Have students play “Guess My Sorting Rule”, where they sort a variety of two-dimensional shapes or three-dimensional objects into two or more categories. Ask them to trade places with a partner and to come up with a rule for their partner’s sort. Then have the pairs of students describe and discuss the rules that they came up with for one another’s sorts. For example, a student has the following set of three-dimensional objects. His rule is that all the shapes have a circular face. His partner's rule is that all the objects roll.

Give students a rule, and ask them to use a geoboard to make a shape that satisfies this rule; for example, the shape must have four sides. A sorting rule might result in more than one shape. Discuss the similarities and differences for the shapes that the students make.

Have students play “Which One Does Not Belong?”, where they each identify a sorting rule, select different shapes or objects that follow the rule and one that does not, and put them all in a “sorting circle”. Next, have students share their sort in a small group. Each of the group members shares their sort, and the others identify the shape or object that does not belong and explain why.

Any disagreements can be discussed and resolved as a class. Emphasize that shapes and objects have many sortable attributes and that the same group of shapes or objects can be sorted in different ways. Draw out the idea that whether something belongs in the sorting circle depends on the sorting rule.

Have students build three-dimensional objects in solid, hollow, and skeleton form. Support them in identifying and naming the sides, vertices, and angles of two-dimensional shapes and the faces, edges, and vertices of three-dimensional objects. Ask them to draw and appropriately label a picture of the two-dimensional shapes on their three-dimensional object.

Have students play “Find My Shape”, where they search inside and outside the classroom for two-dimensional shapes that are part of three-dimensional objects. Ask them to name the shapes they find and describe the attributes they used to identify it

Have students build three-dimensional objects that meet given criteria (e.g., it can stand by itself). Ask them to look at the collection of objects that the class has built and describe what each object has in common (e.g., they all have a flat base). Discuss why a flat base is necessary for something to stand by itself. Then move on to discuss how different shapes are useful for different functions (e.g., objects that stack need a flat bottom, objects that roll need a circular face).

Have students play “Matching Halves Treasure Hunt”, where they find everyday shapes and objects, including objects in nature, that have matching halves and explain how they know that the two halves match (e.g., they can use a mirror to test whether the shapes or objects are symmetrical).

Provide students with paper cut-outs of shapes (e.g., the letters of the alphabet), and have them determine whether they have matching halves by folding.

Ask students to draw shapes or build objects that have matching halves and explain the strategies they used to construct the shape or object, and how they know the two halves match.

Have students follow directions in a game, song, or poem that uses positional language.

Have students write clues to describe the location of one object relative to another. Encourage them to use distance and direction vocabulary to describe the object’s location (e.g., the turtle eggs are buried 20 steps to the right of the pond).

Read (or co-create with students) a story that involves characters travelling on a path. Have students draw and describe the path in the story using the vocabulary of distance and direction. They might use a large floor grid or the grid on an interactive whiteboard to organize and sequence their directions.

Have students write directions from a starting point (e.g., the classroom door) to a given object in the classroom (e.g., the pencil sharpener). Randomly select from the collection of directions, and ask students to test whether the directions lead to the object. If they don’t, ask them how the directions could be adjusted.

Have students program a sequence of steps on a grid that directs a digital image (or robot or classmate) to move through a maze from a starting position to a specific location in the maze, or to the exit. For example, for the grid below, have them both give and follow directions, such as:

• How might you get from the letter X to the dog if you had to go around all the things in the way?
• If I’m at the train and go up 5 and then left 5, what object will I land on?