Geometry Task for Grade 2 from Illustrative Mathematics
1. Color the inside of all the triangles blue.
2. Color the inside of all the quadrilaterals red.
3. Color the inside of all the pentagons orange.
4. Color the inside of all the hexagons green.
5. Circle all the shapes that have sides that are equal.
Shapes are provided with this task.
Commentary from Illustrative Mathematics:
The purpose of this task is to give students practice identifying different types of polygons, namely
triangles, quadrilaterals, pentagons, and hexagons. A complete definition of a polygon is usually either
very technical and dense or very wordy. Here are some ideas for talking about polygons to help students
understand what they are.
A polygon is made up of line segments that meet end-to-end. These line segments are called "sides."
Every side meets exactly two other sides, and three sides never meet at the same point.
Sometimes students talk about the sides meeting at "corners." The technical name for the corners is
"vertices." A polygon always has as many vertices as sides.
A polygon always divides the plane into exactly two regions - one "inside" the polygon and one "outside."
This task asks students to color the region "inside" the polygon. There is one figure in this task that does
not divide the plane into two regions because it is not closed, so it is not a polygon.
Triangles are polygons with 3 sides. Quadrilaterals are polygons with 4 sides. Pentagons are polygons
with 5 sides. Hexagons are polygons with 6 sides. It is a good idea for the class to start by developing a
definition for triangles first, then quadrilaterals, and only then trying to generalize.
There is a great opportunity for students to engage in MP 6, Attend to precision, when talking about
polygons and what they are. Students often get confused when, for example, a triangle isn't oriented with
one side horizontal and at the bottom. They may also have trouble identifying polygon types when they
are not convex (that is, when the sides "push in") or when they are not regular (that is, when they don't
have equal side lengths). The collection of shapes in this task gives students an opportunity to confront all
of these possible misconceptions. As a result, it would be a good idea for the teacher to ask students to
explain how they identified the various shapes to the class when everyone has had a chance to think it
through for themselves.
Students can mark off the side-lengths of the polygons on the edge of a piece of paper if they are not sure
whether the side-lengths are equal or not.
Geometry Task for Grade 3 from Illustrative Mathematics
1. A small square is a square unit. What is the area of this rectangle? Explain.
2. What fraction of the area of each rectangle is shaded blue? Name the fraction in as
many ways as you can. Explain your answers.
3. Shade 1/2
of the area of rectangle in a way that is different from the rectangles
above.
4. Shade 2/
3
of the area of the rectangle in a way that is different from the
rectangles above.
Geometry Task for Grade 4 from Illustrative Mathematics
1. Draw an angle that measures 60 degrees like the one shown here:
2. Draw another angle that measures 25 degrees. It should have the same vertex and
share side BA
3. How many angles are there in the figure you drew? What are their measures?
4. Make a copy of your 60-degree angle. Draw a different angle that measures 25
degrees and has the same vertex and also shares side BA
.
5. How many angles are there in the figure you drew? What are their measures?
Geometry Task for Grade 4 from Illustrative Mathematics
1. Draw at least two examples and two non-examples of each of the quadrilaterals defined
below.  Parallelogram: A quadrilateral with 2 pairs of parallel sides.
 Rectangle: A parallelogram with 4 right angles.
 Rhombus: A parallelogram with 4 sides with equal length.
2. I am a shape that is a parallelogram, a rectangle, and at the same time a rhombus. What
shape am I? Draw a diagram of what I look like. Use the vocabulary words and their
definitions given in part (a) to explain what shape I am.
Geometry Task for Grade 5 from Illustrative Mathematics
Decide whether each of these statements is always, sometimes, or never true. If it is
sometimes true, draw and describe a figure for which the statement is true and another
figure for which the statement is not true.
1. A rhombus is a square
2. A triangle is a parallelogram
3. A square is a parallelogram
4. A square is a rhombus
5. A parallelogram is a rectangle
6. A trapezoid is a quadrilateral
Geometry Task for Grade 6 from Illustrative Mathematics
Make the following triangles on a geoboard. Remember that the pegs are equally spaced in
a square grid. Compare the areas of the triangles. Justify your answers.
1. Which has the greatest area?
2. Which has the least area?
3. Do any of the triangles have the same area?
4. Are some areas impossible to compare?