JPS59229590A - Graphic panel combination teaching aid - Google Patents
Graphic panel combination teaching aidInfo
- Publication number
- JPS59229590A JPS59229590A JP9191983A JP9191983A JPS59229590A JP S59229590 A JPS59229590 A JP S59229590A JP 9191983 A JP9191983 A JP 9191983A JP 9191983 A JP9191983 A JP 9191983A JP S59229590 A JPS59229590 A JP S59229590A
- Authority
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- Prior art keywords
- triangles
- small
- plate
- sides
- boards
- Prior art date
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Abstract
(57)【要約】本公報は電子出願前の出願データであるた
め要約のデータは記録されません。(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.
Description
【発明の詳細な説明】
本発明は算数と図工の学習に役立つことを目的とした1
7個の図形板と、その使用法に関するものである。[Detailed Description of the Invention] The present invention is intended to be useful for learning arithmetic and arts and crafts.
It is about the seven graphic boards and how to use them.
図形板は、半円(1)1個と四分円(2)1個と八分円
(3)2個との合計4個の扇形板と、4個の扇形で作れ
る円(4)板の半径を底辺とする直角二等辺小三角形(
5)板2個・同半径を直角をはさむ辺とする直角二等辺
中玉角形(6)板4個と、間中三角形(6)板2個を辺
で連結してできる直角二等辺小三角形(7)・正方形(
8)・平行四辺形(9)の各板1個ずつと、同小中三角
形(5と6)仮名1個を辺で連結した小台形αO板2個
と、同中太三角形(6と7)仮名1個を辺で連結した犬
台形α℃板2個との総計17個で構成される。The figure board consists of a total of 4 fan-shaped boards: 1 semicircle (1), 1 quadrant (2), and 2 octants (3), and a circle (4) board that can be made from 4 fan shapes. A right-angled isosceles triangle whose base is the radius of (
5) Right angled isosceles small triangle formed by connecting 2 plates and 4 plates (6) and 2 plates (6) with the same radius as the sides that sandwich the right angle. (7)・Square (
8)・One plate of each parallelogram (9), two small trapezoid αO plates made by connecting one small and medium triangle (5 and 6) with the sides, and one plate of the same medium thick triangle (6 and 7). ) It consists of 1 kana and 2 dog trapezoid α℃ plates connected by the sides, making a total of 17 pieces.
扇形以外の13個の図形(5〜11)板を組合すと幾伺
学図形の基本である三角形と正方形を同時に斡とi3)
、 (14と15)、 (16と17)の3通り作る
ことができ。By combining 13 shapes (5 to 11) other than sectors, you can simultaneously create triangles and squares, which are the basics of geometric shapes.
, (14 and 15), and (16 and 17) can be made in three ways.
どれも面積の最小単位である直角二等辺小三角形(5)
を含み2分数学習に有効な構成である。また上記13板
片をひとつに組合せて各種の多角形すなわち、凸多角形
は図形(ト)の長方形をはじめとして4種14通りの四
角形と、4種6通りの五角形と、3種13通りの六角形
と、ひとつの七角形と、3通りの四角形の合計37形、
凹条角形は四角形から四十五角形まで無数に作ることが
できる。扇形板を含めて金板または一部を使ってハート
形(19,20) 、スペード形(2L 22)などを
作ることもできる。All are right-angled isosceles small triangles (5), which are the smallest units of area.
This is an effective configuration for learning 2 fractions. In addition, the above 13 plate pieces can be combined into one to form various polygons, that is, convex polygons, including the rectangle of figure (G), 14 types of squares in 4 types, 6 types of pentagons in 4 types, and 13 types of 3 types. A total of 37 shapes: a hexagon, one heptagon, and three squares.
An infinite number of concave rectangular shapes can be created, from quadrangles to 45 pentagons. Heart shapes (19, 20), spade shapes (2L 22), etc. can also be made using metal plates or parts of them, including fan-shaped plates.
これらの板片(1〜3,5〜11)はすべて厚手のボー
ル紙・プラスチック板・木材その細板状のものを任意に
使用してよい。All of these board pieces (1 to 3, 5 to 11) may be made of thick cardboard, plastic board, wood, or thin boards.
図形板を算数の四則演算の学習に使用する実施例につい
て訝明する。We will discuss an example in which a graphic board is used for learning the four arithmetic operations.
和、たとえば1+2は面積10図形(5)板と面積2の
図形(6)板を組合せてできる台形復Oの面積が3であ
ることを示す。これを2通常行なっている個数の和の学
習と、抽象数の和の数式1+2=3表現との間にはさん
で行なうと、移行の飛躍ギャップを埋めることができ、
理解を深めるのに役立つ。The sum, for example 1+2, indicates that the area of the trapezoid O, which is created by combining a figure (5) plate with an area of 10 and a figure (6) plate with an area of 2, is 3. If this is done in between the usual learning of the sum of numbers and the expression of the sum of abstract numbers in the formula 1+2=3, it will be possible to fill the gap in the transition.
Helpful for better understanding.
差、たとえば5−2は面積1と4の図形(5と8)画板
の組合せ図形の五角形(至)板から三角形(6)板を取
り去った残りの台形を意味して図形(1のである。The difference, for example 5-2, means the trapezoid remaining after removing the triangular (6) board from the pentagonal (to) board of the combination of the drawing boards (5 and 8) with areas 1 and 4, and is the figure (1).
分数の和と差についても同様である。The same goes for sums and differences of fractions.
積、たとえば分数2x8は正方形(負について。The product, for example the fraction 2x8, is a square (for negative.
全体の1である上または下半分の三角形のさらに青にあ
たる三角形(6)の面積2が正方形全体の面積32の−
であることから数式 2’4””1’6の成立を6
学習することができる。The area 2 of the triangle (6) which is bluer than the upper or lower half triangle which is 1 of the whole is - of the area 32 of the whole square.
Therefore, we can learn that the formula 2'4""1'6 holds true.
商、たとえば去÷゛責はやはり面積32の正方形05)
について、全体の妻である上または下半分の面積16の
三角形の中に、全体の責である面積4にあたる図形、す
なわち面積2の三角形(6)の2個がいくつ含まれるか
操作的に調べて4つであることから1÷1 1 ×8
=:4の成立を学習する。The quotient, for example, ÷ ゛, is a square 05 with an area of 32)
, we can operationally find out how many triangles (6) with an area of 2, which is the responsibility of the whole, are included in the triangle with an area of 16 in the upper or lower half, which is the wife of the whole. Since there are 4, 1÷1 1 ×8
Learn the establishment of =:4.
821 整数の積と商についても同様である。821 The same applies to products and quotients of integers.
図形の性質については、算数学習で取り扱われる多角形
の殆んどすべてが図形(5〜11)板に含まれるか、そ
れらから構成できるので2図形の形状と大きさ・対称性
・合同性・相似性などについて操作的な学習を行なうこ
とができる。また2図形の拡大・縮小については、たと
えば三角形は面積1(図形5)、2(図形6.)、4(
図形7)の他に面積8(図形12)、 9.16.1
8.32(図形16)、36(図形13から容易に作れ
る)の直角二等辺三角形を構成することができるので5
辺の長さを2倍・3倍・4倍するとき面積は4倍・9倍
・16倍されることを操作学習することができる。四角
形、五角形、六角形についても同様な学習ができる。Regarding the properties of figures, almost all polygons handled in arithmetic learning are included in the figure (5 to 11) board or can be constructed from them, so the shape and size of the two figures, symmetry, congruence, etc. Manipulative learning about similarities, etc. can be performed. Also, regarding enlarging/reducing two figures, for example, a triangle has an area of 1 (figure 5), 2 (figure 6), and 4 (
In addition to figure 7), area 8 (figure 12), 9.16.1
8. Since the right isosceles triangles of 32 (figure 16) and 36 (which can be easily made from figure 13) can be constructed, 5
You can learn through operations that when you double, triple, or quadruple the length of a side, the area is multiplied by 4, 9, or 16. You can also learn about quadrilaterals, pentagons, and hexagons in a similar way.
本発明は、その構造上、従来の図形組合せ玩具では実行
できな′い算数学習を有効に実行できる効果をもつだけ
でなく、もちろん従来の図形組合せ玩具と同様に人や動
植物・器物など多くのものの影絵作りを行なうことがで
きる。そして、従来のタングラム・ラッキーパズル・ハ
ートパズルをすべて実行できるうえに、スペードパズル
まで新しくつけ加えることができて2図工学習に広い利
用方法を提供し2図形構成能力と美的感覚の養成に役立
つ効果ももっている。Due to its structure, the present invention not only has the effect of effectively carrying out arithmetic learning that cannot be carried out with conventional figure combination toys, but also has the effect of being able to effectively carry out arithmetic learning that cannot be carried out with conventional figure combination toys. You can make shadow puppets of things. In addition to being able to perform all the conventional tangrams, lucky puzzles, and heart puzzles, it can also add new spade puzzles, providing a wide range of uses for 2nd art learning, and has the effect of helping to develop 2nd figure composition ability and aesthetic sense. I have it.
図面は本発明の一実施例を示し、第1図は17板片の平
面図、第2図は第1図の側面図、第3図はこれらの板片
で構成した円と直角二等辺三角形と正方形の平面図、第
4図は扇形板を除いた13板片で構成したひとつの長方
形の平面図、第5図は17板片の一部で構成した二つの
ハート形の平面図。
第6図は17板片の一部と全部で構成したスペード彫工
つの平面図、第7図は板片利用のだし3jと引き算を示
す平面図、第8図は17板片全部を使ったスペードパズ
ルでできる影絵である。
1− 半円板 2− 四分円板
3− 四分円板 4− 構成された円板5− 小三
角形板 6− 中玉角形板7− 大王角形板 8−
正方形板
9− 平行四辺形板 10− 小台形板11−−−−
犬台形板
12、14.16−−−−構成された三角形板13、1
5.17−−構成された正方形板18−一一一構成され
た長方形板
19、20−一構成されたノ・−ト形板21、22−一
一一構成されたスペード形板幻−構成された五角形板
特許出願人 小林茂広
手続補正書(方式)
昭和58年9月74.日
l 事件の表示 昭和58年特許願第91919号2
発明の名称 図形板組合せ教具
3 補正をする者
事件上の関係 特W「出願人
住所 香川県高松市鶴市町1655番地4、補正命令の
日(1昭和58年8月30日5、補正の対称 明細書
6、補正の内容 明細書の浄書(内容に変更なし)手続
補正書(自発)
昭和59年7り/7日
特許庁長官 志賀 学 殿
1 事件の表示 昭和58年特許願第091919号
ず IIIIばん(み1hね さようぐ
し よう+152 発明の名称 図形板組合せ教具と
その使用法3 補正をする者
事件との関係 特許出願人
郵便番号 761(電話番号 0878−33−16
70)4 補正により増加する発明の数 06 補正
の内容
(イ)「図形板組合せ教具jとあるをr図形板組合せ教
具とその使用法jと補正します。
(ロ)(ハ) 別紙の通り
補正の内容 明細書
16発明の名称
図形板組合せ教具とその使用法
2、特許請求の範囲
(1) 円板を半円・四分円・八分円・八分円の4個
の扇形板に分割したものと、当該円の半径を底辺とする
直角二等辺の小三角形2個と、直角をはさむ辺とする直
角二等辺の中玉角形4個と、上記中玉角形2個を辺上辺
で連結してできる直角二等辺の大三角形・正方形・平行
四辺形の各1個と、前記小中三角形容1個を辺支辺で連
結した小台形2個と、前記中大三角形各1個を辺雀辺で
連結した大台形2個との総計17個の図形板組合せ教具
(2)土星17個の図形板の全部、あるいは一部を組合
せて平面上に重ねずにまたは重ねて二重に、並べて図形
を作り、算数における′、”に整 ・へJ四則演算並び
に図形の性質についてそれぞれ−1とパノを融合した
17をさせる吏用 法や2図工における構成能力・美的
感覚を養成する侠朋仏3、発明の詳細な説明
本発明は算数学習、特に数量と図形の融合学習と9図工
学習における図形構成能力や美的感覚養成に役立つこと
を目的とした17個の図形板と、その使用法に関するも
のである。
図形板は、第1図の半円(1目個と四分円(2)1個と
八分円(3)2個との合計4個の扇形板と、4個の扇形
板で作られる第3図の円(4)の半径を底辺とする直角
二等辺小三角形(5)板2個と、同半径を直角をはさむ
辺とする直角二等辺小三角形(6)板4個と。
間中三角形(6)板2個を辺と辺で連結してできる直角
二等辺大王角形(7)・正方形(8)・平行四辺形(9
)の各板1個ずつと、同小中三角形(5と6)仮名1個
を辺と辺で連結した小台形(10)板2個と、同小中三
角形(6と7)仮名1個を辺と辺で連結した大台形(1
1)板2個との総計17個で構成される。各板の表面積
は、最小板片である小三角形(5)板の面積を1とすれ
ば、中三角形(6)板は2.小台形(lO)板は3゜大
三角形(7)・正方形(8)・平行四辺形(9)の各板
はすべて4.大台形(11)板は6であり、扇形板は円
周率を2277として小は11/7.中は22/7.大
は44/7である。
扇形以外の13個の図形(5〜11)板を組合すと幾何
学図形の基本である三角形と正方形を同時に第3図(1
2と13) 、 (14と15) 、 (16と17)
の3通り作ることができ、どれも面積の最小単位である
直角二等辺小三角形(5)を含む、また上記13個の図
形板の一部を組合せてできる凸多角形は三角形から八角
形まで約六百形1面積2から39(最小三角形の面積1
)までの任意の整数にすることかできる1図形板13個
す段て組合せてできる面積40の凸多角形は第4図の長
方形(18)をはじめとして4種14通りの四角形と、
4種6通りの五角形と、3種14通りの六角形と、ひと
つの七角形と、3通りの八角形の合計38形であって、
凹条角形は四角形から四十五角形まで無数に作ることが
できる。更に、扇形を含め−た17個の図形(1〜3,
5〜11)板の一部または全部を組合すと第5図のハー
ト形(19,20)や第6図のスペード形(21,22
)なども作れる。
これらの図形(1−3,5−11)板はすべて厚手のボ
ール紙・プラスチック仮・木材その地板状のものを任意
に使用してよい。
図形板を算数の四則演算の学習に利用する使用法につい
て説明する。
整数和1例えば1+2には任意の図形板1個と2個を合
わせて3個になるという数の和と1面積1の図形(5)
板と面積2の図形(6)板を組合すと第7図の面積3の
小台形(10)板になるという大きさ。
つまり量の和が含まれている。ところで1面積2の図形
は面積1の図形(5)板2個の組合せ方によっては中玉
角形(6)の他に、正方形にも平行四辺形にもなり、さ
らにこれに面積lの図形(5)板を付は加えて組合すと
大きさ3の等脚台形(23)にもなり得る。 このよ
うに、I+2=3は形の違いには関係なく数と量につい
て成立する非常に抽象的な数式である。しかるに通常、
算数では数の和の学習から直ちに抽象数の和の数式学習
に移って、大きな飛躍を学童に押しつけている。この飛
躍ギャップを埋め、理解を深めさせる必要がある。それ
には、当図形板組合せ教具を使って量の和を図形的に学
習させる。それによって、学童に算数をより具体的な目
で確かめられるものにすることができるのである。
このように当発明は、数量と図形の融合学習を可能とす
るものである。
整数の差1例えば5−2についても数量・図形の融合学
習が可能であることは和の場合と同じである。数の差と
しての説明は省略するか、■の差としては例えば面積1
と4あるいは2と3の図形板を組合せた第7図の五角形
(24)または台形(25)から面積2の三角形(6)
や正方形、平行四辺形を取り去った残りの台形を意味す
る図形00)である。
分数の和と差について述べる前に分数の作り方を説明す
る9例えば1分数1/2は小三角形(5)板と中玉角形
(6)板を平面上の分数の棒の上下に数字の代わりに置
くか、または上下2重に重ねると得られる。同様に2分
数1/3は小三角形(5)板と小台形(10)板を用い
て作ることができる。これらは既約分数であるが、未既
約分数の形すなわち2/4゜3/6.4/8や2/6
、3/9などとすることもできる。そして、このような
分数の図形的な作り方は菓子や果物を2等分や3等分し
た生活経験から無理なく会得させることができる。
また、半分すなわち1/2を2つ合わせたり、1/3と
273を合わすと1になる生活の知恵ともいえる既知の
事実を図形板を使って再認識させると分数の大小比較や
加減算を、同じ分母の分数の場合は直接2分子どうしの
大小比較や加減算で、異なる分母の分数の場合はまず両
分数の分母を同じものに作り変えてから9例えば1/2
と173を376と2/6にしてから行なうというしく
みを図形的に理解させることができ加減算の数式演算を
誤ることはない。
整数の掛は算は繰り返し足し算の便法であるから説明を
省略する。整数の割り算については2割り切れる場合の
答えは繰り返し引き算をして無くなるまでの回数であり
1割り切れない場合の答えは小数ではなく5分数で求め
られる。これは次の分数の乗除算の説明の中に含まれる
。
分数の乗除算1例えば■215 X 3や■215÷3
あるいは■215 X 3/4や■215÷3/4を図
形板を手で操作しながら実行させ、計算のしくみを理解
させる方法は
■215 X’3は同じ分母の分数を3つ足し合わずの
で分母はそのまま2分子を3倍した分数を作れはよい。
■215÷3については、求める答えの分数を3倍する
と275すなわち6/15であることがら1分数275
の分母分子をともに3倍して、3で割りきれる分子をも
つ分数(2X3)/(5X3)=6/15に作り変えて
がら3で割り算して2/15(前述のように掛は算は分
子に掛けたが、掛は算の逆操作である割り算も分母はそ
のまま3分子を割ればよい)つまり2/(5X3) −
2/15と分母に3を掛けると答えが得られる。
■215 X 3/4については2分数374は3÷4
であるから215 X (3÷4)=215X3÷4=
615÷4 =G/20=3710となることを図形板
で操作的に確認させ結局。
分数の掛は算は分母は分母どうし2分子は分子どうし掛
は合わす、すなわち215x3/4=(2x3)/(5
X 4) = 6/20 = 3/10となることを理
解させる。
■215÷374は前と同様215÷(3÷4)=21
5÷3×4−2/i5 X 4 = 8/15となるこ
とを図形板で操作的に確認させ結局1分数の割り算は除
数の分数の逆数を被除数の分数に掛ける。すなわち21
5÷374−215x4/3=(2x4)/(5x3)
=8/15となることを理解させる。
次に、算数の図形学習を操作的に行なう方法を説明する
。
円を作って、その性質調べをする。
扇形板を除<13個の図形板の一部または全部を組合せ
て三角形から四角形まで六百余り作れるので、これらの
多角形を利用して算数の図形学習における多角形の性質
・辺や対角線の長さ・角・面積や2図形の合同・拡大と
縮l」い対称性などを学習させることができる、例えば
、三角形は面積1(図形5)、2(図形6)、4(図形
7)の他に面積8(図形12)、 9.16,18,2
5.32(図形16)’、 36 (図形13から容易
に作れる)の直角二等辺三角形を構成することが可能な
ので2辺の長さを2.3,4,5.6倍すると面積は4
,9.16,25.36倍になることを認識させること
などができる。同様に、四角形、五角形、六角形につい
ても拡大と縮小などの学習ができる。
本発明は、その構造上、従来の図形組合せ玩具では実行
できなかった操作的な算数学習を可能にするだけでなく
、従来の図形組合せ玩具と同様に人や動植物・器物など
具象物の影絵作りも行なうことができる。そして、従来
のクングラム・ラッキーパズル・ハートパズルでできた
図形のすへてか作れるうえに、スペードパズルまで新し
く付は加えることができる。スペードパスルで作れる影
絵の数例を第8図に示しである。多くの影絵作りができ
ることは5図工学習にrli広い利用方法を提供し1図
形構成能力や美的感覚の養成にも役立つ効果をもってい
る。
図形構成能力や美的感覚を養成するための使用法の一例
を、説明を簡単にするため面積1,2.3の図形(5,
6と10)板を計8個利用して作る烏について述べる0
面積lと2の各1個を除いた6個で鳥の母体となる首と
胴を第9図(イ)のように作る。
除いた2個を頭にして(ロ)(ハ)をはじめとし図示し
ていないが12態2頭から面積1の小三角形を移動して
尻尾や胸あるいは足にすると(ニ)(ホ)(へ)となり
1頭の付は方は4通りあるから12fiu、首の小三角
形も移動して2つの小三角形を足に使えば長い足(ト)
や短い足(チ)にすることができ9頭と尻尾のバリエー
ションでやはり12態作れる。移動する図形板を他の板
に変えて、結局(イ)の母体から鳥を約508作ること
ができる。また、異なる母体例えば(す)から出発して
できる鳥も、その一部を適当な位置へ移動して容易に五
百態を越す姿態に変えられる5母体として(イ)(す)
の他にも種々作れるので、8個の図形板に限っても数千
熊の鳥ができるのである9種々様々な鳥ができるのであ
るから、なるべく美しい鳥にずべく図形板の組合せ方を
工夫するうちに図形構成能力や美的感覚を養成すること
ができ、さらにすずめで具体的な創造性を高める教育に
利用することも可能である。
4、図面の簡単な説明
図面は本考案の実施例を示し、第1図は17個の図形板
の平面図、第2図は第1図の側面図、第3図はこれらの
図形板で構成した円と直角二等辺三角形と正方形、第4
図は扇形板を除いた13個のし杉板で構成した長方形、
第5図は17個の図形板C一部で構成した二つのハート
形、第6図は17個C図形板の一部及び全部で構成した
スペード彫工て第7図は図形板利用の加減算の図、第8
図は17他全部の図形板を使うスペードパズルでできる
影社の構成例、第9図は面積1,2.3の図形板8個て
作る烏である。
■−半円板 2−四分円板
3・−大分円板 4−構成された円5−小三角形
板 6・−中三角形板7−大三角形板 8−正
方形板
9−平行四辺形板 1〇−小台形板
11−・・大台形板
12、14.16・−構成された三角形13、15.1
7−構成された正方形
I8−構成された長方形
19、20−・構成されたハート形
21、22−・・構成されたスペード形23・−等脚台
形 24−構成された三角形25・−構成された
台形
出願人 小林茂広The drawings show one embodiment of the present invention, in which Fig. 1 is a plan view of 17 plate pieces, Fig. 2 is a side view of Fig. 1, and Fig. 3 is a circle and a right isosceles triangle made up of these plate pieces. Figure 4 is a plan view of one rectangle made up of 13 plate pieces excluding the fan-shaped plate, and Figure 5 is a plan view of two heart-shaped pieces made up of some of the 17 plate pieces. Figure 6 is a plan view of a spade carving machine made up of some and all 17 board pieces, Figure 7 is a plan view showing dashi 3j and subtraction using board pieces, and Figure 8 is a plan view of a spade carving machine made of all 17 board pieces. It is a shadow puppet made of puzzles. 1- Half disk 2- Quarter disk 3- Quarter disk 4- Structured disk 5- Small triangular plate 6- Medium bead square plate 7- Large king square plate 8-
Square plate 9- Parallelogram plate 10- Small trapezoidal plate 11---
Dog trapezoidal plate 12, 14.16 ---- structured triangular plate 13, 1
5.17--Constructed square plates 18--11 configured rectangular plates 19, 20--1 configured notebook-shaped plates 21, 22-1-1 configured spade-shaped plates phantom-configuration Pentagonal plate patent applicant Shigehiro Kobayashi Procedural amendment (method) September 74, 1982. Indication of the case 1982 Patent Application No. 91919 2
Name of the invention Graphic board combination teaching tool 3 Relationship between the person making the amendment and the case Special W "Applicant address 1655-4 Tsuruichi-cho, Takamatsu-shi, Kagawa Prefecture, date of amendment order (1 August 30, 1980, 5, subject of amendment) Specification 6, Contents of the amendment Copywriting of the specification (no change to the content) Procedural amendment (voluntary) July 7, 1980 Manabu Shiga, Commissioner of the Patent Office 1 Indication of the case Patent Application No. 091919 of 1988 III Ban (Mi1h Sayogu)
Let's try +152 Title of the invention Graphic board combination teaching tool and its usage 3 Relationship with the case of the person making the amendment Patent applicant postal code 761 (Telephone number 0878-33-16
70) 4 Number of inventions increased by the amendment 06 Contents of the amendment (a) ``Drawing board combination teaching tool j'' is amended to read ``r drawing board combination teaching tool and its usage j.'' (b) (c) As shown in the attached sheet. Contents of the amendment Description 16 Name of the invention Graphic board combination teaching tool and its use 2, Claims (1) Disc into four fan-shaped boards: semicircle, quarter circle, octant circle, and octant circle The divided one, two small right-angled isosceles triangles whose bases are the radius of the circle, four right-angled isosceles medium triangles whose sides sandwich the right angle, and the two medium sphere triangles above with the top sides. One each of right-angled isosceles large triangles, squares, and parallelograms formed by connecting them, two small trapezoids formed by connecting one of the small and medium triangles with supporting sides, and one each of the medium and large triangles. A total of 17 graphic board combinations with two large trapezoids connected by side edges (2) Combine all or part of the 17 graphic boards of Saturn without overlapping them on a plane or doubly by overlapping them. , to create figures by arranging them, and in arithmetic, ′ and `` are set.
17. 17. Methods and 2. Kyouhobutsu to cultivate compositional ability and aesthetic sense in drawings 3. Detailed explanation of the invention The present invention is designed to improve the ability to compose figures in arithmetic learning, especially the integrated learning of quantities and shapes, and 9. This book contains 17 graphic boards intended to help develop aesthetic sense and how to use them. The figure board is made of a total of 4 fan-shaped boards, including the semicircle (1st eye, 1 quadrant (2), and 2 octants (3)) in Figure 1, and 4 fan-shaped boards. Two plates of right-angled isosceles small triangles (5) whose bases are the radius of circle (4) in Figure 3, and four plates of right-angled isosceles small triangles (6) whose sides have the same radius as the right angle. A right angled isosceles Great triangle (7), a square (8), a parallelogram (9) made by connecting two medium triangle (6) plates side by side.
), two small trapezoidal (10) plates made by connecting one small and medium triangle (5 and 6) kana side by side, and one small and medium triangle (6 and 7) kana. A large trapezoid (1
1) Consists of 2 plates, totaling 17 pieces. The surface area of each plate is 1 if the area of the small triangular (5) plate, which is the smallest plate piece, is 1, and the surface area of the medium triangular (6) plate is 2. The small trapezoid (lO) plate is 3 degrees, and the large triangle (7), square (8), and parallelogram (9) plates are all 4 degrees. The large trapezoid (11) plate is 6, the sector plate has a pi of 2277, and the small is 11/7. Inside is 22/7. Large is 44/7. By combining 13 shapes (5 to 11) other than sectors, we can simultaneously create triangles and squares, which are the basics of geometric shapes, as shown in Figure 3 (1).
2 and 13), (14 and 15), (16 and 17)
It can be made in three ways, all of which include a right-angled isosceles small triangle (5), which is the smallest unit of area, and convex polygons made by combining parts of the above 13 shape plates range from triangles to octagons. Approximately 600 shapes 1 area 2 to 39 (minimum triangle area 1
) The convex polygon with an area of 40 formed by combining 13 one-figure boards, which can be made into any integer up to
A total of 38 shapes, including 6 types of pentagons in 4 types, 14 types of hexagons in 3 types, 1 heptagon, and 3 types of octagons.
An infinite number of concave rectangular shapes can be created, from quadrangles to 45 pentagons. Furthermore, 17 shapes (1 to 3,
5-11) When some or all of the plates are combined, the heart shape (19, 20) shown in Figure 5 or the spade shape (21, 22) shown in Figure 6 can be created.
) can also be created. For these graphic (1-3, 5-11) boards, thick cardboard, plastic temporary, wood, or base board-like materials may be used as desired. We will explain how to use the graphic board to learn the four arithmetic operations. Sum of integers 1 For example, 1+2 is the sum of the numbers such that 1 and 2 of any figure boards add up to 3, and a figure with 1 area of 1 (5)
If you combine the board and the figure (6) board with an area of 2, you will get a small trapezoid (10) board with an area of 3 as shown in Figure 7. In other words, it contains the sum of quantities. By the way, a figure with an area of 2 can be a figure with an area of 1 (5), and depending on how the two plates are combined, it can be a square or a parallelogram, as well as a square or a parallelogram (6), and furthermore, a figure with an area of l ( 5) If you add more plates and combine them, it can become an isosceles trapezoid (23) of size 3. In this way, I+2=3 is a very abstract mathematical formula that holds true for numbers and quantities regardless of the difference in form. However, usually
In arithmetic, school children are forced to make a huge leap forward by immediately moving from learning the sum of numbers to learning formulas for the sum of abstract numbers. We need to fill this leap gap and deepen our understanding. To do this, use this graphic board combination teaching tool to help students learn the sum of quantities graphically. By doing so, we can make mathematics more tangible for schoolchildren. In this way, the present invention enables integrated learning of quantities and shapes. As with the case of sums, fused learning of quantities and shapes is possible for integer differences 1, for example, 5-2. The explanation as a difference in numbers will be omitted, or as a difference in ■, for example, the area 1
A triangle (6) with an area of 2 from the pentagon (24) or trapezoid (25) in Figure 7, which is a combination of the figure boards 4 and 2 and 3.
The figure 00) means the remaining trapezoid after removing the square, parallelogram, and parallelogram. Before we talk about the sum and difference of fractions, we will explain how to make fractions.9For example, for the fraction 1/2, place a small triangular (5) plate and a medium spherical square (6) plate above and below the fraction bar on a plane instead of numbers. It can be obtained by placing it on top or by stacking it on top and bottom. Similarly, the half fraction 1/3 can be made using a small triangular (5) plate and a small trapezoid (10) plate. These are irreducible fractions, but in the form of irreducible fractions, i.e. 2/4°3/6.4/8 and 2/6
, 3/9, etc. Children can easily learn how to create fractions graphically through their daily life experience of dividing sweets and fruits into two or three equal parts. In addition, if you use a diagram board to reaffirm the known facts that can be considered wisdom in daily life, such as adding two halves, or 1/2, or adding 1/3 and 273, you will be able to compare the size of fractions and add and subtract. In the case of fractions with the same denominator, you can directly compare the two numerators or add or subtract them; in the case of fractions with different denominators, first change the denominators of both fractions to the same one, and then use 9, for example, 1/2.
The system of converting 173 to 376 and 2/6 before performing the calculation can be graphically understood, and there is no chance of making mistakes in the mathematical operations of addition and subtraction. Multiplication of integers is an expedient method for repeated addition, so the explanation will be omitted. Regarding division of integers, if the number is divisible by 2, the answer is the number of times the number can be subtracted repeatedly, and if the number is not divisible by 1, the answer is not a decimal but a 5-fraction. This is included in the next explanation of multiplying and dividing fractions. Multiplying and dividing fractions 1 For example, ■215 x 3 or ■215÷3
Alternatively, you can have students understand the calculation mechanism by having them perform ■215 X 3/4 and ■215 ÷ 3/4 while manipulating the diagram board by hand. ■215 X'3 does not add three fractions with the same denominator. Therefore, it is better to create a fraction by multiplying the two numerators by three, while keeping the denominator as is. ■For 215÷3, multiplying the fraction of the answer by 3 gives 275, or 6/15, so 1 fraction is 275.
Multiply both the denominator and numerator by 3 to create a fraction with a numerator divisible by 3 (2 is multiplied by the numerator, but multiplication is the inverse operation of arithmetic, so division can also be done by just dividing the numerator by 3 with the denominator unchanged.) In other words, 2/(5X3) −
Multiply 2/15 and the denominator by 3 to get the answer. ■For 215 x 3/4, the 2 fraction 374 is 3÷4
Therefore, 215 X (3÷4)=215X3÷4=
I ended up using the diagram board to confirm that 615÷4 = G/20 = 3710. To multiply fractions, multiply the denominator by the denominator, and the numerator by the numerator by the numerator, i.e. 215x3/4=(2x3)/(5
Help students understand that X 4) = 6/20 = 3/10. ■215÷374 is the same as before, 215÷(3÷4)=21
5÷3×4−2/i5 X 4 = 8/15 is confirmed manually on the graphic board.In the end, when dividing a fraction, multiply the reciprocal of the fraction of the divisor by the fraction of the dividend. That is 21
5÷374-215x4/3=(2x4)/(5x3)
= 8/15. Next, a method for operationally learning shapes in arithmetic will be explained. Create a circle and investigate its properties. By combining some or all of the 13 shape boards excluding the fan board, you can make over 600 shapes ranging from triangles to quadrilaterals, so use these polygons to learn about the properties of polygons, sides and diagonals when learning shapes in math. You can learn the length, angle, and area of , and the congruence, expansion, and contraction of two shapes.For example, a triangle has areas 1 (shape 5), 2 (shape 6), and 4 (shape 7). ), area 8 (figure 12), 9.16, 18, 2
It is possible to construct a right-angled isosceles triangle of 5.32 (Figure 16)', 36 (which can be easily made from Figure 13), so multiplying the lengths of the two sides by 2.3, 4, and 5.6 yields an area of 4.
, 9.16, 25.36 times, etc. Similarly, you can learn how to enlarge and reduce rectangles, pentagons, and hexagons. Due to its structure, the present invention not only enables manipulative arithmetic learning that was not possible with conventional figure combination toys, but also allows for the creation of shadow puppets of concrete objects such as people, animals, plants, and utensils in the same way as conventional figure combination toys. can also be done. In addition to being able to create a variety of shapes made from the traditional Kungram, Lucky Puzzle, and Heart Puzzle, you can also add new additions to the Spade Puzzle. Figure 8 shows some examples of shadow puppets that can be made with spade puzzles. Being able to make many shadow puppets provides a wide range of ways to use RLI in learning 5 arts and crafts, and also has the effect of helping to develop 1 figure composition ability and aesthetic sense. For the purpose of simplifying the explanation, we will give an example of how to use it to develop figure composition ability and aesthetic sense.
6 and 10) Describe a crow made using a total of 8 boards0
Make the neck and body, which will become the mother body of the bird, using six pieces, excluding one each for areas l and 2, as shown in Figure 9 (a). (2) (E) There are 4 ways to attach one head, so it is 12 fiu, and if you move the small triangle on the neck and use the two small triangles for the legs, you can get long legs (g).
It can be made with short legs (chi), and 12 states can be created with variations of nine heads and a tail. By changing the moving figure board to another board, it is possible to make about 508 birds from the mother body in (a). In addition, birds born from different mothers, such as (su), can be easily changed into more than 500 forms by moving a part of them to an appropriate position.
There are many other types of birds that can be made, so even with just 8 graphic boards, thousands of birds can be created.9 Many different types of birds can be created, so try to combine the graphic boards to create as beautiful a bird as possible. In the process, children can develop their ability to compose figures and develop their aesthetic sense, and sparrows can also be used in education to enhance concrete creativity. 4. Brief description of the drawings The drawings show an embodiment of the present invention. Fig. 1 is a plan view of 17 graphic boards, Fig. 2 is a side view of Fig. 1, and Fig. 3 is a diagram of these graphic boards. The constructed circle, right-angled isosceles triangle, and square, the fourth
The figure shows a rectangle made up of 13 Japanese cedar boards, excluding the fan-shaped boards.
Figure 5 shows two heart shapes made up of parts of 17 figure boards C, Figure 6 shows a spade carving made up of some and all of 17 figure boards, and Figure 7 shows an example of addition and subtraction using figure boards. Figure, 8th
The figure shows an example of the configuration of a shadow puzzle made of a spade puzzle using all the 17 and 17 figure boards, and Figure 9 shows a crow made of 8 figure boards with an area of 1.2.3. ■-Semicircle plate 2-Quadrant disk 3--Large disk 4-Constructed circle 5-Small triangular plate 6--Medium triangular plate 7-Large triangular plate 8-Square plate 9-Parallelogram plate 1 〇-Small trapezoidal plate 11--Large trapezoidal plate 12, 14.16--Constructed triangle 13, 15.1
7-Constructed square I8-Constructed rectangle 19, 20--Constructed heart-shape 21, 22--Constructed spade-shape 23--Isosceles trapezoid 24-Constructed triangle 25--Constructed Trapezoid applicant Shigehiro Kobayashi
Claims (2)
形板に分割したものと、当該円の半径を底辺とする直角
二等辺の小三角形2個と、直角をはさむ辺とする直角二
等辺の中玉角形4個と、上記中玉角形2個を辺で連結し
てできる直角二等辺の大三角形・正方形・平行四辺形の
各1個と、前記小三角形2個個を辺で連結した小台形2
個と、前記中大三角形各1個を辺で連結した大台形2個
との総計17個の図形板の組合せ教具(1) A disk divided into four fan-shaped plates: a semicircle, a quarter circle, an octant, and an octant, and two small right-angled isosceles triangles whose bases are the radius of the circle, Four isosceles right-angled medium polygons whose sides are right angles, one each of isosceles right-angled large triangles, squares, and parallelograms formed by connecting the two medium polygons with their sides, and the small Small trapezoid 2 made by connecting two triangles with sides
A total of 17 graphic board combinations, including two large trapezoids made by connecting one each of the medium and large triangles with their sides.
せて、平面上に重ねずに並べて図形を作り、算数の四則
演算・図形の性質・合同と相似性・拡大と縮小について
学習する方法と2図工の構成能力・美的感覚を養成する
手段とを提供可能な図形板組合せ教具(2) A method for learning about the four arithmetic operations, properties of shapes, congruence and similarity, enlargement and reduction, by combining all or part of the 17 figure boards and arranging them on a plane without overlapping them to create figures. A drawing board combination teaching tool that can provide a means for cultivating the composition ability and aesthetic sense of two-dimensional artists.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP9191983A JPS59229590A (en) | 1983-05-24 | 1983-05-24 | Graphic panel combination teaching aid |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP9191983A JPS59229590A (en) | 1983-05-24 | 1983-05-24 | Graphic panel combination teaching aid |
Publications (1)
Publication Number | Publication Date |
---|---|
JPS59229590A true JPS59229590A (en) | 1984-12-24 |
Family
ID=14039988
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP9191983A Pending JPS59229590A (en) | 1983-05-24 | 1983-05-24 | Graphic panel combination teaching aid |
Country Status (1)
Country | Link |
---|---|
JP (1) | JPS59229590A (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS6462185A (en) * | 1987-09-01 | 1989-03-08 | Buncho Corp | Combination toy |
JPH07472U (en) * | 1992-11-13 | 1995-01-06 | 節 宇治 | 10 piece puzzle toys |
Citations (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS6350672U (en) * | 1986-09-19 | 1988-04-06 |
-
1983
- 1983-05-24 JP JP9191983A patent/JPS59229590A/en active Pending
Patent Citations (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS6350672U (en) * | 1986-09-19 | 1988-04-06 |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS6462185A (en) * | 1987-09-01 | 1989-03-08 | Buncho Corp | Combination toy |
JPH0548712B2 (en) * | 1987-09-01 | 1993-07-22 | Buncho Kk | |
JPH07472U (en) * | 1992-11-13 | 1995-01-06 | 節 宇治 | 10 piece puzzle toys |
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