| OUTCOME/
ESSENTIAL
QUESTION |
|
|
|
|
Entire
year of IMP1 addresses A.B4 (Modeling) and
communication mathematically.
Patterns Unit--(Algebra,
Geometry & Number Sense/Computation)
Why are patterns important in math?
How can I recognize patterns in algebra,
geometry, numbers, etc?
Why is communication so important in math? |
|
Introduce
the IMP method of exploration using graphing
calculators, grouping & presentations
Explore number patterns, geometric patterns, order
of operations.
Explore open-ended problems.
|
|
Be
able to use the graphing calculators to evaluate
expressions.(N.B4.K1 and A.B3.K1,2)
Be able to evaluate expressions correctly using the
order of operations without a calculator.(N.B4.K1,2)
Be able to create an In/Out Table from a rule.
Find a rule using an In/Out table. (A.B2.K1,2)
Develop beginning skills in communicating about
math, both written and oral.(N.B1.K1-3)(Explains) |
|
| Homework,
Classwork, POW 1(N.B4.K3), observation |
|
|
|
Continue to explore number patterns, both linear and quadratic.
Increase number sense.
Discover patterns in geometry.
Introduction to proof as a "convincing
argument"
Introduce concept of perimeter.
Develop strategies to solve problems.
Use concrete mathematical models to develop
mathematical ideas. |
|
Introduce sigma notation for sums.
Be able to express explicit and recursive formulas
for some simple in/out tables.(N.B1.A1)
Given a formula rule, be able to use substitution to
find a missing value. (N.B4.A1)
Be able to add and subtract positive and negative
numbers using a pattern
or hot/cold cube model.
Use a protractor to measure angles.
(G.B2.K1)
Identify the Triangle Sum Theorem (180 degrees).
Extend Triangle Sum theorem to other polygons and be
able to "prove" the result. (G.B1.K1, K2)
|
|
Homework, Classwork, POW 2- 3, observation, presentations,
in-class and take home assessments, portfolio
|
|
Finish Patterns Unit
The Game of Pig Unit
(Data)
Exploring probability
Why is probability a big mathematical idea?
How can I calculate probabilities of some real life
events?
How can I make sound decisions about some life
situations, using probability and expected value?
|
|
Programming
Developing and analyzing strategies to solve
problems.
Learning about independent events, equally likely
events, expected values.
Solving problems using conditional probabilities.
Extending strategies from a simple problem to a
similar but more complex problem.
Communicating about math is stressed throughout. |
|
Develop concept of iteration.
Program calculator as a "function
machine".
Count using patterns and generalize to a formula.
(Perimeter, for example--G.B2.K1)
Entire Patterns Unit addresses
A.B1.A1-2 Supplement to cover terms
"Arithmetic" and "Geometric"
sequences.
Express probability as a value between 0 and 1,
inclusive using fractions, decimals and %.(N.B1K1)
Review % of a number, % increase/ decrease, %
represented by fraction, etc.) (N.B4.K2)
Calculate probabilities, based on equally likely
events and area models (geometric probability).
(D.B1.K1) *Supplement to stress odds from
probability & vise versa.
(D.B1.K3)
Decide whether events are independent or dependent.
Calculate conditional probability.
(D.B1.K2
Use the "long run" to develop the concept
of equally likely events.
Estimate first, then calculate and interpret
expected values.(N.B3.K2) (N.B4.A1)
Solve problems using conditional probability
Make and interpret frequency bar graphs
Compare theoretical analysis of events with
experimental results.
Continue to develop patterns through POW
4
Develop concept of combinations through
examples.
Convert from decimal to percent and vise
versa. |
|
Homework, Presentations, Classwork, Observation, Portfolio and
Assessment
Homework, Presentations, Classwork, POW's |
|
Continue The Game of Pig Unit
|
|
Programming
Introduce the game of "Little Pig" as a
simpler problem to solve.
Prove a strategy is the best strategy
|
|
Simulate a situation on calculator.
Use an area model to analyze results of "Little
Pig"
Find expected values for each of the strategies
developed, for comparison.
Extend best "Little Pig" strategy to
answer unit problem. Entire Unit stresses
(D.B1.A1-4) |
|
Homework, Classwork, Observation, Presentations, Take-Home and
In-Class Assessments, Portfolio.
|
|
Introduce Overland Trail
Unit (Algebra)
Why do I need to know how to work with variables?
How can equations and variables help me answer
questions in my world?
How can graphs help me predict answers to my
questions? |
|
Interpret variables and variable expressions.
Use variables and
variable expressions to model and solve problems.
Interpret and create graphs.
Make connections between graph, In/Out Tables and
function rules. |
|
Be able to write an open sentence symbolically and recognize
equivalency.(N.B1.K1)
Be able to evaluate symbolic expressions using
correct order of operations.
Be able to solve simple open sentences using any
method (trial and error, for example) Determine
reasonableness of answer (whole number, negative
number, fraction)(N.B2.K2)*
*Supplement to meet K1
Given a situation, be able to express that situation
using variables and solve using guess &
check.(N.B1.A1)
Find values that will make a rule true.
Label vertical and horizontal axes and graph the
values that make a rule true, using both linear and
quadratic rules.
(Reasonableness of answers stressed throughout.
N.B1.A2)
Application of properties to solve problems, and
explaining methods mathematically stressed
throughout.(N.B2.A1) |
|
| Homework, Classwork, Presentations, POW's, observations |
|
Continue Overland Trail Unit
|
|
Make predictions with graphs.
Developing a budget.
Organize data into graphs in order to make
decisions.
Develop concept of dependent and independent
variable and the continue to develop concept of
function.
Represent a problem using words, graphs, symbols and
tables
|
|
Fit a line of best fit to a set of points.
Create a graph from a written situation.
Use a graph to make
predictions and decisions. (A.B3.A2,3)
Write equations in function form, ie y =
<expression>
Use the graphing calculator to graph relationships
between variables.
Estimate rates, calculate based on smaller sample,
and adjust. (N.B3.A1)
Calculate rate of change.
Represent rate of change using variables.
(Entire Unit stresses A.B3.A1,3)
|
|
Homework, Classwork, POW's, Take-home and In-class assessment,
observation, portfolio, participation
|
|
Introduce The Pit and the Pendulum Unit (Data)
What
does this story have to do with math???
What factors affect the pendulum?
How can I measure these factors through
experimentation?
|
|
Data gathering
Experimenting by controlling all factors but 1 in a
model
Measuring
Variations in measurement
Developing the concept of standard deviation
Calculator skills |
|
Use a concrete model to represent a situation.
Explore the factors affecting a situation.
Analyze the situation for the mathematics involved.
Gather data.
Ex: Estimate pulse/min, then count pulse/6 sec and
adjust. (N.B3.A1)
Calculate mean, median,
mode and range from various types of
graphs/charts. Apply to solve and analyze problems (D.B2.A1)
Create and use frequency bar graphs to chart data.
Introduce the concept of normal distribution
Develop concept of rare events.
*Supplement so
student can explain affect on measures of central
tendency. (D.B2.K4)
Entire Unit stresses A.B4.A1i,
and A.B4.A2. Supplement
to review box and whiskers, circle graphs, stem and
leaf)
|
|
Homework, Classwork, POW's, Presentations
|
|
Finish Pit and the Pendulum Unit
|
|
Apply the mathematics of the unit to solve the unit problem.
|
|
Use standard deviation to
make statistical predictions and decisions.
Analyze graphs for misleading properties.
Use calculator to create scatter plot.
Develop a formula based on statistical data and
curve of best fit. (D.B2.K5,A6) Unit
solution uses radical equation.
Stress to meet A.B2.K3d
|
|
Homework, Classwork, Presentations, Assessments, Portfolio
|
|
Begin Shadows Unit (Geometry)
How can I predict the length of a shadow?
Why would I need this skill? |
|
Similarity & congruence
Ratio & Proportion
Measurement
Right Triangle properties, including trig
Continue to develop proof |
|
Find functions that represent how shadows can change length
(proportions)
Discover ways to solve proportional equations.
A.B2.K3e
Compare and identify corresponding angles, alternate
angles and same-side angles formed by parallel lines
cut by a transversal.
(G.B1.K7)
Form definitions of similar and congruent triangles.
Discover SSS, SAS and ASA postulates for congruent
triangles.* (G.B1.K6)
*Supplement with reflexive and transitive properties
of congruence and equality to meet (N.B2.K4)
Use AA Similarity rule , SAS and SSS Similarity
Theorems for triangles.
Generalize to prove other polygons are
similar. (G.B1.K4)
Applying similar triangle principles to solving
indirect measurement problems.
Discover Triangle Inequality Theorem
Right triangle terminology, such as leg, hypotenuse,
opposite and adjacent.
Use similarity in right triangles to develop sine,
cosine and tangent functions.
Proof--work with counterexamples, formulating and
refining conjectures, proving vertical angles are
congruent, proving triangle sum property
(G.B1.A3) |
|
| Homework, Classwork, Presentations, POW's |
|
|
|
|
Use angle of elevation and angle of depression in indirect
measurement problems.
Identify conditional statements, hypothesis and
conclusion.
Use counterexamples to disprove conjectures.
Continue to work on writing proofs as a convincing
argument supported by mathematical thinking. |
|
| Homework, Presentations, Classwork, POW's, Assessment, Portfolio |
|