Advancing Equity and Strengthening Teaching through Elementary Mathematical Modeling

Reasonable Assumptions

Reasonable Assumptions routines support students in making relevant assumptions and decisions, support students in making decisions about how quantities and relationships that aren’t known could be represented in a situation. Learn more by exploring this page.

This routine helps focus students on developing their observation and problem posing skills.

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To read a Quick Guide to Reasonable Assumptions

Goals
To support students in making relevant assumptions and decisionsTo affirm students’ identities as knowers and doers of mathematicsTo support students in making decisions about how quantities and relationships that aren’t known could be represented in a situationTo advance equity in math learning
Planning to Advance Equity
Select an image or object that will “hook” student curiosities and decide how you will share it Mirror: Choose an image/object that children have some knowledge about, portrays people that look like them, activities or places they spend time as interesting and important. Ideally these come from families or the community.Lens: Choose an image/object that children may not have knowledge about and will support them to develop positive images of different peoples, cultures, spaces and activities.Prepare to Advance EquityEnsure that multiple students, with diverse ideas and experiences, will contribute to the discussionProvide varied opportunities and modalities for students to contribute ideas (partner or whole-class talk, in writing, via images, in diagrams, or with stories)Think about how you will communicate to each and every student that you are curious about their thinking and honor their ideas.
Planning the Discussion
Introduce the image/object to childrenTell children about the image/item.If the image/item comes from one of the children, invite them to tell about it.Promotes curiosity and connections
Present a QuestionFacilitate a short discussion identifying what you would need to know to figure out the question.Identify several “need to knows” where the information is not readily available. These are places where students will need to make assumptions or decisions.Develops an understanding of the scenario and question
Reasonable, Unreasonable, AssumptionAsk children to discuss the meaning of the words “reasonable”, “unreasonable”, and “assumption”.Establishes a shared vocabulary
Routine: Reasonable and Unreasonable AssumptionsAsk students to work in pairs/small groups to generate a list of reasonable and unreasonable assumptions for each “need to know”.Ask students to select a reasonable assumption and explain how they know it is reasonable.Ask students to select an unreasonable assumption and explain how they know it is unreasonable. Promotes communication about and through mathematics
Scaffolds and Variations
Offer a list of assumptions for a situation and ask students to decide which are reasonable and which are unreasonable. Share an unreasonable assumption and ask students to revise it so that it is reasonable.