Manipulatives (such as cube blocks, rocks, dominoes, or sticks – anything that can be used to represent “seeds”)
Chart paper and markers at each workstation
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.
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.
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?
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?