### Clarifications

*Clarification 1:*Instruction includes classifying angles using benchmark angles of 90° and 180° in two-dimensional figures.

*Clarification 2: *When identifying angles, the expectation includes two-dimensional figures and real-world pictures.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**Strand:**Geometric Reasoning

**Standard:**Draw, classify and measure angles.

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Acute Angle
- Angle
- Obtuse Angle
- Reflex Angle
- Right Angle
- Straight Angle

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to begin the understanding of angles and how they can be identified in lines and shapes. Understanding angles will be used to define shapes by their attributes. This builds on the work students completed in grade 3 to identify perpendicular lines in shapes in mathematical and real-world situations (MA.3.GR.1.1).- During instruction, students should gain experience using benchmark angles of 90° and 180° (MTR.6.1). For right angles (90°) students can use the corner of a piece of paper. By lining the edge of the corner of the paper on one ray to the vertex of the angle, students can determine that angles that are smaller than the corner are acute and angles that are larger than the corner are obtuse. Similarly, students can use the side of a piece of paper to determine if the angles are greater than 180°. Students believe a wide angle with short sides may seem smaller than a narrow angle with long sides. Students can compare two angles by tracing one and placing it over the other. Students will then realize that the length of the sides does not determine whether one angle is larger or smaller than another angle. The measure of the angle does not change.

### Common Misconceptions or Errors

- Students believe a wide angle with short sides may seem smaller than a narrow angle with long sides. Students can compare two angles by tracing one and placing it over the other. Students will then realize that the length of the sides does not determine whether one angle is larger or smaller than another angle. The measure of the angle does not change.

### Strategies to Support Tiered Instruction

- Instruction includes providing a graphic organizer and several examples of each type of angle (acute, right, obtuse, straight and reflex). The graphic organizer will have angles labeled on them for the students to use to help them classify the figures provided.
- For example, the teacher provides a graphic organizer similar to the one shown below. Along with the graphic organizer, the teacher provides examples of various angles to classify.

- Instruction includes providing a right angle and a straight angle printed on a clear transparency or sheet protector. Students lay the angles over angle examples provided by the teacher to help them classify the angles as less than 90 degrees (acute angle), greater than 90 degrees (obtuse angle), exactly 90 degrees (right angle), exactly 180 degrees (straight angle), or greater than 180 degrees (reflex angle). Students trace one angle and place it over the other to compare them.
- For example, the teacher may provide the student with a clear transparency with a right angle printed on it. The teacher provides sample angles and asks students to place the transparency over the angles. The students sort the angles into greater than 90 degrees, less than 90 degrees, and equal to 90 degrees. The teacher will then provide a straight angle printed on a transparency and have students use that to classify the angles that were sorted as greater than 90 degrees into an additional grouping. Students will determine if the angles are equal to 180 degrees or greater than 180 degrees.

### Instructional Tasks

*Instructional Task 1 *(MTR.4.1)

Part B: Draw and label and example of 3 objects that have an acute angle.

Part C: Draw and label an example of 3 objects that have an obtuse angle.

Part D: Is it possible to find an object with a reflex angle? Why or why not?

### Instructional Items

*Instructional Item 1 *

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Expert

## Perspectives Video: Teaching Ideas

## Problem-Solving Task

## Tutorials

## MFAS Formative Assessments

Students are asked to identify right, acute, and obtuse angles in a two-dimensional figure, and explain the differences among these types of angles.

Students are asked to circle figures that show angles from a set of figures and then describe the defining attributes of angles.

## Original Student Tutorials Mathematics - Grades K-5

Classify and name angles in two-dimensional shapes to help a robot create a path using angles in this interactive tutorial.

Identify right triangles and explain the properties shared by all right triangles in this interactive tutorial.

## Student Resources

## Original Student Tutorials

Classify and name angles in two-dimensional shapes to help a robot create a path using angles in this interactive tutorial.

Type: Original Student Tutorial

Identify right triangles and explain the properties shared by all right triangles in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Task

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.

Type: Problem-Solving Task

## Tutorials

This Khan Academy tutorial video identifies acute, right, and obtuse angles and justifies each identification.

Type: Tutorial

This Khan Academy tutorial video demonstrates the relationship between the measurement of an angle and the arc of a circle.

Type: Tutorial

This Khan Academy tutorial video presents how an angle is formed and labeled.

Type: Tutorial

## Parent Resources

## Image/Photograph

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

## Problem-Solving Task

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.

Type: Problem-Solving Task