- Identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts
- Demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts

- Students gather with the teacher for a read aloud of Anno’s Magic Seeds. After, students work in groups or individually at their workstations.
- Students should understand how to recognize and represent patterns. Familiarity with exponential growth patterns may also help.

- Book:
*Anno’s Magic Seeds*by Mitsumasa Anno- Read Aloud Available – Anno’s Magic Seeds: Approaching Math Through Story

- Anno’s Magic Seeds Recording Tables (Appendix A)
- Manipulatives (such as cube blocks, rocks, dominoes, or sticks – anything that can be used to represent “seeds”)
- Chart paper and markers at each workstation

Introduction:

- Introduce
*Anno’s Magic Seeds*to the students:*Today, we are going to read about a young man named Jack who receives two magic seeds from a wizard. Let’s see what happens with the Magic Seeds…* - Read the whole story through so students can engage with the narrative context before focusing on the mathematical components.

Lesson:

- Ask students what they noticed about the seed growth sequence:
*What did Jack do with the two magic seeds the wizard gave him?*He ate one and buried the other. The following year, he ate one again and buried the other, and so on…*What happened when Jack buried both seeds*- Both buried seeds produced two seeds each, so Jack ended up with four seeds the following year.

*How many seeds did Jack bury after he made the change of burying both seeds?*- He ate one, and buried the remaining three seeds. Each of the three buried seeds produced two seeds, so he ended up with six seeds the following year.

- He ate one, and buried the remaining three seeds. Each of the three buried seeds produced two seeds, so he ended up with six seeds the following year.
- Have students represent the pattern of Jack’s seed growth across the years in small groups, using a Recording Table (Appendix A)
- Make manipulatives available to help students model the seed growth pattern and record it, if needed.

- Have students explore the patterns they see in their recorded data. Prompt them with exploratory questions:
*How do the numbers grow from year to year*

- Explain to students that they can model the growth of the seeds using an algebraic expression.
- Have them come up with an expression they think might work to describe Jack’s first strategy of seed growth:
- Start with two seeds, eat one and bury the second, and repeat.

- Have students come up with an expression to describe Jack’s second strategy of seed growth:
- Start with two seeds, and bury both the first year. Next year, there are four seeds: eat one, and bury the remaining three. The following year, there are six seeds: eat one, and bury the remaining four. The pattern continues in this way.

- When students have found an expression to represent the first and second patterns, have them test their expressions.
- Ask:
*Does your expression work*every*time? How do you know?*

- Ask:

- Have them come up with an expression they think might work to describe Jack’s first strategy of seed growth:

Conclusion:

- Have students share their algebraic expressions representing Jack’s two growing strategies. Tell them that their expressions represent a
*generalization*of Jack’s growing patterns!

- What prior knowledge do students show when recognizing and representing the patterns?
- What language is being used when students describe the patterns of the seed growth?
- What ways of thinking are students using when determining their representation of the seed growth?

Share on facebook

Share on twitter

Share on email