# Shapes and Angles

Students are introduced to the more abstract concepts of points, lines, line segments, rays, and angles, as they learn to measure angles and then analyze shapes by their angles and lines of symmetry.

## Unit Summary

Unit 4 in Grade 4 introduces students to the more abstract geometric concepts of points, lines, line segments, rays, and angles. Students learn to measure angles and then use this skill to classify shapes based on their angle measure, a geometric property. Students also develop an understanding of reflectional symmetry, identifying line-symmetric shapes and drawing their lines of symmetry.

This unit builds on lots of work in prior grades with shape recognition and categorization (1.G.1, 2.G.1, 3.G.1). In order to differentiate a square from a rhombus, students must attend to the angle measure of the corners, or vertices. Thus, this unit introduces students to the vocabulary that will allow them to talk about angle measure as an attribute of plane figures (both polygons and more abstract figures, such as sets of intersecting lines), as well as the measurement system used to quantify angle measure precisely.

The unit begins with students drawing points, lines, line segments, rays, and angles, and continues to general classifications based on angles, including distinguishing between right, obtuse, acute, and straight angles as well as parallel, perpendicular, and intersecting lines. Then, students develop a more precise idea of angles as geometric figures that can be measured, and learn to do so. Students also learn to think of angles not just as objects but as actions—they can indicate a turn or change in direction. Students also see that angles are additive, just like other geometric measures they’ve explored in prior grades, such as length in Grade 2 (2.MD.1—6) and area in Grade 3 (3.MD.5—7). Next, students use their deepened understanding of angles to classify and draw triangles according to their angle measure (right, obtuse, and acute) as well as side length (equilateral, isosceles, and scalene) and quadrilaterals according to the parallel and/or perpendicular nature of their sides. Lastly, students explore lines of symmetry, finding and drawing them in figures.

This unit allows for particular focus on MP.2, MP.5 and MP.6. For example, when students are “shown two sets of shapes and asked where a new shape belongs,” they are reasoning abstractly and quantitatively (MP.2) (G Progression, p. 16). Students also learn to use a new tool, the protractor, precisely, ensuring they line up the vertex and base correctly and read the angle measure carefully (MP.5, MP.6).

This work continues to formalize much of the work students have already done in understanding geometric figures, which will continue to formalize in coming years. This unit prepares students to hierarchically classify two-dimensional figures in Grade 5 (5.G.3, 5.G.4). It also introduces students to drawing geometric figures, which they will see again in Grade 7 (7.G.1—3) and even high school Geometry and the trigonometric aspects of Algebra II. Thus, while all of the standards addressed in the unit are additional cluster standards, they lay an important foundation for geometric work in years to come.

Pacing: 20 instructional days (18 lessons, 1 flex day, 1 assessment day)

## Assessment

This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.

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## Unit Prep

### Essential Understandings

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• Points have location but no dimension. Lines are infinite in extent in one dimension.
• Angle and length measure are independent. That is, the measure of an angle is not dependent on the length of the sides of the angle.
• Angles can describe both static and dynamic contexts. For example, an angle can be used to describe the measure of the spread at the vertex of a two-dimensional shape, or it could be used to describe a change in direction.
• Like other geometric measurements students have learned in the past, such as length and area, angle measure is additive.
• Polygons can be described and classified by their sides and angles.
• Some shapes can be reflected across one or more lines passing through the shape so the shape folds onto itself exactly. This symmetry is not a defining attribute of the shape, however.

### Vocabulary

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 acute angle obtuse angle acute triangle obtuse triangle adjacent angle parallel, ${\parallel }$ angle, ${\angle}$ perpendicular, ${\perp}$ arc point arc length protractor degree, ${^{\circ}}$ ray, ${ \overrightarrow{AB}}$ equilateral triangle right angle intersecting lines, intersect right triangle isosceles triangle scalene triangle line, ${\stackrel{\leftrightarrow}{AB}}$ straight angle line of symmetry, symmetric vertex line segment, ${\overline{AB}}$

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### Intellectual Prep

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#### Intellectual Prep for All Units

• Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan.
• Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind.
• Take the unit assessment.

## Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

### Core Standards

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##### Geometry
• 4.G.A.1 — Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

• 4.G.A.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.

• 4.G.A.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.

##### Measurement and Data
• 4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

• 4.MD.C.5.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.

• 4.MD.C.5.B — An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

• 4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

• 4.MD.C.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 for the unknown angle measure.

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• 1.G.A.2

• 3.G.A.1

• 1.OA.D.8

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• G.CO.A.1

• 5.G.B.3

• 7.G.B.5

• F.TF.A.1

### Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.