Math- 8 Core- Quarter 3
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Squares and Square Roots Pythagorean Theorem Transformations Similarity |
Quarter 3 |
Squares and Square Roots Square Root Principal Square Root Perfect Squares Estimating Square Roots Ordering Square Roots Rational and Irrational Roots Expressions wlith Square Roots Real and Imaginary Roots Graphing Irrational Numbers
Pythagorean Theorem Determine parts of right triangle They hypotenuse of a right triangle is always the longest side The right angle of a right triangle is always included between the legs Regect negative root, because its a length Using Pythagorean Theorem to determine a missing side Determining if a triangle is a right triangle (converse of Pythagorean Theorem) Pythagorean Triples
Transformations Symmetry Isometric Figures Translation Reflection Rotation Composition of Transformations Dilation Similarity Proportionality of sides
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Squares and Square Roots How can you find the side length of a square when you are given the area of the square? Why can't we find the root of a negative number? How do the roots of numbers help us classify numbers as rational and irrational numbers? If we add a constant to an irrational number is the sum rational or irrational? How can we use knowledge of perfect squares to estimate values of square roots? How many real roots do square roots of positive real numbers have? Are both negative and positive roots always reasonable solutions?
Pythagorean Theorem How are the lengths of the right triangle connected? Is there a common rule to determine the length of the diagnol of a triangle? Is there on side of a right triangle whose length is always the longest? What is a theorem? How can we demonstrate Pythagorean Theorem on a coordinate plane? Can you prove that a radicand is a group? Is the hyponetuse of a right triangle always opposite the right angle? How can we determine the legs of a right triangle? Can you use Pythagorean Theorem in geometric applications of area and perimeter? How does Pythagorean Theorem help us with indirect measurement? Why is it useful to know the Pythagorean Triples?
Transformations What does congruence mean? Do rigid movements change size or shape of figures on a plane? Does sliding a figure from one position to another maintain congguence? How can we describe a slide (translation)? Can we create a general rule to apply to coordinates for translations? How do descriptive words of a translation affect the coordinates of the original image? How can we distinguish the new image from the original on a graph? What is a reflection? Can you describe a real life reflection? Why do you think a reflection is described as a flip? Can we reflect images over the x-or y-axes? What affect do reflections over the axes have on the coordinates? Can a figure that is drawn over two or more quadrants be reflected? What is significant about the distances from reflected points to the original? How can you determine if a figure is reflected or translated if the new image appears to be either reflected or translated? Can we create a general rule to apply to coordinates for reflections? Can you describe what a rotation means to you in real life? How do we turn an object on a plane? What are the two directions objects can be rotated? Why is it important to know the center point of rotation, how does it affect the movement? What are the quarter turn degrees of a coordinate plane? What is rotational symmetry? Can we describe the same position multiple ways? Can we create general rules for rotations and how the affect the coordinates? Can we do multiple transformations and maintain congruence? How can we determine which image is first, second, last? Why do you think multiple movements are called compositions? How does that word applyinyour life? What conclusions can you draw about corresponding angles and sides when translations, reflections and rotations are performed on a figure? What does it mean to dilate? Can you think of any real life situations where you have heard the word dilation before? How does a scale factor affect the size of a figure? What are the parameters of the scale factor that make a figure reduce in size? What are the parameters of the scale factor that make a figure enlarge? How is the distance from the center of the dilation to each point relate when compared to the dilated new images' points? Are dilated figures congruent or similar? What is the affect on corresponding sides and angles? How do corresponding sides look on a graph? What is the relationship you see? Can we develop a general statement in regard to corresponding sides and parallelism? Can we develop a general rule that applies to the coordinates when doing dilations? What value must the scale factor be to be similar and congruent? Can we use proportions to determine corresponding segment length? How does similarity help us measure distances that cannot be measured easily with rulers?
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Squares and Square Roots Determine the parts of a radical (index, radicand, radical) Determine the square roots of of whole numbers Explain why square roots less than zero are imaginary Determine when to use the principle root, the negative root or both Simplify expressions with radicals Estimating roots, using knowledge of perfect squares Determine if square roots are rational or irrational Place square roots on the number line Solve equations with square roots
Pythagorean Theorem Recognize if a triangle is a right triangle Determine the parts of the right triangle (hypotenuse, legs) Draw conclusions about the length of the hypotenuse in relation to the legs Demonstrate the understanding of the sum of the squares of the legs is equal to the square of the hypotenuse on the coordinate grid Use Pythagorean Theorem to find a missing side of a right triangle Find the perimeter and area of a right triangle or other geometric figures, after using Pythagorean Theorem (with and without square root sides) Use the converse of the Pythagorean Theorem to determine if a triangle is in fact a right triangle Discover real life applications where Pythagorean Theorem would be helpful to know
Transformations Demonstrate understanding of congruence State corresponding sides of figures Write statements of congruence using symbol and proper labeling of figures Perform translation from words, the T symbol, rules to coordinates Determine the translation rule used for given points and apply rule to another point Graph and translate figures with proper notation for pre-image and new-image Perform a reflection through the x-axis and y-axis, label images properly Perform a reflection through vertical and horizontal lines (not axes) Establish the distance from points to the line of reflection are congruent Determine the reflection based on the changes described to the coordinates Determine degrees and direction of quarter turns on coordinate plane using origin as center Graph rotations of quarter and 180 degree rotations by rotating plane Graph rotations of quarter and 180 degree rotations by using protractor and ruler Graph rotations of quarter and 180 degree rotations using coordinate rules Determine the applied rotation when given pre-image and image points Graph compositions of rigid transformations, with proper image labeling Verbally explain why figures maintain size and shape (congruence) Identify combined transformations Graph dilations and label new image Identify scale factors that result in reductions and those that result in enlargement Write rules of dilations based on scale factor Write similarity statements between original and new images Identify the relationship between corresponding sides of similar figures Finding missing sides of similar figures Demonstrate understanding that angles of corresponding sides are congruent in similar figures Determine similar figures from markings of angles and sides Write similar statements in corresponding form Use similarity to measure indirectly Examine slope triangles and connect to parallelism Establish that corresponding sides of similar figures are parallel
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Squares and Square Roots Square Root Radicand Radical Index Rational Irrational Principle Root Negative Root Perfect Squares Irrational Rational Real Imaginary hypotenuse legs perpendicular right angle between included angle converse base height pythagorean triples angle of rotation center of dilation center of rotation congruent dilation scale factor image line of reflection preimage reflection rotation rotational symmetry transformation translation composition of transfomations corresponding angles
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Math Chat Writing prompt Classroom assessments Pass paper Judy Dodge exits Exit tickets Daily and weekly spirals Benchmarks IXL |
Glencoe Course 3 Text Big Ideas Text-Grade 8 Holt-McDouglal Mathematics Grade 8 IXL New York State Modules |
