What are Equivalent Fractions?

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2022-08-08 20:50

Coordinate Geometry Geometric Construction

In collections Erstes Rechnen mit Brüchen - Addieren

This example illustrates the concept of equivalent fractions. Key mathematical concepts include the properties of fractions. Construction highlights the use of GeoGebra commands such as Midpoint, Polygon, and Textfield. Suitable for 5th to 6th grade students learning to add fractions.

GeoGebra Commands & Parameters

Midpoint(Corner[Text39, 1], Corner[Text39, 3]) → M1
Polygon(I, J, K, L) → v3, i, j, k, l
Polygon(M_{2}, N_{2}, O_{2}, P_{2}) → rectN, m_{2}, n_{2}, o_{2}, p_{2}
Polygon(M_{1}, N_{1}, O_{1}, P_{1}) → rectB, m_{1}, n_{1}, o_{1}, p_{1}
Polygon(M, N, O, P) → rectZ, m, n, o, p
Midpoint(Corner[textBruchstrich, 1], Corner[textBruchstrich, 3]) → MPBruchstrich
Midpoint(Corner[textNenner, 1], Corner[textNenner, 3]) → MPNenner
Midpoint(Corner[textZähler, 1], Corner[textZähler, 3]) → MPZähler
Textfield(textTest) → InputBox1
Textfield(textTest2) → InputBox2
Textfield(textTest3) → InputBox3
Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 5, 10, 0, 0, 9, 9, 4, 7, 10, 8, 4, 3, 8, 8, 8, 6, 7, 10, 2, 1, 8, 4, 0, 0, 5, 2, 9, 8, 10, 4, 1, 1, 5, 9, 8, 2, 3, 3, 7, 4, 9, 3, 5, 6, 0, 4, 5, 4, 9, 7, 8, 8, 8, 0, 8, 7, 7, 2, 5, 10, 3, 7, 2, 9, 4, 5, 1, 0, 4, 5, 6, 9, 1, 4, 0, 3, 8, 9, 2, 9, 5, 0, 5, 10, 6, 10, 4, 3, 5, 4, 10, 1, 1, 2, 3, 6, 7, 1, 10}
Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {1, 3, 6, 5, 6, 4, 2, 9, 7, 6, 5, 9, 3, 0, 3, 7, 6, 9, 4, 4, 5, 8, 6, 2, 6, 2, 8, 1, 9, 3, 10, 9, 7, 0, 5, 6, 8, 5, 4, 2, 7, 1, 5, 4, 10, 2, 2, 5, 3, 0, 7, 5, 1, 8, 10, 8, 5, 4, 3, 0, 9, 6, 8, 4, 1, 8, 2, 3, 6, 9, 2, 3, 7, 9, 8, 1, 10, 7, 8, 7, 3, 9, 7, 2, 1, 10, 10, 7, 1, 7, 6, 1, 10, 9, 5, 3, 5, 10, 5, 8}
Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
Textfield(input1) → Eingabefeld1
Textfield(input2) → Eingabefeld2
Textfield(input3) → Eingabefeld3
Textfield(input4) → Eingabefeld4
Textfield(input5) → Eingabefeld5
Textfield(input6) → Eingabefeld6
Textfield(input7) → Eingabefeld7
Textfield(input8) → Eingabefeld8
Textfield(input9) → Eingabefeld9
Textfield(input10) → Eingabefeld10
Textfield(input11) → Eingabefeld11
Textfield(input12) → Eingabefeld12
Polygon(A, B, C, D) → v1, a, b, c, d
Polygon(E, F, G, H) → v2, e, f, g, h
Midpoint(Corner[erlaubteZeichen, 1], Corner[erlaubteZeichen, 3]) → MP_{erlaubteZeichen}
Midpoint(Corner[textTest, 1], Corner[textTest, 3]) → MP_{textTest}
Midpoint(Corner[textTest2, 1], Corner[textTest2, 3]) → MP_{textTest2}
Midpoint(Corner[textTest3, 1], Corner[textTest3, 3]) → MP_{textTest3}
Midpoint(Corner[textCountCorrect, 1], Corner[textCountCorrect, 3]) → MP_{textCountCorrect}
Midpoint(Corner[hintText, 1], Corner[hintText, 3]) → MP_{hintText}
Midpoint(Corner[questionText, 1], Corner[questionText, 3]) → MP_{questionText}
Midpoint(Corner[inactiveButtonBackgroundColor, 1], Corner[inactiveButtonBackgroundColor, 3]) → MP_{inactiveButtonBackgroundColor}
Midpoint(Corner[answerText, 1], Corner[answerText, 3]) → MP_{answerText}
Midpoint(Corner[solutionText, 1], Corner[solutionText, 3]) → MP_{solutionText}
Midpoint(Corner[text1, 1], Corner[text1, 3]) → MP_{text1}
Midpoint(Corner[text2, 1], Corner[text2, 3]) → MP_{text2}
Midpoint(Corner[altText, 1], Corner[altText, 3]) → MP_{altText}
Midpoint(Corner[hintTypicalError, 1], Corner[hintTypicalError, 3]) → MP_{hintTypicalError}
Midpoint(Corner[correctText, 1], Corner[correctText, 3]) → MP_{correctText}
Midpoint(Corner[Text1, 1], Corner[Text1, 3]) → MP_{Text1}
Midpoint(Corner[Text2, 1], Corner[Text2, 3]) → MP_{Text2}
Midpoint(Corner[Text3, 1], Corner[Text3, 3]) → MP_{Text3}
Midpoint(Corner[Text4, 1], Corner[Text4, 3]) → MP_{Text4}
Midpoint(Corner[Text5, 1], Corner[Text5, 3]) → MP_{Text5}
Midpoint(Corner[Text6, 1], Corner[Text6, 3]) → MP_{Text6}
Midpoint(Corner[Text7, 1], Corner[Text7, 3]) → MP_{Text7}
Midpoint(Corner[Text8, 1], Corner[Text8, 3]) → MP_{Text8}
Midpoint(Corner[Text9, 1], Corner[Text9, 3]) → MP_{Text9}
Midpoint(Corner[Text10, 1], Corner[Text10, 3]) → MP_{Text10}
Midpoint(Corner[Text11, 1], Corner[Text11, 3]) → MP_{Text11}
Midpoint(Corner[Text12, 1], Corner[Text12, 3]) → MP_{Text12}
Midpoint(Corner[Text13, 1], Corner[Text13, 3]) → MP_{Text13}
Midpoint(Corner[Text14, 1], Corner[Text14, 3]) → MP_{Text14}
Midpoint(Corner[Text15, 1], Corner[Text15, 3]) → MP_{Text15}
Midpoint(Corner[Text16, 1], Corner[Text16, 3]) → MP_{Text16}
Midpoint(Corner[Text17, 1], Corner[Text17, 3]) → MP_{Text17}
Midpoint(Corner[Text18, 1], Corner[Text18, 3]) → MP_{Text18}
Midpoint(Corner[Text19, 1], Corner[Text19, 3]) → MP_{Text19}
Midpoint(Corner[Text21, 1], Corner[Text21, 3]) → MP_{Text21}
Midpoint(Corner[Text22, 1], Corner[Text22, 3]) → MP_{Text22}
Midpoint(Corner[Text23, 1], Corner[Text23, 3]) → MP_{Text23}
Midpoint(Corner[Text24, 1], Corner[Text24, 3]) → MP_{Text24}
Midpoint(Corner[Text25, 1], Corner[Text25, 3]) → MP_{Text25}
Midpoint(Corner[Text26, 1], Corner[Text26, 3]) → MP_{Text26}
Midpoint(Corner[Text27, 1], Corner[Text27, 3]) → MP_{Text27}
Midpoint(Corner[Text28, 1], Corner[Text28, 3]) → M2
Midpoint(Corner[Text29, 1], Corner[Text29, 3]) → M3
Midpoint(Corner[Text30, 1], Corner[Text30, 3]) → M7
Midpoint(Corner[Text31, 1], Corner[Text31, 3]) → M4
Midpoint(Corner[Text32, 1], Corner[Text32, 3]) → M8
Midpoint(Corner[Text33, 1], Corner[Text33, 3]) → M11
Midpoint(Corner[Text34, 1], Corner[Text34, 3]) → M5
Midpoint(Corner[Text35, 1], Corner[Text35, 3]) → M6
Midpoint(Corner[Text36, 1], Corner[Text36, 3]) → M10
Midpoint(Corner[Text37, 1], Corner[Text37, 3]) → M9
Midpoint(Corner[Text38, 1], Corner[Text38, 3]) → M12
Corner(textNenner, 1) → Q
Corner(textZähler, 1) → R
Corner(textBruchstrich, 1) → S
Intersect(a, d) → T
Intersect(j, k) → V
Polygon(T, U, V, W) → vGes, t, u, v, w
Polygon(B_1, E_1, D_1, C_1) → v4, b_1, e_1, d_1, c_1
If(MPNenner ∈ rectN ∨ MPNenner ∈ rectB ∨ MPNenner ∈ rectZ, Append[MPNenner, listFirstBoxes]) → l1
If(MPZähler ∈ rectN ∨ MPZähler ∈ rectB ∨ MPZähler ∈ rectZ, Append[MPZähler, l1]) → l2
If(MPBruchstrich ∈ rectN ∨ MPBruchstrich ∈ rectB ∨ MPBruchstrich ∈ rectZ, Append[MPBruchstrich, l2]) → appended
CountIf(x ≠ 0, appended) → append

AI Drawing Prompt Reference

Draw two identical rectangles, each divided into four parts by dashed lines to represent the numerator and denominator of a fraction. Below the rectangles, draw a long bar with midpoints connecting its ends, and label the value of the fraction at the midpoint. Use color and shape variations to illustrate the equivalence of different fractions, suitable for explaining the basic properties of fractions and the concept of equivalent fractions.

The prompt above was compiled from the original drawing commands and is for reference only.