1.  Recognize the structure of a non-routine problem and apply the appropriate problem solving strategy. (1:4)

Heuristics:

  look for a pattern

  make an organized list

  make a table

  guess and check

  work backward

  use logical reasoning

  draw a diagram

  solve a simpler problem

2.  Develop the number sense necessary for estimation, and evidence mastery of basic facts. 

(6.12)

Thinking strategies for basic facts:

   Using doubles

   Bridging to ten

 Related properties:

   identity (0+ n, 1 x n)

   commutative

   associative

   distributive

3.  Develop a sense of the magnitudes of whole numbers and use pattern-based thinking to understand extensions of the whole number system.

(11.9) (11.13)

Numeration concepts:

    magnitude of number

    density of number

    exponential models

   Place value-

    quantity vs value

    compare/order numbers

Distinguish between use of

exact vs rounded numbers

Numeration conventions:

    standard notation

    expanded notation

    exponential notation

4.  Develop, select, and use a variety of mental math and estimation strategies to solve problems and to determine reasonableness of results. (6.10) (8.6) (10.5) (10.6) (10.8) (10.10)

Mental math strategies:

  Look for special numbers

  Use compensation

  Break apart numbers

  Use equivalent forms

Estimation strategies:

  Rounding

  Front-end estimation

  Compatible numbers

  Clustering

  Compare to referent point

Under vs. over estimates

5.  Apply number theory concepts to real-world and mathematical problem situations. (6.17)

Patterns of divisibility

   on charts

   sorting tasks

Prime factorization

   tree diagrams

   exponential notations

LCM & GCF

   spread sheets

   Venn diagrams

6.  Extend the understanding of the number system by constructing meanings for fractions.

(6.11) (6.13) (6.15) (6.16)

Concepts

   part/whole meaning

   density and magnitude

   unit & nonunit fractions

   mixed numbers

Relations

   order and sequence

   relation to half

7.  Extend the understanding and use of arithmetic operations to fractions; develop, apply and explain procedures for computation and estimation with fractions.  (8.8) (8.10)

Addition & subtraction -

  review w/ like denom.

  reinforce unlike denom.

  regroup w/ mixed no.

  estimation

  equations with fractions

Multiplication & division - 

  estimation

  mult/div by whole no.

  mult./div by fractions

  equations with fractions

8.  Identify and apply the properties of lines and planes and intersecting lines and planes and their angles of incidence. (7.14)

Recognize / label:

   point            line

   segment      ray

Distinguish lines or planes that are:   intersecting

    parallel     perpendicular

Angles:  classify, measure, 

    determine supplement 

    or complements              

9.  Understand and use rectangular coordinate system for graphing points and transformations.

(13.9) (7.15)

Using the coordinate plane

   locate points

   plot points

Graphing transformations

   slides

   flips

10.  Develop the relationships among geometric transformations, tesselations, and congruence and symmetry.

(7.15) (7.12)

Symmetry and congruence

   Transformations:

      translations (slides)

      reflections (flips)

      rotations (turns)

11.  Extend their understanding of the number system by constructing meanings for decimals.

(6.11) (6.10) (6.13) (6.15) (6.16) (15.6) (15.9)

Concepts

   part/whole meaning

   density and magnitude

   non-terminating decimal

   significant digits

Relations

   order and sequence

Applications

   money

   scientific notation

12.  Develop, apply and explain procedures for computation and estimation with decimals.  (8.10) (8.8) (15.6) (15.9)

Choosing a computational

   method

Estimation

Significant digits

Addition & subtraction -equations with decimals

Multiplication & division -equations with decimals

13.  Investigate the relationships among fractions, decimals, and percents, and use all of  them appropriately.  (6.18) (10.9)

Developmental sequence:

Build equivalent models

   on geoboards

   with base ten blocks

      andCuisenaire rods

Record models as

   fractions and decimals

Convert symbolically

14.  Develop meaning for ratios, proportions, and percents;  develop, apply, and explain methods for solving problems involving proportions and percents in a variety of situations.

(6.14) (6.18) (8.11) (7.12) 

Ratios   part to part

            part to whole

   ratios vs. fractions

   equal ratios and rates

Proportions

   conceptual meaning

   logical language

   applications:  unit rates

     scales     similar figures

Percents  meaning

               estimations

               applications

Converting fractions,

   decimals, and percents      

15.  Convert measurement units from one form to another, and carry out calculations that involve various units of measure.

    Determine the degree of accuracy need in a given situation and choose unit. (9.7) (9.8) (9.9) (9.13) (9.14)

Metric measures

Standard measures

Use proportions to:

   set up relationships

   make conversions

   solve real life problems

       map scales

Review measuring skills

16.  Identify, describe, compare, and classify plane and solid geometric figures. Relate two-and three- dimensional geometry using perspectives and projections. (7.13) (7.11) (7.19)

Two dimensional shapes:

Classify according to

   sides & angles

   convex/concave

   regular/irregular

Composite figures

Three dimensional shapes:

  polyhedra    cylinders

   pyramids    cones

   spheres

   Platonic solids

Geometry in nature

Real-world applications

17.  Develop, explain, and apply a variety of strategies for determining perimeter, circumference, area, surface area, and volume. Demonstrate and explain the impact of the change of an object’s linear dimensions on its perimeter, area, surface area, or volume.

(7.16) (9.7) (9.10) (9.11) (9.15) (9.16) (15.10) (15.11)

Measurement concepts:

   unit selection

   unit iteration

   transitivity

   invariance

Apply understanding of

measurement to construct shapes

Recognize that all measures of continuous quantities are approximate

Develop formulas for solving problems related to measurement.

18.  Determine the probability of a dependent or independent event. Model situations involving probability, using both simulations and theoretical models.

(12.13) (12.14) (12.16) (14.6)

Recognize non-numeric notions regarding probability: fairness,

      certain, possible,

      impossible, likely

Predict, then find the probability of a simple  and compound events

     - list sample space

Geometric probabilities

Interpret probabilities as ratios and percents.

19.  Make inferences and formulate and evaluate arguments based on data analysis and data displays. (12.11)

20.  Select and use appropriate graphical representations and measures of central tendency for sets of data. (12.10)

Measures of center

          mean

          mode

          median

Effect of outliers

Box and Whisker plots

21.  Generate, collect, organize, and analyze data and represent this data in tables, charts, and graphs.(12.9)

Read and interpret graphs:

 distinguish between types

 identify misleading display

 compare values in two

     sets of data

 determine if scatterplot

     suggests a trend

Organize and display data:

  use tallies, frequency

     charts and line plots

  choosing scale

  construct stem and leaf

     diagrams

22.  Expand the understanding of the number system and the sense of magnitudes of number to include integers, absolute value, and negative rational numbers.

(6.11) (6.13) (6.15) (6.16)

Integer concepts

   meaning

   equivalence rule   

   properties

Integer relations

   order / sequence

Absolute value

Negative rational numbers

23.  Develop, apply and explain procedures for computation and estimation with integers, and negative rational numbers. (8.8) (8.10)

Development meaning for

   operations with integers:

        addition

        subtraction

        multiplication

        division

Solve problems using multiple strategies or models (including spreadsheet)

24.  Understand and apply the standard algebraic order of operations.  (8.12)

Developmental sequence:

  1. Model logic with cubes

  2. Draw representations

       for real life grouping

  3. Investigate patterns

       with calculators

  4. Generate the rule

25.  Understand and use variables and expressions. and equations. (13.5)

Variables as a placeholder

  concrete representations

  pictorial representations

  symbolic representations

Expressions

  intuitive/logical meaning-

     time

     position

     like elements

26.  Solve simple linear equations using concrete, informal, and graphical methods, as well as appropriate paper-and-pencil techniques.(13.10)

Equations

  Balance representation    

  Related logical language

27.  Represent, analyze and describe mathematical relationships with tables, rules, simple equations, and graphs. (11.7) (13.6)

Informal development -

Explore drawing graphs of equations by plotting points based on rules written with words

28. Understand and describe the relationships among various representations of patterns and functions. (11.8)

Patterns- repeating,

   growing, and    visual

29. Recognize common discrete mathematical models, explore their properties, and design them for specific situations. (14.7)

Networks & matrices

Map coloring activities

Glyphs

Fibonacci applications

Fractals