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Adding and subtracting fractions is similar to whole number computation in that it adds and subtracts two number line quantities. When fractions are greater than one, they are still a sum of unit fractions. To add and subtract fractions, they must have common denominators.

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Multiplying a fraction by any fraction with the same numerator and denominator is the same as multiplying by 1. Find equivalent fractions by multiplying by a fraction equivalent to 1 in the form of n/n.

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Recognize and draw line(s) of symmetry and line-symmetric figures (may be multiple or no lines of symmetry given the shape). Squares have 4 lines of symmetry (vertical, horizontal, and diagonals in both directions). Rectangles have 2 lines of symmetry (horizontal and vertical), a trapezoid has 1 (vertical), and a parallelogram has 0 lines of symmetry. Identify and draw lines of symmetry in quadrilaterals. Given half of a shape, draw the other half to create a symmetric figure.

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Types of angles are right (exactly 90), acute = less than 90, and obtuse = greater than 90. Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length. Parallel lines never intersect. They are named using two points along each line with the parallel line notation. A line is perpendicular to another if it meets or crosses it at right angles (90°). They are named by using the names of the two lines with the perpendicular notation.

Equilateral triangles have 3 congruent sides and 3 congruent angles. Isosceles triangles have 2 congruent sides that are opposite of each other. The angles formed by the isosceles sides with the 3rd side are also congruent. Scalene triangles have no congruent sides or angles. Acute triangles have 3 angles that are each less than 90. Right triangles have one angle that is exactly 90. Obtuse triangles have one angle that is greater than 90. Classify triangles by side and by angle using the above terms. Classify parallelograms, rectangles, squares, trapezoids, rhombuses using parallel and perpendicular lines.

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A point is an exact position or location on a plane surface. It is important to understand that a point is not a thing, but a place. It is drawn with a dot and named with a letter. A ray starts at a given point and goes off in a certain direction forever, to infinity. The point where the ray starts is called the endpoint. It is drawn as a line with an arrowhead on one end and named using the letters of the endpoint and another letter on the ray. A line is a geometrical object that is straight, infinitely long, and infinitely thin. You can draw a line with an arrowhead on each end as shown below. The arrowheads mean that the line goes off to infinity in both directions. You can name a line by using any two points along the line.

A line segment is a part of a line defined by 2 endpoints. It is drawn using two exact points to define the length of the line segment and is named using the letters of the points defining the line segment. An angle is the union of two rays, a and b, with the same initial point P named the vertex. The rays can be made to coincide by rotating one to the other about P; this rotation determines the size of the angle between a and b. Angles are named using 3 points where the point in the middle is the vertex. Types of angles are right (exactly 90), acute = less than 90, and obtuse = greater than 90.

When sketching an angle, draw a ray, align the protractor with the endpoint of the ray, and make a mark at the desired angle length. Use the ruler side of the protractor to sketch a line connecting the endpoint of the first ray and the mark made for the desired angle measurement. Sketch the line to form a vertex. Construct shapes with acute, obtuse, and right angles. Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length. Parallel lines never intersect. They are named using two points along each line with the parallel line notation. A line is perpendicular to another if it meets or crosses it at right angles (90°). They are named by using the names of the two lines with the perpendicular notation.

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Angles are measured with reference to a circle with its center at the common endpoint of the rays and the rays intersection points in relation to their fraction of the circular arc. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and degrees are the unit used to measure angles. Present angles in a variety of situations; shapes, maps, slopes, openings. Angles can be added together or decomposed into non-overlapping parts. The angle measure of the whole is the sum of the angle measures of the parts. Find the measurements of unknown angles on a diagram in real-world and mathematical problems.

Two angles are called complementary if their measurements have the sum of 90. Two angles are called supplementary if their measurements have the sum of 180. Two angles with the same vertex that overlap only at a boundary (i.e., share a side) are called adjacent angles. Decompose an angle measurement. Recognize angle measurement as the additive of the decomposed angle. Solve problems involving unknown angles. Write an equation with a symbol for an unknown angle measure.

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In an angle, each ray determines a direction and the angle size measures the change from one direction to the other. Angles are measured with reference to a circle with its center at the common endpoint of the rays and the rays intersection points in relation to their fraction of the circular arc. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and degrees are the unit used to measure angles. Measure angles using a circular protractor to avoid the mental trap of shapes of angles. Using a protractor, accurately sketch an angle with a given angle measurement.

When measuring an angle, the center point should align with the center point of the protractor, and one arm or ray should align with the base of the protractor. The other arm will determine the angle measure in relation to the first ray. When sketching an angle, draw a ray, align the protractor with the endpoint of the ray, and make a mark at the desired angle length. Use the ruler side of the protractor to sketch a line connecting the endpoint of the first ray and the mark made for the desired angle measurement. Sketch the line to form a vertex. Measure angles using a protractor. Estimate angle measures. Identify which angle is constructed to show a given angle measure.

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Understand equal partitioning and unit iteration to understand angle and turn measure. An angle is the union of two rays, a and b, with the same initial point P. The rays can be made to coincide by rotating one to the other about P; this rotation determines the size of the angle between a and b. In an angle, each ray determines a direction and the angle size measures the change from one direction to the other. Angles are measured with reference to a circle with its center at the common endpoint of the rays and the rays intersection points in relation to their fraction of the circular arc.

An angle that turns through 1/360 of a circle is called a “one-degree angle,” and degrees are the unit used to measure angles. An angle that turns through n/360 of a circle is called an “n-degree angle” – use multiple values for n. A ray that moves from point A to point B one degree at a time has an angle measure of n degrees. The number of one-degree angles in an angle that measures n degrees is n.

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Understand equal partitioning and unit iteration to understand angle and turn measure. Angle measure is a “turning point” in the study of geometry. An angle is the union of two rays, a and b, with the same initial point P. The rays can be made to coincide by rotating one to the other about P; this rotation determines the size of the angle between a and b. Identify the measure of an angle that turns through a fraction of a complete circle. Limited to benchmark fractions 1/2, 1/3, 1/4, and 1/8. Identify the angle measure, in degrees, given the fraction the ray of an angle turns. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and degrees are the unit used to measure angles. An angle that turns through n/360 of a circle is called an “n-degree angle” – use multiple values for n.

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Scale line plots with measurements to show fractions of a unit (1/2, 1/2, and 1/8). Use information from line plots to answer questions and solve problems. Problems from line plots include the addition and subtraction of fractions. Fractions must first be converted into a fraction with the same denominator before adding or subtracting. Use measurements to show equivalent fractions built on unit fractions of 1/2, 1/4, and 1/8.

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