ACORN HOARDING [DAY 3]
GROWING & SHRINKING LINEAR PATTERNS
Explore growing & shrinking visual patterns and linear relationships by constructing pattern rules in words, tables of values and equations.
Intentionality
Spark Curiosity
Fuel Sensemaking
During Moves
Student Approaches
Next Moves
Consolidation
Reflect and Consolidation Prompts
Resources & Downloads
Educator Discussion Area
Intentionality & Unit Overview
Length of Unit: 5 Days
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Students will analyze a squirrel’s acorn eating pattern. They will determine the pattern rule and make predictions by extending the pattern.
Intentionality…
In this task, students will analyze data based on a squirrel’s acorn eating behaviour. Students will describe the pattern rule in words and extend the pattern to determine an unknown value. Some of the big ideas that may emerge in this lesson include:
- Patterns can be extended because they are repetitive by nature.
- Pattern rules are generalizations about a pattern, and they can be described in words.
- A pattern can be extended to make a prediction.
- For far predictions, calculations are required for efficiency.
- In a shrinking pattern, the values increase.
- In a linear pattern, the values increase/decrease at the same rate.
- Graphical representations of linear growing and shrinking patterns appear as straight lines.
Spark Curiosity
What Do You Notice? What Do You Wonder?
Show students the following video that shows a collection of 60 acorns beginning on day 0. Each day, acorns are removed and the total number of acorns decreases from 60 to 56 to 52 and so on.
Then, ask students:
What do you notice?
What do you wonder?
Give students 60 seconds (or more) to do a rapid write on a piece of paper.
Replaying the video can be helpful here.
Then, ask students to share with their neighbours for another 60 seconds.
Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.
Some of the noticing and wondering that may come up includes:
- I notice there are 60 acorns.
- I notice that on day one, the number is now 56.
- I notice that every day, the total decreases by four.
- I notice that by the fifth day, there are 40 acorns left.
- I wonder if the squirrel is eating them.
- I wonder how long until he runs out.
Fuel Sense-making
Crafting A Productive Struggle: Prompt
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During Moves
While Students Are Productively Struggling…
Monitor student thinking by circulating around the room and listening to the mathematical discourse. Select and sequence some of the student solution strategies and ask a student from the selected groups to share with the class from:
- most accessible to least accessible solution strategies and representations.
- most common/frequent to least common/frequent strategies and representations; or,
- choose another approach to selecting and sequencing student work.
The tools and representations you might see students using to convince their peers and/or the teacher include:
- Counting backwards
- Counting on
- Skip counting by four
- Counting backwards by four
- Repeated subtraction
- Repeated addition
- Multiplication
Have students share their strategies and reasoning for how to represent the number of days. Ask them to convince you and their peers that their answer is correct by sharing mathematical models.
Discuss their strategies and elicit student thinking during your consolidation to build off of their current prior knowledge and understanding rather than “fixing” or “funnelling” student thinking to a strategy and/or model that does not connect to their strategy and/or approach.
Student Approaches
Student Approach #1: Counting Backwards With a Table
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Student Approach #2: Repeated Subtraction (Pictorial)
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Student Approach #3: Multiplication Using Partial Products
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Next Moves
Reveal
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Consolidation
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Reflect and Consolidation Prompts
Provide students an opportunity to reflect on their learning by offering these consolidation prompts to be completed independently.
Consolidation Prompt #1:
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Consolidation Prompt #2:
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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.
Resources & Downloads
Videos, Images & Media Files
Apple Keynote Presentation
Powerpoint Presentation
Printable Consolidation Prompts
Educator Discussion Area
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