options: Use coordinates to prove simple geometric theorems algebraically.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Analyze, compare, create, and compose shapes.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Experiment with transformations in the plane.

Visualize relationships between two-dimensional and three-dimensional objects.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Prove theorems involving similarity.

Solve real-world and mathematical problems involving area, surface area, and volume.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Understand similarity in terms of similarity transformations.

Understand and apply the Pythagorean Theorem.

Apply trigonometry to general triangles.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

Classify two-dimensional figures into categories based on their properties.

Prove geometric theorems.

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Explain volume formulas and use them to solve problems.

Understand and apply theorems about circles.

Translate between the geometric description and the equation for a conic section.
problem_activity: Narrative
The purpose of this activity is to introduce the language of
a half of
and
a fourth of
a
shape. Students begin by applying the language of halves and fourths, or quarters, to partition each shape. Students are asked to describe “how much” of each shape is shaded to elicit a variety of responses that include half, fourth, or quarter, including the phrases “of the square” or “of the circle.” Monitor for a variety of words and phrases to share in the synthesis including:
phrases that reference the pieces only (“one piece”).
phrases that reference that some, but not all of the shape is shaded (“part of it,” “a little bit”)
phrases that name the pieces (“a half,” “a fourth,” “a quarter”)
phrases that name the pieces in reference to the whole shape (“a half of the square,” “a fourth of the circle”)
All responses should be shared and compared in the synthesis to help build students understanding of the new vocabulary and the concept of fractional pieces of a whole (MP6).
Required Materials
Materials to Gather
Colored pencils or crayons
Launch
Groups of 2
Give students access to colored pencils or crayons.
Activity
Read the task statement.
2 minutes: independent work time.
2 minutes: partner discussion
Monitor for a range of ways to describe the amount shaded such as “some is shaded,” “one piece of the square is shaded,” “one out of two pieces is shaded,” or “a half is shaded.”
Student Facing
Split the square into halves.
[IMG]
Color in one of the halves.
How much of the square is colored in?
Split the circle into fourths.
[IMG]
Color in one of the fourths.
How much of the circle is colored in?
Student Response
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Activity Synthesis
Invite previously identified students to share for each problem. Sequence the students in the order described in the narrative.
“One piece of a shape split into two pieces that are the same size is called
a half
. One piece of a shape split into four pieces that are the same size is called
a fourth
.”
For each shape, invite students to describe how much is colored in. (A half of the square is colored in. A fourth of the circle is colored in.)


correct_option_index: 16