Mathematics throughout the curriculum

Mathematics throughout the curriculumAuthor(s): HELEN B. FRYESource: The Arithmetic Teacher, Vol. 16, No. 8 (DECEMBER 1969), pp. 647-650Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187567 .

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In the classroom Charlotte Ж Junge

Mathematics throughout the curriculum

HELEN B. FRYE University of Dayton, Dayton, Ohio

If "Take a Mathematical Holiday," which appeared in the November 1968 issue of The Arithmetic Teacher, stimulated as much thought in other teachers' minds as it did in mine, many mental wheels have been turning.

Of special interest to me are game and puzzle-type activities for older students and the coordination of mathematics with other curricular areas.

Let me share with you a few ideas that combine these two interests. Figures 1 and

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0 5 10 15 20 25 30 Solid lines are drawn on the master copy.

Dots and broken lines show what is filled in by students.

Locate the following points and connect the points in each set, in order, with line segments. A = ((5, 12), (4, 10), (2, 12), (0, 11), (2, 14), (3, 15),

(4, 15), (5, 14), (5, 13), (4, 12)} В = ((б, ,12), (8, 12), (9, 15), (10, 15), (12, 14),

(13, 16), (14, 16), (14, 15), (12, 13), (11, 13), (11,10)}

С = {(11, И), (12, 10), (15, 10), (14, 11), (12, И), (12, 13)}

D = {(17, 4), (17, 3), (15, 3), (16, 4), (16, 5), (18, 7) (20, 8), (21, 8), (20, 9)}

E = {(20, 10), (22, 10), (22, 8), (23, 7), (24, 7) (25, 6), (23, 5), (23, 6)}

F - {(23, 7), (22, 5), (20, 4), (18, 4), (16, 5)} G = {(19, 4), (19, 3), (20, 2), (21, 2), (20, 3), (20, 4)}

Now locate the following points and connect each pair with a line segment.

(5, 13) and (6, 13) (3, 14) and (3, 13) (5, 10) and (10, 10) (3, 13) and (2, 12) (21, 8) and (22, 8)

Figure 1

Excellence in Mathematics Education - For All 647



2, variations of the connect-the-dots type of activity, represent different levels of locating ordered pairs on a graph. Both are examples of correlating mathematics and literature. When the points are correctly located and connected, figures will be formed that illustrate a well-known piece

of literature - the fable, "The Hare and the Tortoise" in figure 1, and the epic Robin Hood in figure 2.

This type of activity can be used as a review of various stories, poems, fables, or books that have been read; after completing the drawing, students can either tell or

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Solid lines are drawn on the master copy. Dots and broken lines show what is filled in by students. Locate the following points and connect the

points in each set, in order, with line segments. A = {(-5, -11), (-4, -7),(-3, -5), (-5, -4),

(-6, -7), (-6, -11)) В - {(-6, -12), (-7, -13), (-7, -.14), (-6,

-14), (-5, -12)} С - {(-1, -5), (-1, -7), (0, -12), (0, -13),

(1, -14), (2, -14), (2, -13), (1, -12), (1,-11), (1,-7), (1,-4))

D - {(-6, 12), (-3, 12), (-2, 11), (-1, 11), (0, 10), (-2, 8), (-1,7), (1,7), (10, 11), (9, 11))

E = {(1, 18), (2, 18), (4, 16), (8, 10), (7, 9), (7, 8), (6,7))

F = ((9, 8), (8, 1), (7, -1), (1,7), (2, 18)) G = {(1, -3), (0, 0), (-4, 0), (-5, -3)) H = j(l, 5), (0,1), (-4,1), (-4, 3)1 / = {(-5, 6), (-3,6), (-1,7)1

'

/ = K-4, 9), (-3, 8), (-3, 7), (-5, 7), (-7, 5), (-6,4)1

Now locate the following points and connect each pair with a line segment.

(9, 10) and (10, 11) (-2, 11) and (-4, 11) (-1,6) and (1,6) (2,7) and (7, 9) (-4, 1) and (-4,0) (-5,6) and (-3,6) (0,1) and (0,0) (-3,6) and (-1,7)

Figure 2

648 The Arithmetic Teacher /December 1969



write something about the piece of literature illustrated. Another possible use is as an introduction to literature, with the com- pleted drawing being the clue to what is to be read. Cooperative problem-solving

ordinate axes before beginning. Still more difficult activities (for both the student and the teacher) might employ linear, quad- ratic, and even cubic equations in forming outlines. Able students might be interested

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Across 1. 10 more than the number of years ago the

telescope was invented. 5. Temperature at center of sun is more than

million degrees Fahrenheit. 6. The number of Saturn's satellites is percent

of the number of Mars' satellites. 8. The difference between the number of satel-

lites of Uranus and the sum of the satellites of Mars, Neptune, and Earth.

9. The approximate number of complete rises and falls of the tide during a 6-day period.

11. The sum of the radius of the largest moon crater and the height of the tallest moon mountains.

12. The last 2 digits of the year in which Halley's comet will next appear.

Down

1. Rotation of the sun on its axis takes more earth days at the poles than at the equator.

2. The fourth power of the number of planets between Earth and Pluto.

3. The ratio of the diameters of the sun and the moon is about : 1.

6. To the nearest tenth, how many times farther from the sun is Neptune than Venus?

7. The decimal equivalent of the ratio of the diameters of the earth and the sun (to the nearest hundredth).

10. The largest even integer less than the number of days required for a rotation of the moon.

13. The longest tail observed on a comet is '/n of a billion miles.

Figure 3

efforts of a small group or the entire class are possible if a transparency is made for the overhead projector. Simpler versions can be made by having more lines drawn in by the teacher. More difficult versions can consist of only an instruction sheet, requiring students to set up their own co-

in making up similar activities on their favorite stories.

Figure 3 illustrates the coordination of mathematics and science. Cross-number puzzles are really not difficult to devise if they are kept small. The one illustrated features quantitative information on the

Excellence in Mathematics Education - For All 649



solar system and can be used as a study guide or review.1 It also provides a quick review of many mathematical skills and terms, with emphasis on understanding of concepts rather than ability to do difficult computations.

It seems only fair to warn you, though -

i Wilbur L. Beauchamp, John C. Mayfield, and Paul DeHart Hurd, Science Is Explaining, Grade 7 (Glenview, 111.: Scott, Foresman & Co., 1963), pp. 305-37. (See Unit 11.)

working up these activities can be habit- forming. So get the habit; help take the "numb" out of numbers and put more "force" into reinforcement.

Editor's Note. - Dr. Frye offers the challenge. Learning that is to be held at a mastery level requires frequent reinforcement through review and practice. Will you share with us those activities that you have found successful in maintaining skills? - Charlotte W. Junge

Editorial feedback VERNE G. JEFFERS Mansfield State College, Mansfield Pennsylvania

jL noted with interest the article entitled "Mathematicalosterms" by Sally Mathison in the January 1969 issue of The Arith- metic Teacher. I have been using a ver- sion of this puzzle for a number of years

but had never attached a name to it. How- ever, seeing the idea in print did give rise to another idea which, like "Mathematica- losterms," may not be original, but has not had popular usage. It involves using nu-

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3 72 17 (4 X (7 + 6)= 52) 2 26 50 72

650 The Arithmetic Teacher/ December 1969



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Mathematics throughout the curriculum