This warm up is a review through symmetry. Students use their whiteboards to draw shapes and create a line of symmetry for three different shapes: a square, a triangle and a basic fish based on an oval for the body and a triangle for the tail.
Because this lesson is focused on half, I want the students to divide the shapes into as many different halves as possible. The use of the square is important to this warm up because of the many different options for lines of symmetry. The other two shapes will have not offer this option.
Using different models of patterns with halves, I show the students how halves are represented in real life. An important emphasis is that halves are not always clearly identifiable as a half. One example of this is a checkerboard. Even though this is a very common item, I find with my students their exposure to traditional board games is limited, and many have not actually used a checkerboard or relate it to half so if I haven't been using it in my classroom as a game board, I do more than just show the shape - I explain it as well.
Other items I use to show half include a fifty cent coin and fifty pennies, yin yang symbol, and an Oreo cookie. The students discuss whether these items show half and explain their thinking in a group discussion.
Students will go on to use square tile during this lesson to create non traditional models of halves.
Using two different colors of square tiles, students select a random quantity to arrange to show a non-traditional half. The random selection of tiles is important to this lesson because it creates a problem solving situation for students. They have to use this random selection to create a design with halves.
I want my students to further develop their understanding of a half is not always indicated by a straight vertical or horizontal line. I challenge them to create as many different models as possible. Although it may be necessary for some students to create two clearly defined halves, they can then rearrange and create new patterns and shapes to show halves.
The students record models on grid paper to record in their journals that did not include single horizontal lines or vertical lines. They recorded the most complex model that would not be easily identifiable. Next they were asked to change one square of the same model so that it would not show half.