enVision Mathematics Topics 15-16
4th Grade; April – May (4 weeks); 3rd Trimester
Embedded Files
Topic Title(s):
Geometric Measurement: Understand Concepts of Angles and Angle Measurement (Topic 15)
Lines, Angles, and Shapes (Topic 16)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP5. Use appropriate tools strategically.
MP7. Look for and make use of structure.
Standard(s):
3. Data, Statistics, and Probability
4. Geometry
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
4.MD.C. Measurement & Data: Geometric measurement: Understand concepts of angle and measure angles.
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: (CCSS: 4.MD.C.5)
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. (CCSS: 4.MD.C.5.a)
An angle that turns through n one-degree angles is said to have an angle measure of n degrees. (CCSS: 4.MD.C.5.b)
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. (CCSS: 4.MD.C.6)
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. (CCSS: 4.MD.C.7)
4.G.A. Geometry: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. (CCSS: 4.G.A.1)
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. (CCSS: 4.G.A.2)
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. (CCSS: 4.G.A.3)
Analyze and measure the size of angles in real-world and mathematical problems. (Entrepreneurial Skills: Inquiry/Analysis)
Reason abstractly and quantitatively about angles and angular measurement. (MP2)
Make observations and draw conclusions about the classification of two-dimensional figures based on the presence or absence of specified attributes. (Entrepreneurial Skills: Inquiry/Analysis)
Use appropriate tools strategically to draw lines (parallel, perpendicular, lines of symmetry), line segments, rays, and angles (right, acute, obtuse). (MP5)
Identify ways in which a shape is structured such that it displays line symmetry. (MP7)
Inquiry Questions
How is measuring angles with a protractor similar to measuring line segments with a ruler?
We can describe the fraction 3/100 as 1/100 + 1/100 + 1/100. How does this apply to the measurement of angles, such as an angle of 3 degrees?
Where do you see parallel lines, perpendicular lines, or lines of symmetry in the real world?
What kind of angle can you find most often in the real world: right, acute, or obtuse? Why do you think that is the case?
What kinds of shapes have many lines of symmetry and what kinds of shapes have no lines of symmetry?
In what ways might the lines of symmetry for a shape be related to dividing the shape into fractional parts?
Coherence Connections
This expectation is in addition to the major work of the grade.
In previous grades, students create composite shapes, recognize and draw shapes having specified attributes, and understand that shapes with shared attributes can define a larger category.
In Grade 4, this expectation connects with drawing and identifying lines and angles, classifying shapes by properties of their lines and angles, and with understanding a fraction as a sum of unit fractions.
In Grade 4, this expectation connects with understanding concepts of angle and measuring angles.
In Grade 5, students classify two-dimensional figures into categories based on their properties.
In Grade 7, students solve real-world and mathematical problems involving angle measure, area, surface area, and volume.
Academic Vocabulary & Language Expectations:
Point, line, line segment, ray, right angle, acute angle, obtuse angle, straight angle, degree, unit angle, angle measure, protractor, vertex, parallel lines, perpendicular lines, intersecting lines, right triangle, obtuse triangle, acute triangle, equilateral triangle, isosceles triangle, scalene triangle, parallelogram, rectangle, square, rhombus, trapezoid, line symmetric, line of symmetry
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topics 15-16
Additional enVision Mathematics Resources
Let's Investigate! Roof! Roof! (TE) (supports Lessons 15-1, 15-2)
Let's Investigate! Landscape Design (TE) (supports Lessons 16-5, 16-6)
3-Act Math Recording Sheets (Topic 15)
Additional Math Games: Geometry (additional materials and preparation may be required)
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