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

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

Understand and apply theorems about circles.

Prove geometric theorems.

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

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

Analyze, compare, create, and compose shapes.

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

Find arc lengths and areas of sectors of circles.

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

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

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

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.

Understand similarity in terms of similarity transformations.

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

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

Apply trigonometry to general triangles.

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

Prove theorems involving similarity.

Make geometric constructions.

Apply geometric concepts in modeling situations.

Explain volume formulas and use them to solve problems.

Translate between the geometric description and the equation for a conic section.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.
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: 26