Lesson 10 | Shapes and Angles | 4th Grade Mathematics

Objective

Decompose angles using pattern blocks.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Measurement and Data

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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Understand that the measures of all of the angles at a point with no gaps or overlaps add up to 360°, and use that understanding to find the measures of pattern blocks’ angles.
Find the measure of various angles by filling the angle with pattern blocks and adding the angle measures of those pattern blocks together.
Understand that angle measure is additive (i.e., 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) (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

The teacher may want to display pattern blocks so that they are visible to all students, which can be done by placing them on an overhead projector, by sticking magnets on a set of pattern blocks to use on their white/chalkboard, or by using an online applet (like this one from NCTM Illuminations).

Lesson Materials

pattern blocks (4 squares, 6 triangles, 3 hexagons, 6 blue rhombuses, 12 tan rhombuses, per student or small group) — These are also needed for the Problem Set.
180° Protractor (1 per student)

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. Place square pattern blocks around the point below so that their corners meet at the point. Fit them like puzzle pieces. How many angles meet at this central point? What is the measure of each of them? Write a number sentence to represent this relationship.

b. Go through the same process as above with triangle pattern blocks.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 9 — Concept Development, Problem 1

Grade 4 Mathematics > Module 4 > Topic C > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Using pattern blocks and their known measure, find the measure of the angle indicated by the arc.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 9 — Concept Development Problem 3

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

What are the measures for the acute and obtuse angles of the tan rhombus? What did you discover when you fit the acute angles around a vertex?
How are the different angles in the pattern blocks related?
What was the measure of $${\angle HIJ}$$? $${\angle L}$$? $${\angle O}$$? $${\angle R}$$? How did you find the angle measures? What combination of blocks did you use? How did your method compare with your neighbor's?
What did you learn about adding angles?
How can you verify an angle's measure?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Find the measurements of the angles indicated by the arcs.

Pattern blocks	Angle measure	Addition sentence

Problem 2

Use two or more pattern blocks to figure out the measurements of the angles indicated by the arcs.

Pattern blocks	Angle measure	Addition sentence

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 9

Lesson 11

Lesson Map

Topic A: Lines and Angles

Identify and draw points, lines, line segments, rays, and angles.

4.G.A.1 4.MD.C.5

Identify and draw right, obtuse, and acute angles.

4.G.A.1

Identify and draw perpendicular lines.

4.G.A.1

Identify and draw parallel lines.

4.G.A.1

Topic B: Measures of Angles

Use iteration with one physical nonstandard unit to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Understand that an angle that turns through $${{1\over360}}$$ of a circle is called a “one-degree angle” and can be used to measure angles. Use a makeshift protractor to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Measure angles that are less than 180° using a 180° protractor. Distinguish angle measure from other attributes.

4.MD.C.5 4.MD.C.6

Sketch angles of specified measure using a 180° protractor.

4.MD.C.5 4.MD.C.6

Identify and measure angles as turns and recognize them in various contexts.

4.MD.C.5 4.MD.C.6

Topic C: Measures of Adjacent Angles

Decompose angles using pattern blocks.

4.MD.C.7

Solve problems involving the measure of two adjacent angles.

4.MD.C.7

Solve problems involving the measure of more than two adjacent angles.

4.MD.C.7

Measure and sketch angles that are greater than 180°.

4.MD.C.5 4.MD.C.6 4.MD.C.7

Topic D: Shapes and Lines of Symmetry

Analyze and classify triangles based on side length, angle measure, or both.

4.G.A.1 4.G.A.2

Draw triangles from given criteria.

4.G.A.1 4.G.A.2

Analyze and classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size.

4.G.A.1 4.G.A.2

Draw quadrilaterals from given criteria.

4.G.A.1 4.G.A.2

Identify and draw lines of symmetry in two-dimensional figures.

4.G.A.3

Shapes and Angles

Objective

Common Core Standards

Core Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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