**4.1-Unit 6: Geometry and Measurement**Students have been exploring and describing geometric shapes since kindergarten with greater specificity each year. In fourth grade, they explore lines, rays, and angles in greater depth to allow them to analyze and describe shapes.

The key ideas focused on in this unit include:

- drawing and identifying various types of lines and angles
- identifying angles as acute, obtuse, and right
- measuring angles with a protractor, and drawing angles of a specified measurement
- understanding angle measurement as additive
- classifying shapes by properties of their lines and angles, including classifying triangles
- recognizing a line of symmetry and identifying figures that have lines of symmetry

__Understanding Lines and Rays__

Students will explore basic concepts about lines and then explore various types of lines including parallel, intersecting, and perpendicular lines.

__Understanding and Measuring Angles__

Fourth grade students are introduced to measuring angles as rotation, like the hour hand of a clock moving around a circle from 12:00, forming different measurements. They use the benchmark measurements of 90 degrees (right angle) to estimate the measurements of other angles. To find the exact measurement, students are taught to use a protractor. They use the protractor to measure angles and to draw angles when given a specific degree measure.

Through investigations, observations, and discussions, students learn that angle measure is additive. Two angles that share a side are called adjacent angles. The sum of the measurements of adjacent angles is the measurement of the angle formed when the two are joined. Students are challenged to find the measure of the missing angle when given the total sum of the two angles and the angle measure of one of the angles.

__Classifying Shapes__

In fourth grade, students use their understanding of lines and angles to describe and classify shapes based on the types of lines and angles that appear in the shape. This ability to classify geometric shapes is also dependent on their understanding and skills in measurement since they must be able to identify and measure angles. The classification of triangles and quadrilaterals are explored in depth.

Understanding Symmetry

The concept of line symmetry is introduced in fourth grade. A shape or design that has line symmetry can be folded along the line of symmetry to make two congruent shapes that fit exactly on top of each other. Through investigations and discussions, students explore the meaning of symmetry, identify shapes that have one or more lines of symmetry, and draw the line of symmetry in shapes.

At the end of Unit 6, students should be able to:

- identify and name points, line segments, rays, lines, and angles
- identify perpendicular lines, parallel lines, and intersecting lines within shapes
- use a protractor to measure and draw angles
- identify a larger angle as the sum of two angles
- classify triangles and quadrilaterals
- identify and draw a line of symmetry in a figure

Vocabulary

It is extremely important that students understand the vocabulary for this unit. Students have all of the vocabulary for the unit in their math journals and should be studying it and reviewing it regularly. Students are also encouraged to practice vocabulary on their own by making flashcards (paper or digital), etc.

Homework for this unit will continue to be the Iready "My Path" lessons. Students should be doing 20 minutes each night (Monday - Thursday). Working on these lessons will help to fill in gaps that students have and is greatly beneficial in learning and mastering grade level curriculum. If they miss a night, they can double up another night, etc. as long as they have 80 minutes by the end of the week.

The study guide for Unit 6 will be sent home near the end of the unit so students can use it to prepare for the unit assessment.

The Unit 5 Assessment will be given on Friday, April 3

The Unit 5 Study Guide will be sent home on Thursday, March 26

__4.1 Standards for Unit 6:__**MGSE4.G.1**Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

**MGSE4.G.2**Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

**MGSE4.G.3**Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

**MGSE4.MD.5**Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one degree angles is said to have an angle measure of n degrees.

**MGSE4.MD.6**Measure angles in whole number degrees using a protractor. Sketch angles of specified measure.

**MGSE4.MD.7**Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol or letter for the unknown angle measure.

*4.MD.2 is a standard that will appear in every unit in 4th grade and will be covered more thoroughly in Unit 7