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### What’s Next?

Pre-K-2, 3-5

In this lesson, students make patterns with objects, read patterns and find patterns in the environment. They should be encouraged to classify patterns by type (i.e. AAB, ABC). They continue learning about patterns by extending a given pattern, identifying missing elements in a pattern, and recording a pattern.### Exploring Other Number Patterns

Pre-K-2, 3-5

Students make and extend numerical patterns using hundred charts. They also explore functions at an intuitive level. This lesson integrates technology.### Growing Patterns

Pre-K-2, 3-5

Students explore growing patterns. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns differently, this is an opportunity to engage them in communicating about mathematics.### Maintaining the Balance

3-5

In this lesson for grades 3‑5, students participate in activities in
which they focus on patterns and relations that can be developed from
the exploration of balance, mass, length of the mass arm, and the
position of the fulcrum. The focus of this lesson is determining the
position necessary to balance uneven objects and the effect on balance
of moving the fulcrum.### Plastic Packaging

3-5

Students participate in an activity in which they investigate the data
in connection with recyclable materials and develop plans to help the
environment. Specifically, students explore recycling plastic
containers.### Collecting The Rays

3-5

In this lesson, students explore how variations in solar collectors
affect the energy absorbed. They make rectangular prisms that have the
same volume but different linear dimensions. Students investigate
relationships among the linear dimensions, the area, and the volume of
rectangular prisms.### What Comes Nex_?

3-5

The following activities deal with patterns and the importance of
looking at data from more than a single perspective. Included are
explorations designed to encourage open-mindedness and to help students
develop alternative viewpoints. Students investigate a series of items
that appear to be ordered in some "obvious" ways. Students also explore
ways of sorting items into two disjoint groups on the basis of some
definable characteristic. This lesson was adapted from "What Comes
Nex_?", written by William R. Speer & Daniel J. Brahier. It
appeared in the October, 1995 *Teaching Children Mathematics*Vol. 2, no. 2.

### The Variable Machine

3-5

This lesson provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words.

This lesson was adapted from a lesson by Gilbert Cuevas and Karol Yeatts, as found in *Navigating Through
Algebra in Grades 3 ‑ 5*, from the *Navigations* Series, NCTM 2001.

### Single Runner

3-5

In this activity, students use a software simulation of one runner
along a track. Students control the speed and starting point of the
runner, watch the race, examine a graph, and analyze the
time-versus-distance relationship. This activity helps students
understand, describe, and compare situations involving constant rates
of change.### Two Runners

3-5

In this activity, students use a software simulation of two runners
along a track. Students control the speed and starting point of the
runners, watch the race, examine the graphs, and analyze the
time-versus-distance relationships. This activity helps students
understand, describe, and compare situations involving constant rates
of change.