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An enrichment program for elementary grades Author(s): ANNA MARIE EVANS, MILDRED HEADLEY and JUDITH LEINWOHL Source: The Arithmetic Teacher, Vol. 9, No. 5 (MAY 1962), pp. 282-286 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41184632 . Accessed: 12/06/2014 22:35 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 22:35:12 PM All use subject to JSTOR Terms and Conditions

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Page 1: An enrichment program for elementary grades

An enrichment program for elementary gradesAuthor(s): ANNA MARIE EVANS, MILDRED HEADLEY and JUDITH LEINWOHLSource: The Arithmetic Teacher, Vol. 9, No. 5 (MAY 1962), pp. 282-286Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41184632 .

Accessed: 12/06/2014 22:35

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 91.229.229.212 on Thu, 12 Jun 2014 22:35:12 PMAll use subject to JSTOR Terms and Conditions

Page 2: An enrichment program for elementary grades

In the classroom Edwina Deans

An enrichment program for elementary grades ANNA MARIE EVANS, MILDRED HEADLEY, and JUDITH LEINWOHL Cincinnati Public Schools, Cincinnati, Ohio. The authors are elementary supervisors in the Cincinnati Public Schools.

A continued concern of teachers is that of adjusting instruction to meet the varying abilities of pupils within a classroom. Cin- cinnati initiated a program in 1959-60 to provide opportunity for able children in arithmetic in Grades 3-6 to proceed at a rate commensurate with their ability. Generally, two groups moving at different rates are formed within the class.

Children are selected for acceleration when in the judgment of the teacher, principal, and supervisor they have suc- cessfully completed the basic textbook for the grade and have reached the objectives for the grade as set forth in the Cincinnati curriculum guides. After successfully com- pleting the work for the grade level, the accelerated pupils use a supplementary text designed for the next grade level, with emphasis given to breadth and depth of understanding. A supervising teacher serves as full-time coordinator of the pro- gram.

As a part of the in-service educational program, workshops, institutes, and meet- ings are planned for teachers in the experi- ment. These conferences provide ideas to improve instructional techniques, arouse interest in and appreciation for arithmetic, and enrich the teacher's mathematical background.

Following the close of school in 1961, a five-day workshop was held in coopera- tion with the University of Cincinnati. Dr. Glenadine Gibb, State College of Iowa, and Dr. John Marks, San Jose State Teachers College, served as consultants. Teacher committees worked independ- ently to explore the application of the workshop discussions to classroom ac- tivities. As a result, two bulletins, "Arith- metic Enrichment Ideas for Grades 1, 2, 3" and "Arithmetic Enrichment Ideas for Grades 4, 5, 6," for classroom use were de- veloped and distributed to all teachers in Grades 1-6.

The material in these bulletins provides stimulating and challenging enrichment experiences for many children, will help to increase their appreciation of and interest in arithmetic, and inspire them to create materials of their own. The exercises are designed so that pupils may use them chiefly for independent activities while working individually or in small groups from chalkboard directions, charts, study cards, or from self-administering work- sheets provided by the teacher. Suggested grade placement is indicated for the more advanced activities. Implementation of the material will vary from school to school. It is from these bulletins that the

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Page 3: An enrichment program for elementary grades

activities suggested in this article are taken.

Activities for grades 1, 2, 3

Division readiness Make an accordion book about 3's. Use

it to work these problems. Write your answers to tell "how many."

Answer 1. How many 3's = 6? □ 2. How many 3's = 15? D 3. How many 3's = 21? □ 4. How many 3's = 30? □ 5. How many 3's = 18? □

Review of fundamental operations Do you know what a Magic Square is?

This is one. What can you discover about it? Find the sum of each row, column, and main diagonal. Then you will know!

Magic Square

10 3 8

5 7 9

6 11 4

Experiment with the given Magic Square. Draw lines for a new square and call it Square A. Add 7 to each number of the given Magic Square and write the answers in the correct spaces. Is Square A a Magic Square? Prove it.

Square A

Experiment again. Draw lines for a new square and call it Square B. Subtract 2 from each number in the given Magic Square and write the answers in the cor- rect spaces. Is Square В a Magic Square? Prove it.

Square В

Experiment again. Draw lines for a new square and call it Square C. Multiply each number in the given Magic Square by 5 and write the answers in the correct spaces. Is Square С a Magic Square? Prove it.

Square С

Number sentences Can you make number sentences for

problems and show the operations to per- form to get the answer?

Example: Bill had groups of 3's. When he put them together, he had 12. How many groups did he have? nX3 = 12, 12-7-3=4, 4X3 = 12. Answer: 4 groups.

Now make number sentences for these problems and show the operations to per- form to get the answer. 1. Ann had 5 in each group. When she put

her groups together she had 15. How many groups did she have?

2. Jack had 3 groups of the same size. He put them together and had 18. How many were in each group?

Next write a story problem for these

May 1962 283

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Page 4: An enrichment program for elementary grades

number sentences. Draw a picture to show the meaning of each number sentence.

1. 2X5 = n 2. 4X2 = n

Complete the following number sen- tences :

1. 2D5 = 10 2. 9D2 = 11 3. 7ХП==56 4. DX9 = 36 5. 15D8 = 7 6. (3D9)+6 = 2 7. (3X5)D27 = 42 8. (27D3)D6 = 15 9. (8D7) + D = 5

10. 6XD = 18

Locating points Could you show where you lived on a

map of city streets? Example: If you lived on the corner of

1st and A streets, it is indicated with an X.

6

F

E

ю л z ш л Š С л

в

А I х ' ' ' MAIN ist 2^0 3»» 4th 5th 6th

STREETS

Indicate the following: 1. E and 3rd streets with a check 2. A and 5th streets with a plus sign 3. С and 5th streets with a minus sign 4. F and 2nd streets with a dot 5. D and 4th streets with a circle

Activities for grades 4, 5, 6

Concepts of fractions Supply the missing number in each box.

Given fraction I i i s è I Write a fraction 3 times as large as the fractions in the first row

Write a fraction twice as large as the given fraction

Write a fraction half as large as the given fraction

Write a fraction that tells how much to add to the given fraction to get a sum equal to 1

Write a fraction whose denominator is one more than the denominator of the given fraction

Fundamental operations with fractions 1. Given the answer §, make up a number

sentence by supplying numbers in the frames. The frames must contain a unit fraction.

a) D + D = | b) D + D = è c) D+D+D=è d) D+D+D=è e) D + D+D+D = i /) D+D+D+D = è

2. Given the answer f , supply unit frac- tions in the number frames to make a true number sentence.

a) D + D = f b) D+D = f c) D + D = f

3. Write f as the sum of 3 unit fractions.

a) D + D + D = f b) D+D+D = f c) D+D+D = f d) D+D+D = f

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Page 5: An enrichment program for elementary grades

4. Write I as the sum of 4 unit fractions.

a) D+D+D+D = l b) D+D+D+D = f c) D+D+D+D=f Illustrating percent problems Illustrating the problem by a diagram

often helps the child to organize his think- ing.

Problem: 20% of the cost of a trip was $60. What was the cost of the trip? 1. Draw a sketch by marking off a rec-

tangular shape to represent 20%. Con- tinue adding more rectangles until the sum of the percents equals 100%.

20%

20%

20%

20%

20%

2. Answer these questions: How much money is represented by 20%? How many $60's do we have indicated on the diagram? What was the cost of the trip?

3. Make up another problem and a dia- gram to support the answer.

An intuitive approach to percent Use the intuitive method in working

with percent. 1. Study Example A: 15% of 40 = w

Find 10% of 40 (.10X40=4) Find 5% of 40 (5% of 40 = | of 4=2) 15% of 40 = 6

2. Work these exercises by the intuitive method. a) 12£%of40 = n b) 15% of 50 =n c) 35% of 40 = n d) 45% of 40 = n e) 95% of 50 =n

3. Study Example B: 20% of = 16 Find 100% of number (5X20 = 100; 5X16 = 80)

4. Work these exercises by the intuitive method. a) 15% of = 18

5% of = 100% of =

b) 175% = 56 25% =

100% = c) ¿%of = 3

l%of = 100% =

5. Study Example C: % of 40 = 6 10% of 40 = 4 5% of 40 = 2

15% of 40 = 6

6. Work these exercises by the intuitive method. a) % of 40 = 8 b) %of 50 = 7J c) % of 40 = 18 d) % of 40 = 5 e) %of50 = 47¿

Working with ratios Use the equal ratio method in working

these examples. 1. Study these problems.

Example A : Candy bars sell at 3 for 10¿. What is the cost of 6 candy bars?

3 _ 6

2X3 _ 6 2X10~n

n = 20

Example B: 20% of 200 =n

20 n ÍÕÕ~2Õ0

2X20 _ n 2X100~2ÕÕ

n = 40

May 1962 285

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Example С: n% of 80 = 20

20 n 8Õ"lÔÕ

20X5/4 _ n

80Х5/4~ПЮ

n = 25

Example D: 20% of n = 16

20 16 100

~ n

20X4/5 16

100X4/5~80 n = 80

2. Make up 10 examples and solve them by the equal ratio method.

Editor's note

While these bulletins are not available for distribution outside the Cincinnati school system, excerpts from them provide informa- tion on types of experiences offered and indi- cate procedures for other school systems wish- ing to prepare materials for able learners.

Annual meeting "snapshots"

We share with you a few "snapshots" from the program of the Fortieth Annual Meeting of the National Council of Teachers of Mathematics. We hope to bring to our readers during this next year some of the papers presented at this meet- ing.

"Basic themes provide the structure in mathe- matics. The development of concepts relative to these themes or basic ideas builds understanding of the operations we use in arithmetic." - M. Vere DbVault in "It1 s The Idea That Counts- The Distributive Property.11

"The junior-high-school programs need con- tinuity and flexibility. They must build on what the student has and lead toward his an- ticipated needs. Major emphasis should be placed on the development of the number system Systems of numeration and abstract mathemati- cal systems play a role in aiding discovery of pat- terns and properties. Conversion and computing in different bases tend to be greatly overem- phasized. Sets belong only as they contribute to understanding and not as a topic within them- selves. In geometry, relations among points, lines, planes, and space can be developed excel- lently through a unit of nonmetric geometry. The deductive nature of mathematical proof beyond the intuitive introduction deserves at- tention, especially in goemetry. Distinction must be made between the measure of a quan- tity and the process of measuring.

"Mathematics, especially at the junior high school, must be alive, vital, and meaningful. Traditional or modern, the mathematics cur-

riculum must reflect these characteristics." - Evan M. Maletsky in "Role of Experimental Ideas in a Traditional Program11

"It should be possible to introduce many of the fundamental concepts of modern algebra by starting from the tables of multiplication and other arithmetical operations and generalizing them. A program based on this approach should be developed from an early stage in elementary school and should culminate in an introduction to modern algebra in Grades 11 and 12." - Marshall H. Stone in "Modern Algebra for Schools.11

"One role of the supervisor as he helps new teachers is that of the expediter, one who knows the facilities of the local building and the central administrative offices. Another role he serves is that of a buffer for the new teachers - between them and administration, faculty, pupils, community, but most of all between their philosophy of teaching and the implemen- tation of that philosophy.

"When helping new teachers, there are three orders of skills needed: technical know-how, human relation aspects, and the conceptual. As the concept for seeing relationships increases, emphasis on the help with techniques decreases." - Helen M. Jones in "Orienting New Teach- ers."

Use of NDEA funds in facets of instructional improvement in mathematics other than equip- ment for classroom use was discussed. Such ideas as the following were developed: in-service programs, conferences, curriculum guides, use of local personnel, and workshops for adminis- trators. - Isabelle P. Rucker in "Neophytes, Docente, and Erudite Administrators.11

{Continued on page 297)

286 The Arithmetic Teacher

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