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Use translations and reflections in tessellations

8.EE.A.1

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

sample

math

Ex. 1:

Ex. 2:

Counting reflection symmetries of a regular hexagon

<p>- [Instructor] Hi, welcome to the question right here. So what can we do, what type of transformation can we do to get this tessellation? Well, if you look at it.you can actually choose let's say reflection. My first answer is, I'm going to pick my reflection. The reason I pick my reflection is because I can simply take this whole thing right here, do you see that? I can pick this as one figure. Then, I'm just going to reflect it to the left. That's it. Reflect it on the Y axis, it works. I can also reflect on the X axis which is over here. See, if I reflect it down I get the exact same graph. I can reflect it here, I get the exact same graph, okay? Well, is that the only choice I have? No, what about translation? Have you ever done translation before?<br />
Translation just means that you can move it left and right. So that is I just pick this whole thing right here, the first one right here. Pick it up, translate to the right, I also get the same graph or the same pattern. So that way, I can create my tessellation using the reflection also using the translation. Both method will get you the answer for sure. Oh I'm sorry, will get you the tessellation, okay? In terms of the last one, the transformation I'm probably thinking that it may not work by looking at it. It may or may not. Okay? Because I can't really see it by rotating just the yellow-- No we have to do the yellow and the gray at the same time. So it looks like that there's no room for your rotation. So just these two will be your final answer. Okay? Thanks for watching.</p>


Identifying reflection, translation, and rotation in a tessellation

Identifying reflection and translation in a tessellation pattern

Identifying translation as the transformation for a tessellation

Translations and reflections are two of the few ways of how tessellations are created. We will use a tile as an example here. Reflection means flipping over the tile by its edge. On the other hand, translation means picking the tile up and putting it down to the space originally next to it.

Introduction to transformations

Horizontal and vertical distances