Transfer Goals, Overarching Understandings and Overarching Essential Questions
(Students will be able to use their learning to…)
Make sense of never-before-seen “messy” problems (problems that lend themselves to a variety of approaches, representations and solutions) and persevere in solving them, using appropriate tools and the correct degree of precision.
Using Intellectual and Physical Tools
Use a variety of tools (e.g. tables, graphs, charts, numbers, pictures, patterns, words, manipulatives, technologies) to reason abstractly and quantitatively in order to make decisions, draw conclusions, and solve problems.
Thinking Independently and Collaboratively
Work independently and collaboratively to solve problems, valuing multiple approaches and perspectives.
Critically evaluate your own thinking and the thinking of others by using appropriate language and logical arguments to critique the reasonableness of a solution.
Explore mathematical ideas in ways that stimulate curiosity, cultivate enjoyment and develop depth of understanding.
Overarching Understandings and Essential Questions
(Students will understand that…)
Overarching Essential Questions:
(Students will keep understanding…)
- Problem solving is an integral part of all mathematical activity.
- There can be different strategies to solve a problem, but some are more effective and efficient than others.
- Finding the best math model requires knowledge, accuracy, and perseverance.
- Math is a shared, universal language that connects us with people across continents and through time.
- What strategies could be used to solve a problem?
- What makes a strategy both effective and efficient?
- What do effective problem solvers do when they get stuck?
- Does the solution make sense?
- What are the limits of a particular mathematical representation/modeling?
- Why is the ‘correct’ mathematical answer not always the best solution to a real-world problem?
- How can mathematical thinking be proven?
- How does math help us to understand and explain our world?
Number, Operations and Relationships:
- Numbers can be represented in multiple ways.
- Being able to compute fluently means making smart choices about which tools to use and when to use them.
- Answers need to be reasonable based on the context of the problem.
- The relationships among the operations and their properties promote computational fluency.
- Why does it make sense to represent numbers visually? Algebraically? Concretely (use of manipulatives)?
- What numerical patterns and relationships do I recognize?
- What makes an answer reasonable?
- How do mathematical operations relate to one another?
- How can patterns and relationships be modeled?
Measurement, Data, and Statistics:
- What is measured influences how it is measured.
- Standard units of measure and statistical techniques allow us to describe objects, interpret events and make comparisons in a way that can be universally understood.
- There are a variety of factors (some more effective than others) that impact the validity and reliability of data.
- How is math connected to the world?
- How do concepts and procedures of data analysis allow citizens to make informed decisions?
- Does a real world problem always have a correct answer, or can there be more than one?
- Why does the context of a problem matter?
- Algebraic expressions and equations generalize relationships.
- Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other quantities.
- Patterns and relationships can be represented numerically, graphically, symbolically, and verbally.
- Why are some relationships best modeled algebraically?
- How does observing patterns and modeling with algebra help us solve problems?
- How is thinking algebraically different than thinking arithmetically?
- How are things compared?
- How are algebraic expressions used to analyze and solve problems?
- The physical world can be modeled and described by considering an object's position, orientation, and attributes.
- The properties of geometric figures determine the construction of man-made objects and explain the structures found in nature.
- Geometric figures can change size and/or position while maintaining proportional attributes.
- Tools and/or technology can be used to describe mathematical relationships among geometric figures.
- What spatial patterns and relationships do I notice?
- How can two- and three-dimensional objects be described, classified, and analyzed by their attributes?
- What are the relationships between two similar or congruent objects?
- How can an object’s location on a plane or in space be described quantitatively?
- How are linear measurement, area, and volume related?
HWRSD Mathematics Transfer Goals, 6.21.16