| OUTCOME/
ESSENTIAL
QUESTION |
|
|
|
|
Entire
year of IMP2 addresses A.B4 (Modeling) and
communication mathematically.
Solve It! Unit
(Algebra)
How can I use equations to solve problems?
What do I need to know in order to solve equations? |
|
Review
calculating with negative numbers.
Order of Operations.
Write equations to fit situation. |
|
Be
able to use pan balance metaphor to solve equations.
Correctly evaluate expressions using Order of
Operations and substitution. (N.B2.K3) |
|
| Homework,
Classwork, Observation |
|
| |
Review functions, function notation and graphs of functions;
Algebraic methods to solve equations;
Graphic methods to solve equations;
Area model
Connect algebraic expressions, tables and graphs.
|
|
Determine when expressions/ equations are equivalent. (N.B1.K1)
Subtract expressions in parentheses;
Represent problems algebraically, in tables and
graphically. A.B1.A1
Use area model to multiply monomial times binomial
and binomial times binomial.
Generalize area model to state the distributive
property.(N.B2.K3)*
*Supplement to stress commutative and associative
properties.
Analyze linear functions in the form y = ax + b and
how a and b affect the graph. A.B2.K1 and
A.B3.K6 (Stress
parameter that represents rate of change) Use
"Get It Straight" activity to stress
slopes of parallel and perpendicular lines.
(G.B4.K4)
Solve linear equations explicitly for 1 variable.(N.B4.A1)
Supplement--Put linear equation in function
form to graph by slope/y-int.
(G.B4.K6)
Use skills to
develop algebraic methods for solving linear
equations in one variable.(N.B2.A1)*
*Supplement to name additive and multiplicative
identities and inverses.(N.B2.K3) |
|
Homework, Classwork, Observation, Presentations, POW's,
POW 3 (N.B4.K3) |
|
Finish Solve It! Unit
Begin Is There Really a Difference?
Unit (Data)
Do differences in small populations wrt a
characteristic really mean there is a statistical
difference in the populations from which the samples
come? |
|
Connect
graphing calculators to the algebraic methods being
developed
Double Bar graphs.
Data snooping and hypothesis testing.
Comparing problems using a theoretical sample to
those using a subsample of the population. |
|
Continue developing number sense and patterning ability through
use of POW's. Entire Solve It! Unit addresses
A.B2.K1-3. Supplement
to include absolute value equations.
(A.B2.Kf)
Describe characteristics of a good sample.
Develop stages of investigation
Making a null hypothesis
Using proportional reasoning to determine expected
values
Develop concept of sample fluctuation.
Use decimals and % to calculate expected values. |
|
Homework, Classwork, Observation, Presentations, POW's,
Assessments, Portfolio
Homework, Classwork, Observations, etc. |
|
| Finish Is There
Really a Difference?
Unit |
|
Determine whether to accept or reject null hypothesis
Review standard deviation and discuss
"weirdness"
Use simulation to estimate X^2
statistic and probability chart
Using X^2
statistic to make decisions and compare populations |
|
Construct and draw inferences from double bar graph frequency
charts A.B4.K1l
and A.B4.A1i. Supplement to review Venn diagrams,
box & whiskers)
Understanding consequences of rejecting null.
Compare normal distribution with X^2
distribution
Calculating and interpreting X^2
to compare real data to theoretical.
Calculating and interpreting X^2
to compare real data of two populations. |
|
| Homework, Classwork, Presentations, Unit Project, Observation,
Unit Assessments, Portfolio, POW's |
|
Begin "Do Bees
Build it Best? Unit
(Geometry)
Why do Bees build their honeycombs as hexagons? ie,
What prism has the largest volume for a fixed
lateral surface area and height?
And Which
base for a prism gives the largest area for a fixed
perimeter? |
|
Concepts of area and perimeter are developed
Right Triangle properties
Justification for area, through formulas or geoboard
model. |
|
Concept of perpendicular height is discovered.
Formula for areas of a triangle, rectangle,
parallelogram and trapezoid.
(G.B2.K4)
Uses geoboards/paper, nets, etc.
(A.B4.1h)
Using proper units to measure area and perimeter and
volume. (G.B2.K2)
Use similar triangles and proportion to find missing
sides. (G.B2.K6)
Review right triangle trig
Discover, prove and apply the Pythagorean Theorem to
solve problems. (N.B4.A1, G.B1
K4 and G.B1.A1b, G.B4.K5) |
|
Homework, Classwork, Observation, POW's, Presentations,
Participation, Assessments
POW 5 (N.B4.K3) |
|
|
|
Investigate relationship between area and perimeter of regular
polygons
Investigate Tessellations
General concept of inverse functions
Terminology and notation for inverse trig functions
Investigate volume and surface area of right prisms
Synthesize ideas of unit to solve unit problem
Stress estimation throughout unit to meet N.B3) |
|
Approximate a square root between two integers.(N.B3.K4)
Introduce concept of irrational number (ie, root 2).
Investigate results of rounding error with
irrational numbers. (N.B3.K3) (N.B3.A3,4)
Establish square has largest area for quadrilaterals
with fixed perimeter. Investigate simple quadratic
equations and their parameters.
(A.B3.A3.)
Generalize to other regular polygons.
Given a value of a trig function be able to find the
corresponding angle.
Analyze ranges of three basic trig functions
Develop formula for area of regular polygons
Discover that ratio of areas of similar figures is
the scale factor squared.(G.B3 K and G.B3.A)
Use tessellation POW to review flips, slides
and turns, using transformational terms (G. B3.K)
Developing concept of volume, unit measurement
Relating volume and surface area of a prism to the
area and perimeter of its base.
Standardizing formulas for volume of a right prism V
= Bh and surface area SA = Ph + 2B
Solve problems using surface area and volume
formulas. (N.B4.A1 and
G.B2.A1)
Establish ratio between volumes of
similar prisms is the scale factor
cubed.(G.B3.K and G.B3.A) |
|
| Homework, Classwork, Observation, Presentations, POW's,
Assessments, Portfolio |
|
Begin Cookies Unit
How can I make decisions that will maximize my
profit within the limitations that I have?
(Algebra) |
|
Inequalities as constraints
Determining feasible region
Profit lines as a family of parallel lines |
|
Writing constraints symbolically as inequalities
Writing the expression to be maximized or minimized
symbolically
Review solving linear equation for 1 variable in
terms of another.
Graph inequalities in 1 and 2 variables by hand and
with graphing calculator. A.B3.K4) Find points that
lie on the line.
(G.B4.K2)
Develop methods for solving inequalities in 1
variable
Solve system of 2 equations on graphing calculator |
|
| Homework,
Classwork, Observation, Presentations, POW's, |
|
|
|
Inconsistent and Dependent Systems
Develop reasoning based on graphs
Creating problems to fit a linear programming
situation. |
|
Develop method for solving two equations and two unknowns
algebraically.
Recognize inconsistent or dependent systems
graphically
Recognize inconsistent or dependent systems
algebraically
Find the maximum or minimum of a function over the
feasible region graphically and algebraically.
(Graphing process requires analysis of scale and
scale changes. G.B4.A4)
Create and solve a linear programming problem in two
variables. Entire
Cookies Unit addresses A.B2.K3c and A.B2.A1-2,
G.B4.K8) |
|
| Homework, classwork, observation, presentations, assessments,
portfolio |
|
Begin All About Alice Unit (Algebra)
What does it mean to increase or decrease by a fixed
factor over time?
Can I have fractional or negative exponents? |
|
Develop laws of exponents of counting numbers
Introduce concept of zero as an exponent
Extend to negative and fractional exponents
Extend inverse function idea to logarithms
Use scientific notation
Further develop concept of logic and deductive
reasoning |
|
Graph
non-linear relationships
Express specific non-linear relationships in terms
of exponents
Recognize base, exponent, increasing, decreasing
graphs and the relationship between them and the
base.
What happens to the graph as the base increases or
decreases.
Evaluate growth functions. (N.B4.A1)
Explain a^0 = 1 in terms of the graph, the story of
Alice, and the graph.
Develop rules for multiplying and dividing a^x and
a^y, (a^x)^y and (ab)^x. (N.B1.K1)
Continue the pattern to discover the meaning of
negative exponents.(N.B1.K1)
Compare growth rate of linear functions, exponential
and power functions.
ie, which is larger,
2x 2^x or x^2?
Supplement to solve simple exponential
equations with same base. A.B2.K3g. |
|
|
| Finish All About Alice Unit |
|
Logs as inverse function
Order of Magnitude
Scientific Notation
Proof of nonsense problems using logic |
|
Extend pattern to include fractional exponents.
Introduce concept of irrational numbers
Introduce concept of very large and very small
numbers using scientific notation.(N.B1.K1)
Calculate using numbers in scientific notation
Write equivalent values in scientific notation and
standard numerical notation.
Use scientific notation to solve real problems.
Use order of magnitude to compare numbers. (N.B1,K2)
Introduce concept of logarithm as inverse of
exponentiation.
Graph some simple log equations.
Solve simple log equations, such as log (base 2) 8 =
x
Entire Unit stresses alternative models for a
concept (A.B4.A1) |
|
| Homework, Classwork, Presentations, Observation, Assessment,
POW's and Portfolio |
|