of_measurement Wikipedia ] 

Metric units of measurement [http://en.wikipedia.org/wiki/Metric_system_of_measurement Wikipedia]
}}

'''Special Note: No formal definition of RATIO is being made within these activities. Please refer to your textbook, curriculum guide, national syllabus, etc. for the definition to be used.'''

{{Objectives 
| Upon completion of this module:
*  The students should improve their ability to guess and estimate answers.
*  The students should be able to give some basic information on what a ratio is.
*  The students should be able to give examples of ratios which they come into contact with daily.
* The students through their work with the exercises will review various units of measurement. 
}}

'''Materials needed: '''

'''Classroom needs:''' yard (meter) stick, foot (metric) ruler, tablet of paper, cardboard rectangles with the following dimensions: 3 by 9 inches, 6 by 12 inches, 6 by 18 inches, and 12 by 24 inches [ Do not put the dimensions on the backs of these rectangles, and work with a different rectangle in each class ].

'''Students need to bring:''' ruler and notebook.

{{Activity 
| Activity:
''If you have an original activity on RATIO which has worked for you in your classroom, and would like to share please use this space to enter it.  Please do not use activities that are copyrighted.''   }}

{{Activity 
| Activity 1:
To develop the concept of ratio several objects of varying lengths should be presented to the students so that the objects can be compared. For example, a yard stick and a foot ruler (a meter stick and a 10 centimeter ruler) - “How can we compare these?” [Many answers possible] “Which is bigger?” “How much bigger? [the yard stick is three times as big as the foot ruler. Meter stick is 10 times the big as the 10 centimeter ruler] Encourage the students to be as accurate in describing the comparison between the objects.
}}

{{Activity 
| Activity 2:
Have two students in the class stand up. “Who is the taller?” [writer their names on the chalk board with a check by the tallest student name] “How tall are they?” [Encourage the students to estimate in feet, inches, decimeters or centimeters] Have the estimates put under the appropriate name on the chalkboard with the unit of measure being used. Place the two dot notation for a ratio between each. “The two dots [semicolon] are read as 'to' “ Have the learners read out loud the ratios they have on the chalkboard. Since students at this age grow fast, encourage the students to actually measure their height and put the information on the chalkboard with the ratio symbol being used. Let the students know that each of these comparisons is a ratio.


“What was the ratio of the foot ruler (centimeter ruler) to the yard stick (meter stick)?” What is the ratio of the yard stick (meter stick) to the foot ruler (centimeter ruler)?” “Inches to foot ruler?” “Centimeters to meter stick?” Place the answers on the chalkboard with the correct notation, and have the class read what has been written.

Have the students list some 'facts' about ratios on the chalkboard [comparison of two objects. Ratio involves numbers. The words 'how much' are used. It can involve a measurement. Etc.] Do not define the word ratio; nor to correct the 'facts' the students have listed on the chalkboard. Ask the students if they agree with all the 'facts'? If they do not agree they need to provide examples that question the 'facts'. Let the class decide the value of what is being said. Summarize on the chalkboard what is being said and agreed upon. The students should copy the 'facts' down in their notebooks for future reference [close the notebooks, and have the students attention directed to the front of the classroom]. Erase what has been put on the chalkboard.
}}
'''Note''' A certain amount of confusion is to be accepted as many different but correct ratios can be developed in working with these activities – it is a question of how precise do we need to be [equivalent and simplest form ratios will be covered in the next chapter]. Standards of accuracy in measurement to be used in this class can be covered [more on this in rounding off decimals].

{{Activity 
| Activity 3:
“When we compare, how many things must we compare?” Hold up one of the previously prepared cardboard rectangles. “What king of shape is this?” “What kind of comparisons can be made with this?” “What do we know about rectangles?” “If we refer to the long side as the length, we call the short side the...?” “Can we compare these?” On the chalkboard write LENGTH : WIDTH. Make an estimate of what the ratio is between the length and width. Write some of the estimates on the chalkboard; a couple should be turned around so that the students catch errors and correct them.

“How can we find out which is the most accurate?” [measuring] “Suppose we do not have a ruler to measure with, how can we get a better answer than estimating?” [One way is to use a piece of notebook paper and fold it so that it is as long as the width.] “Using this folded paper how long is the width?” [1] Place this information on the chalkboard FOLDED PAPER 1 : “ There are how many folded papers in the length of the rectangle?” On the chalkboard complete the FOLDED PAPER line of information. “Is this ratio more accurate than our estimations?”

Have the students take out their rulers. “Your ruler is divided into?” [inches, centimeters, etc] “What is the width and length of the rectangle?” Add the information the students find to the chalkboard list INCH __ : ___. “Is this ratio more accurate than our folder paper?” Encourage the students to make comments about the ratios they have come up with for the rectangle – estimation, paper folding, and ruler developed ratios. List the comments the class generally agree upon on the chalkboard. Now have the students open their notebooks and copy the information that is on the chalkboard. 
}}

'''Questions to Consider'''

----

1. Write the ratio for each:[[/ratiojk-Answer1/|<span style="font-size:120%">ANSWER</span>]]

a. 5 to 12

b. 5 inches to 12 inches

c. five inches to twelve inches

d. 5 inches to 1 foot

e. Tony has 3 oranges and Julie has 5 oranges.

f. This week has two vacation days in it. 
  

2  Write the ratio for each:[[/ratiojk-Answer2/|<span style="font-size:120%">ANSWER</span>]]

a. The number of sides of a triangle to the number of sides of a quadrilateral.

b. One side of an equilateral triangle to the number of sides of that triangle.

c. The perimeter of a square to one of its sides.

d. The diameter of a circle to the circumference of that circle.


3. In a rectangle find the ratio of:[[/ratiojk-Answer3/|<span style="font-size:120%">ANSWER</span>]]

a. Two adjacent interior angles of a rectangle.

b. The  interior angle at a vertex to the exterior angle at that vertex;

c. Two adjacent sides.


4. There are 25 teachers in a school with 250 students. What is the teacher to student ratio in the school? What is the teacher to student ratio in your school?[[/ratiojk-Answer4/|<span style="font-size:120%">ANSWER</span>]]


5. This is a simple single gear bicycle. There are 45 teeth on the gear that is attached to the back wheel of bike. There are 15 teeth on the gear attached to the pedal. One revolution of the back wheel, will require how many revolution of the pedal?[[/ratiojk-Answer5/|<span style="font-size:120%">ANSWER</span>]] 


6. What happens if one of the quantities that is being compared is a zero?  0 : 4 [[/ratiojk-Answer6/|<span style="font-size:120%">ANSWER</span>]]


7. Given AB is 4 meters and AC is 1 meter. Find the ratios of the following:[[/ratiojk-Answer7/|<span style="font-size:120%">ANSWER</span>]]

   A ------------- C ------------------------------- B

		a)  AC : CB
		b)  AC : AB
		c)  CB : AC
		d)  AB : AC
		e)  CB : AB
		f)  CA : AC

<h2> tables </h2>


{| border="1" cellpadding="5" cellspacing="0"
|colspan="13"|
===Adding by regrouping===
|-
|
|K (age:  5)
|1 (age:  6) 
|2 (age:  7)
|3 (age:  8) 
|4 (age:  9)
|5 (age: 10) 
|6 (age: 11)
|7 (age: 12) 
|8 (age: 13)
|9 (age: 14) 
|10 (age: 15)
|11 (age: 16)
|-
| 1
| -
| -
| 2-039
| 2-040
| 2-042
| -
| -
| 3-058
| 3-021
| -
| -
| -
|-
| 2
| -
| -
| 3-153
| 4-085
| 4-041
| 4-059
| -
| -
| -
| -
| -
| -
|-
| cnx
| *
| -
| [http://cnx.org/content/m32449/latest/ 2]
| -
| -
| -
| -
| -
| -
| -
| *
| *
|}

usage code - page number ( for online textbook click on usage code to link to the page )

Series:

1. Harcourt, Brace, Jovanovich series: Let's Begin (K), One by One (1), Two by Two (2), Harbrace Mathematics - Green (3), Harbrace Mathematics - Orange (4), Harbrace Mathematics - Purple (5), Harbrace Mathematics - Brown (6) 1972 Payne, Beatty,.

Key Ideas in Mathematics (7th and 8th grades age 12/13) 1974 Gerardi, Jones .;

Algebra One(9th grade age 14) 1972 Payne, Zamboni ;

Geometry (10th grade age 15) 1972 Ulrich and Payne;

Algebra Two(11th grade age 16) 1972 Payne, Zamboni


2. D. C. Heath Company: Heath Elementary Mathematics (K-6th grade) 1972 Dilley, Rucker, Jackson;

Heath Mathematics (7-8th grade) 1973 Rising and Smith;

High School Mathematics - 1(9th grade age 14) 1964; High School 

Mathematics - 2(10th grade age 15) 1965; High School Mathematics - 3(11th grade age 16) 1966; Beberman and Vaughan 


CNX. (online with www.cnx.org )

Mathematics Grade 1 Uploader, S. http://cnx.org/content/col11126/1.1/, Oct 12, 2009   

Mathematics Grade 2 Uploader, S. http://cnx.org/content/col11131/1.1/, 
Oct 15, 2009.

Mathematics Grade 3 Uploader, S. http://cnx.org/content/col11128/1.1/, 
Oct 14, 2009.


usage codes:
           
4 The term is present and is being defined.

3 The term is present but not being defined.

2 The term is not present but a synonym is being used.

1 The term is present but not part of the lesson proper; it is part of an enrichment activity.

- The term is not present.

*- Textbook unavailable for reviewing.


[[Category:Mathematics]][[Category:Primary Education]]