For
this lesson, students need a set of pattern blocks. (Only the yellow
hexagons, red trapezoids, blue rhombi, and green triangles are needed.
Students do not use the orange triangle or the tan rhombus for this
lesson.) If students are seated at tables, one set of pattern blocks
can be shared by the group.
Have students work in pairs to explore relationships. Guiding
questions are provided to facilitate the exploration and concentrate on
the mathematical focus of this lesson. Students should use pattern
blocks to find relationships and to determine the answer. If overhead
pattern blocks are available, the two pattern blocks being compared can
be modeled on the overhead projector. Questions may be made available
to students in hard copy. Please see Region Relationships 2 activity sheet. An overhead transparency of this worksheet can be made for use with the entire class.
Again ask each of the guiding questions from the first lesson, Investigating with Pattern Blocks, but follow each question with another question about the fractional relationship. For example,
How many green triangles are in one blue rhombus ? [Two.]  The green triangle is what fraction of the blue rhombus ? [One out of two, or ½.] 

Model the written form of each fraction by recording each
fraction on the board or overhead in standard (fraction) form. Have the
students record fractions in their math journals. For example,
The students should have little difficulty expressing this
relationship as a fraction. They have used the fraction ½ on numerous
occasions even prior to kindergarten. This lesson should focus on the
written format and what it really means. Lead the students in
identifying and defining the numerator and denominator. Ask the
students to explain what the top number in the fraction represents.
[Students should indicate that this top number is the numerator and
shows the number of parts of the whole.] The students should also
identify the purpose of the bottom number, or denominator, as the
number that indicates the number of parts into which the whole is
divided.
Continue with all other pattern block relationships, recording the
fractions. You may choose to have the students record the relationships
in a math journal to which they may refer later. Each group should
record relationships on chart paper to share with the whole class. As
each group shares, have the students record in their journal any
relationships that they may have missed.
Have the students repeat the activity using virtual pattern blocks on the computer. They should be directed online to The Shape Tool.