SCHOOL OF FISH [DAY 3]
DEVELOPING PLACE VALUE UNDERSTANDING
Explore efficient strategies to subtract values within 50
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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​​Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.
Students will solve a subtraction question using the take away strategy of decomposing the subtrahend.Â
Intentionality…
Students will solve a subtraction question using the take away strategy of decomposing the subtrahend.Â
Some of the big ideas that may emerge through this task include:
- Understanding hierarchical inclusion allows for flexible composing and decomposing of numbers
- Numbers can be decomposed by separating a whole into two or more parts
- Subtraction names the missing part in terms of the whole
- Different subtraction situations will elicit different strategiesÂ
- Number relationships provide the foundation for strategies to help students remember basic facts
- Subtraction can be used in either take away, comparison, or missing addend situations. This task will explore the take away method.
- Models can be used to connect concrete to abstractÂ
Before starting this unit, students should be familiar with:
- Facts of 10 ( e.g., 6+4 = 10, 10-4 = 6)
- Flexibility when decomposing numbers (e.g., 13 can be decomposed into 10 and 3, but also 9 and 4, 8 and 5, etc)
- The Down and Under Ten strategy which can be explored in the Fruit Picking Unit.Â
Spark Curiosity
What Do You Notice? What Do You Wonder?
Show students the following video:
Then, ask students:
What do you notice?
What do you wonder?
Give students about 30-60 seconds to do a rapid write on a piece of paper or silent individual think time.
Replaying the video can be helpful here if appropriate.Â
Then, ask students to pair share with their neighbours for another 60 seconds.
Finally, allow students to individually share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other way that is visible to all. This helps students to see the thinking of their classmates and ensures each student that their voice is acknowledged and appreciated. Adding student names or initials next to their notice/wonder is one way to acknowledge their participation and can motivate others to join in.
Some noticings and wonderings that may come up:
- There are fish swimming around
- There are different colour of fish
- Is this a lake or an ocean?
- How many fish are there?
- I see fish behind the rocks.
- And many more
Estimation: Prompt
After we have heard students and demonstrated that we value their voice, we can land on today’s question. Acknowledging that the question came from students underscores their identities as thinking mathematicians who are making sense of problems.
How many fish are there?
Follow up that question with:
How do you know?
Have students make estimates first by thinking about an amount of fish that they believe will be too low, followed by an amount that they think will be too high.
Challenge students to be risky with their low/high estimates.
Then, have them pick their best estimate and share with their neighbours before sharing and recording on the chalk/whiteboard or chart paper as a class.
Ask students what information they might need in order to figure out the answer.
While Students Are Estimating…
Monitor student thinking by circulating around the room and listening to the mathematical discourse. You may identify some students whose thinking would be valuable to share when the group’s estimates are collected.
Encourage students to make estimations rather than 1:1 counting each fish. The video may be paused for longer before it goes blank but we want students to make estimations based on their mathematical understanding and spatial sense.Â
Similar to collecting their noticings and wonderings, collect students’ range of estimates and/or best estimates along with initials or names. Having some students share justifications is an opportunity for rich, mathematical discourse.
Estimation Reveal
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Fuel Sense-making
Crafting A Productive Struggle: Prompt
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During Moves
While Students Are Productively Struggling…
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Student Approaches
Student Approach 1: Using a Tool to Direct Model and Count All
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Student Approach 2: Counting All with a Drawing
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Student Approach 3: Open Number Line to decompose the subtrahend by taking away tens then counting back
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Student Approach 4: Open Number Line to decompose the subtrahend by taking away tens then ones
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Student Approach 5: Open Number Line to decompose the subtrahend by taking away ones then tens then the ones
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Next Moves
Reveal #1
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Reveal #2
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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 and then discussed as a class.
Consolidation Prompt #1:
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Consolidation Prompt #2:
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Consolidation Prompt #3:
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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
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Educator Discussion Area
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