Students classify triangles and quadrilaterals based on the properties of their side lengths and angles, and learn about lines of symmetry in two-dimensional figures. They use their understanding of these attributes to solve problems, including problems involving perimeter and area.
Unit Narrative
In this unit, students deepen their understanding of the attributes and measurement of two-dimensional figures.
Prior to this unit, students learned about some building blocks of geometry—points, lines, rays, segments, and angles. Students identified parallel and intersecting lines, measured angles, and classified angles based on their measurement. In this unit, they apply those insights to describe and reason about characteristics of shapes.
In the first half of the unit, students analyze and categorize two-dimensional shapes—triangles and quadrilaterals—by their attributes. They classify two-dimensional shapes based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Students also learn about symmetry. They identify line-symmetric figures and draw lines of symmetry.
Quadrilaterals N, U, and Z are parallelograms.
Quadrilaterals AA, EE, and JJ are rhombuses.
Write 4–5 statements about the sides and angles of the quadrilaterals in each set.
Each statement must be true for all the shapes in the set.
The second half of the unit gives students opportunities to apply their understanding of geometric attributes to solve problems about measurements (side lengths, perimeters, and angles).
Included in this unit are three optional lessons that offer opportunities for students to strengthen and extend their understanding of symmetry and other attributes of two-dimensional figures.
Classify triangles (including right triangles), parallelograms, rectangles, rhombuses, and squares based on the properties of their side lengths and angles.
Identify and draw lines of symmetry in two-dimensional figures.
Section Narrative
This section prompts students to consider different ways of looking at two-dimensional figures: by the number of sides, length of sides, size of angles, presence of parallel or perpendicular lines, and symmetry. Students examine these attributes in figures, classify the figures by the attributes, and explain their classifications. For example, they identify quadrilaterals as parallelograms if they have two pairs of parallel sides, as squares if they have four equal sides and four right angles, and so on.
In studying symmetry, students characterize figures based on whether they can be folded into two equal halves that match up exactly, draw lines of symmetry, and complete drawings of figures that are halved by a line of symmetry.
Lin folds pieces of paper in different figures. She sorts them into two categories based on the folding lines.
Study the figures in each category. What do you think a "line of symmetry" means?
The section includes one optional lesson in which students apply their understanding of two-dimensional figures to complete or create drawings of figures with specified attributes.
Razonemos sobre características para resolver problemas
Section Goals
Solve problems involving unknown side lengths, perimeter, area, and angle measurements using the known attributes and properties of two-dimensional shapes.
Section Narrative
In this section, students apply their knowledge of geometric attributes to reason about measurements in various two-dimensional figures. They find the perimeter of figures where the side lengths are all given. Then they move on to cases where the side lengths are not explicitly given but can be deduced based on information about the figures.
Later, students are given the perimeter and some information about a figures and find any unknown side lengths. The activities also enable students to practice performing operations on whole numbers and fractions.
Here are four figures, each with a perimeter of 64 inches. Figures P, R, and S each have 1 line of symmetry. Figure Q has 4 lines of symmetry.
Draw the lines of symmetry of each figure and find the unknown side length.
In the last two lessons, students use what they have learned about symmetry to solve problems related to perimeter and unknown angle measurements in two-dimensional figures. This work deepens students’ understanding of the concepts from this unit and offers opportunities to practice reasoning about angle measurement, but it is not required by grade 4 standards. These lessons are therefore optional.
