Math News! 4 th Grade Math Module 4: Angle Measure and Plane Figures. Focus Area Topic A Lines and Angles

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1 Grade 4, Module 4, Topic A Module 4: Angle Measure and Plane Figures This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Module 4 of Eureka Math (Engage New York) covers angle measures and plane figures. Focus Area Topic A Lines and Angles Point -precise location in the plane Line - straight path with no thickness that extends in both directions without end Line segment part of a line connecting two endpoints Ray - a part of a line which starts at a point and goes off in a particular direction to infinity. Always name a ray by starting with its endpoint Focus Area Topic A Lines and Angles Arc -connected portion of a circle Angle - union of two different rays sharing a vertex Vertex - a point, often used to refer to the point where two lines meet, such as in an angle or the corner of a triangle Obtuse angle - angle with a measure greater than 90 degrees but less than 180 degrees Acute angle - angle with a measure of less than 90 degrees OBJECTIVES OF TOPIC A Identify and draw points, lines, line segments, rays, and angles and recognize them in various contexts and familiar figures. Use right angles to determine whether angles are equal to, greater than, or less than right angles. Draw right, obtuse, and acute angles. Identify, define, and draw perpendicular and parallel lines.

2 Module 4: Angle Measure and Plane Figures In topic A students use their understanding of angles to explore relationships between pairs of lines, defining and recognizing intersecting, perpendicular, and parallel lines. Their knowledge of right angles leads them to identify and define as well as construct perpendicular lines. Students learn how lines that never intersect also have a special relationship and are called parallel. They explore these concepts by finding parallel and perpendicular lines in common shapes and objects. Label points on the figure and then use those points to label and name representations of each of the following in the table below: ray, line, line segment, and angle. Parallel - two lines in a plane that do not intersect Perpendicular -Two lines are perpendicular if they intersect, and any of the angles formed between the lines is a 90 angle. Intersecting lines - lines that contain at least one point in common Trace at least one pair of lines that are perpendicular. Trace at least one pair of lines that appear to be parallel.

3 Grade 4, Module 4, Topic B Module 4: Topic B: Angle Measurement This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Module 4 of Eureka Math (Engage New York) covers angle measures and plane figures. Protractor Types Students will use two different types of protractors in class. The Standard Protractor or Half Protractor Focus Area Topic B Angle Measurement Students are asked to identify the measures of angles. In this example, they will place the center point of the protractor over point L. Then match the 0 line of the protractor along line segment LJ. They can then read where line segment LK crosses the edge of the protractor to find the angle measurement. The Circular Protractor OBJECTIVES OF TOPIC B Use protractors to measure and draw angles. Sketch given angle measures and verify with a protractor. Identify and measure angles as turns and recognize them in various contexts. The measure of this angle is 40. The students will write angle KLJ is 40 or.

4 Using a Protractor to Draw Angles Students are asked to draw angles that match a certain degree measure. These are steps for drawing a 70 angle. Step 1 - Draw a ray and label the endpoint A. Step 2 - Line up the protractor, placing the center over endpoint A making sure the ray lines up with the 0 line.. Step 4 - Use the straight edge of the protractor to draw the next ray beginning at point A and continuing to the mark you made above the 70. Step 3 - Find 70 on the protractor and draw a small point right above it. Step 5 - Use the protractor to verify the angle is 70. Angles as Turns Students further explore angle measure as an amount of turning. They reason that a ¼ turn is a right angle and measures 90, a ½ turn measures 180, and a ¾ turn measures 270. They go on to identify these angles in their environment. Example Question and Answer Joe stood in the middle of the yard and faced the house. Joe turned 90 to the right. To what was Joe now facing? Answer: Joe would be facing the park.

5 Grade 4, Module 4, Topic C Module 4: Topic C: Problem Solving with the Addition of Angle Measures This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Module 4 of Eureka Math ( Engage New York) covers angle measures and plane figures. Focus Area Topic C Addition of Angle Measures In class, students will use concrete examples to discover the additive nature of angle measure. Working with pattern blocks, they see that the measures of all of the angles at a point, with no overlaps or gaps, add up to 360 degrees, and they use this fact to find the measure of the pattern blocks angles. Degree -measure of an angle Subdivide the length around a circle into 360 arcs of equal length. A central angle for any of these arcs is called a one-degree angle and is said to have angle measure of 1. Adjacent angle - two angles are adjacent if they have a common side and a common vertex (corner point) and don't overlap. Consider the example below. Complementary angles - two angles with a sum of 90.. The students will write addition and subtraction equations to solve unknown angle problems. Write an equation and solve for the measure of. In this example, angle A measures 40 and angle B measures 50. Together they form a 90 angle. They are complementary. The student should see angle BDA is a 90 angle or a right angle. Since angle CDA has a measure of 20, they can subtract the angle they know to find the unknown angle OBJECTIVES OF TOPIC B Decompose angles using pattern blocks. Use the addition of adjacent angle measures to solve problems using a symbol for the unknown angle measure. 90 = 20 + X or = X X = 70

6 Grade 4, Module 4, Topic D Module 4: Topic D: Two-Dimensional Figures and Symmetry This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Module 4 of Eureka Math (Engage New York) covers angle measures and plane figures. Focus Area Topic D Two-Dimensional Figures and Symmetry Triangle - A triangle consists of three points and the three line segments between them. The three segments are called the sides of the triangle and the three points are called the vertices. Obtuse triangle - triangle with an interior obtuse angle Line of Symmetry - line through a figure such that when the figure is folded along the line two halves are created that match up exactly Consider figures A, B, and C. Only one of them shows a line of symmetry. Students will need to see that figure A can be folded along the dotted line making the halves line up exactly. Therefore, figure A has the line of symmetry. OBJECTIVES OF TOPIC B Recognize lines of symmetry for given two-dimensional figures; identify line-symmetric figures and draw lines of symmetry. Analyze and classify triangles based on side length, angle measure, or both. Define and construct triangles from given criteria. Explore symmetry in triangles. Classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size. Reason about attributes to construct quadrilaterals on square or triangular grid paper. Right triangle- triangle that contains one 90 degree angle Scalene triangle - triangle with no sides or angles equal Isosceles triangle - triangle with at least two equal sides Students are asked to decide if a given triangles can be described as right triangle and an isosceles triangle. Consider this example. Can be described as a right triangle and an isosceles triangle? Answer: Yes because it has a right angle and two equal sides.

7 Module 4: Topic D: Two-Dimensional Figures and Symmetry Two-Dimensional Figures and Symmetry Attribute - a characteristic that describes an object Polygon - closed two-dimensional figure with straight sides Quadrilateral - polygon with four sides Follow the directions below to draw a figure. Rectangle - quadrilateral with four right angles Square - rectangle with all sides of equal length Rhombus - quadrilateral with all sides of equal length Parallelogram - quadrilateral with two pairs of parallel sides Trapezoid - quadrilateral with at least one pair of parallel sides Explain the attribute that makes a square a special rectangle. Which figure did you draw? What attributes does it have? A rectangle has 4 sides and 4 right angles. A square has 4 sides and 4 right angles as well so a square is a rectangle. We say it is a special rectangle because it has 4 equal sides. I drew triangle JKL or. It has 3 sides. It is a scalene triangle because it has no sides or angles that are equal.