In this section, students explore the idea of halves and fourths as equal pieces of a whole.

Students learn that when decomposing a shape into two equal pieces, each piece is “half of” the shape, and the pieces are called “halves.” When a shape is decomposed into four equal pieces, each piece is “a fourth of” the shape, and the pieces are called “fourths” or “quarters.”

To create two and four equal pieces, students fold paper shapes and then draw lines to split the shapes. They consider the size of a fourth and a half in relation to the same whole, and notice that as the number of pieces increases, each piece gets smaller.

In this section, students explore and reason about attributes of two- and three-dimensional shapes. They begin by sorting and describing shapes in ways that make sense to them. They name shapes (cone, sphere, cylinder, cube, square, rectangle, triangle, rhombus and hexagon), but do not need to hear or produce formal definitions of the shape. 

Students identify the defining attributes (numbers of straight sides and corners) of triangles, rectangles, and squares, and distinguish them from nondefining attributes (color, orientation, size). They describe why a shape belongs in a certain category, using their own language. For example, “These shapes are all triangles, because they have three straight sides and three corners. This shape is not a triangle, because the sides don’t touch.”

Students learn that a square is a special rectangle, because it has the defining attributes of a rectangle (four sides, four square corners) and also has the defining attribute of a square (four equal-length sides).

Students then compose shapes from smaller shapes to deepen their understanding of two- and three-dimensional shapes. The spatial reasoning here builds a foundation for understanding future mathematical concepts, such as symmetry, congruence, fraction, area, and volume.

Geoblocks are used throughout the section. Standard geoblocks sets do not include cylinders, spheres, and cones. When these shapes are required, “solid shapes” are indicated as required materials. If solid shapes are not available, students can work with everyday items that represent each shape.

In this section, students learn to tell time in hours and half hours on both analog and digital clocks, by interpreting the position of the hands on the former and the digits of the latter. They connect the language of “o’clock” and “half past” to the times shown on analog and digital clocks.

Students begin by interpreting clock faces that show only an hour hand. This is to draw their attention to the fact that the hour hand will point directly to a number at the hour and halfway in between two numbers at the half hour. Given their understanding of halves, students see that when the minute hand starts at the 12 and rotates to point at the 6, it has moved halfway around the clock.

To build students’ concept of time, consider preparing an alarm that goes off each half hour to draw attention to time in hours and half hours. When the alarm goes off, students can look at the clock, draw the hands on a blank clock, and record the time, using numbers.

Fill in the clocks to show what time each activity starts.

Although the lessons in this section focus on 12-hour clocks, students who are familiar with 24-hour clocks should be invited to share what they know.