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Enduring
Understandings
-
important ideas that students should carry with them years
beyond the instruction received this year.
Numbers have properties.
Solutions must be reasonable.
Order
is important.
There
are different ways of estimating.
Computation and reasoning are vital mathematical tools.
Algebra
is a language
Patterns
are a way of understanding the world.
Functions
model the real world.
Geometry builds our world.
Units matter.
Measurements are used to compare.
Scale matters.
Formulas are used in the real world.
Dimensional change affects geometry.
Data
can be used and represented in many forms.
Data can be used to draw conclusions.
Data displays can be misleading.
Models assist in determining outcomes.
Through probability predications are made.
Models or counting techniques assist in determining outcomes.
Essential
Questions - most
important “big picture” questions students should be able to
answer after completing learning activities.
-
How are characteristics
of numbers and number concepts identified and used?
-
How are properties of
numbers like the rules of a game?
-
When is the "correct"
answer not the best solution?
-
How is the order of
operations similar to following the rules of a game?
-
How do you select,
apply, and explain the strategies chosen to solve a problem?
-
How do you decide and
justify your problem solving technique?
-
How do
you convert from one representation to another?
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How
would you describe a pattern algebraically?
-
How do
you predict and describe how a change in one quantity affects another in a
functional relationship?
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How do
you solve linear equations using a variety of methods?
-
How do you decide which mathematical strategy to use when solving
problems involving ratios, proportions, and similarities?
-
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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How is measurement used to describe and make comparisons?
-
How would you read and interpret scales in a variety of visual
representations?
-
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 organize and construct displays of data?
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What conclusions or predictions could
you make from data organizers?
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How would you display and use measures
of central tendency and variability in problem solving situations?
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How do you know if data has been
misused?
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How would you analyze data to make
convincing arguments?
Quarter 1 Big Ideas:
Integers, Algebra, Order of Operations, Use Decimals and Fractions
Quarter 2 Big Ideas: Geometry, Measurement, Proportional Reasoning,
Geometric Patterns, Percents
Quarter 3 Big Ideas: Probability, Statistics, Pythagorean Theorem
Quarter 4 Big Ideas: Algebra
CSAP
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.
1.2 Compare and
order integers, fractions, decimals, and percents (include a number line
also)
Standard 2:
(Algebra and Functions) Students use algebraic methods to explore,
model and describe patterns and functions involving numbers, shapes,
data, and graphs in problem-solving situations and communicate the
reasoning used in solving these problems.
2.1
Describe algebraic (number) patterns and make connections between tables,
graphs, and rules for these patterns.
2.2
Complete a pattern and write a rule/equation (find the nth term for the
pattern).
2.2
Find the constant rate/slope and the starting point/y-intercept of a table
and graph.
2.4
Distinguish between linear and non-linear graphs and tables.
2.5
Write and solve simple linear equations.
Standard 3:
(Statistics and Probability) Students use data collection and
analysis, statistics, and probability in problem-solving situations
and communicate the reasoning used in solving these problems.
3.1
Read and construct display of data: circle graphs, scatter plots,
box and whisker, stem-and-leaf, histogram
3.2
Compute range, mean, median, and mode
3.6
Find probability using tree diagrams and lists
(Experimental/Theoretical)
3.7
Using counting principles to determine the number of possible
outcomes: (permutations/combinations)
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
4.5 Use formulas and solve problems with area, perimeter, surface area, and
volume of right prisms and cylinders
4.6 Reflect, translate and rotate figures on a coordinate grid.
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.
5.4 Use formulas and solve problems with area, perimeter, surface area, and
volume of right prisms and cylinders
5.5 Describe how changes in linear dimensions affect area, perimeter,
surface area, and volume.
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.
6.2 Add, Subtract, Multiply, and Divide Integers
6.4 Compute to solve
problems with fractions, decimals, percents, and integers. Check for
reasonable answers.
6.2 Order of
Operations with Integers
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