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Enduring Understandings
- important ideas
that students should carry with them years beyond the instruction received
this year.
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Proportional reasoning solves real world problems.
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Numbers have properties.
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Solutions must be reasonable.
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Geometry builds our world.
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Geometry issued to solve problems.
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Geometry connects us to the real world.
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Geometry is used to solve problems.
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Units matter.
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Measurements are used to compare.
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Scale matters.
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Formulas are used in the real world.
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Dimensional change affects geometry
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Proportional reasoning solves real world problems.
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There are different names for the same measurement.
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There are different ways of estimating.
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Computation and reasoning are vital mathematical tools.
Essential Questions - most important
“big picture” questions students should be able to answer after completing
learning activities.
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What skills/methods would you use to solve proportional reasoning
problems?
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How do number relationships help solve problems?
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How are properties of numbers like the rules of a game?
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When is the "correct" answer not the best solution?
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How do you apply the attributes of two and three dimensional shapes?
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How do you decide which mathematical strategy to use when solving
problems involving ratios, proportions, and similarities?
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How would you solve problems in real-world situations using coordinate
geometry?
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How do you determine which strategy to use when solving problems
involving perimeter, area, surface area, and volume?
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How can figures be transformed to determine congruency?
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When do you solve problems applying line and rotational symmetry?
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How do you select and apply the appropriate units of measure?
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How is measurement used to describe and make comparisons?
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How would you read and interpret scales in a variety of visual
representations?
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How would you develop and use formulas and procedures to solve problems
involving measurement?
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How does changing dimensions affect the characteristics of two- and
three- dimensional figures?
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How would you build a model that connects proportional reasoning
concepts to real world situations?
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How would you convert units of measurement within the English standard
system?
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How would you convert units of measurement within the metric system?
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How do you decide and justify your problem solving technique?
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How do you solve problems using rational numbers and know your answer is
reasonable?
Standards
Highest Frequency
 High
Frequency
 Other
Standards and E-Skills
Standard 1: (Number Sense) Students develop number sense and use numbers and
number relationships in problem solving situations and communicate the
reasoning in solving these problems.
1.4 Apply proportional reasoning using similar triangles and scale factor
Standard 4: (Geometry) Students use geometric concepts, properties, and
relationships in problem-solving situations and communicate the reasoning
used in solving these problems.
4.3 Apply ratios, proportions and similarity in problem solving situations
Standard 5: (Measurement) Students use a variety of tools and techniques to
measure, apply the results in problem-solving situations, and communicate
the reasoning involved in solving these problems.
5.2 Use measurements to make comparisons (direct and indirect)
5.3
Read/interpret scales on a map
Standard 6: (Computation) Students link concepts and procedures as they
develop and use computational techniques, including estimation, mental
arithmetic, paper-and-pencil, calculators, and computers, in problem-solving
situations and communicate the reasoning involved
6.1 Use ratios, proportions, and percents to solve problems
6.4 Compute to solve problems with fractions, decimals, percents (ex. Unit
rates, sales tax, discounts)
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