Early College Initiative
Katz, Gary / Math 6 / Grade 6 (AED)
May 24, 2011, 11:51AM /
/ Essential Questions / Content / Skills / Key Vocabulary / Assessment / Resources /
On-going Assessment and Test Readiness
(Week 1, 35 Weeks) / Where are my students today? and where will they be tomorrow? / Performance Series
Self Assessment
tri-annual and on-going measurement of strength and weakness areas
Number Sense
(Week 2, 10 Weeks) / What are the many functions of numbers?
How do numbers WORK for us?
Problem Solving: 4-Step plan/strategy / Numerancy
Sequence
Measurement
Bar Graph
Pie Chart
Line Graph
Number Line
Positive/Negative Integers / § decimal place value
§ expanded notation
§ place value
Identify, read, create:
1. bar graph
2. pie chart
3. line graph
Perform mathematical functions using a number line in the positive and negative domains
Apply multiple strategies to complete equations and word problems
Write and solve real-world word problems exhibiting mastery of content
as_v049_0303_001.pdf
decimalplacevaluechart.pdf
expanded_1thousand_001.pdf
Mathematics Knowledge and Skills - 7th grade.webarchive
money_count_coins_001.pdf
mult_frenzy1_001.pdf
numbersformsconversion_001.pdf
order50_001.pdf
place_value_hundred_thousands_001.pdf
place_value_hundreds_001.pdf
place_value_thousands_001.pdf
placevaluechart.pdf / quantity
positive
negative
rational
integer
place value
sequence
expanded notation
measurement
Order of Operations
exponent
base
equation
expression / Number Sense
Student Portfolio
Collection/Array of Classroom Activities and Daily Tasks that show grade-level proficiency
Was student engaged in lesson?
Did student attend to work?
Does student have a level of independence with this concept/Task?
Number Sense Pre-Test
Standardized Test
Learn student's base-line knowledge of subject
Obtain a classroom "snap shot" of strengths and weaknesses
Formulate strategies to guide level of instruction
Determine amount of time needed to teach unit
Determine amount of extension work of accomplished learners /
1-1 A Plan for Problem Solving.doc
1-2 Prime Factors.doc
1-3 Powers and Exponents.doc
1-4 Order of Operations.doc
1-5 Algebra-Variables and Expressions.doc
Create a Bar Graph 10 20 2010.doc
Create a Bar Graph II 10 21 2010.doc
IMPACT_Math_C2_CH3_Assessment_Checklist-1.doc
1-6a Algebra-Functions.doc
1-6 Algebra-Functions.doc
Converting Decimals to Fractions A.pdf
Converting Fractions to Decimals A.pdf
Lesson 1 Three Way Tie.doc
Whole to Part to Whole Iditarod 12 15 10.doc
Assignment Verbal Expressions + Order of Operations + Distributive Property.pdf
Expressions and Equations
(Week 11, 10 Weeks) / What is Algegra?
What is Algebraic Reasoning?
What is Mental Math and Why is it different than the math I've been doing?
Why is Algebra Important?
Why is "Trial and Error" impractical at this point? / expression
equation
variable
equivalent
reciprocal / Algebra Unit Pre-Assessment
Standardized Test
pre-unit measurement on student readiness
prepare for learning
spiral materials for later learning
Algebra Medial Assessment
Student Portfolio
interactive notebook
portfolio check
completion of daily work
teacher observations
daily assessments
Post Unit Assessment
Written Test
summative assessment
Real-World Word Problems
display reasoning
use appropriate strategies
diagram/draw/visually represent
solve
reason
prove /
1-6 Algebra-Functions 11 07 2010.doc
1-6 Algebra-Functions.doc
1-6a Algebra-Functions 11 08 2010.doc
1-7 Problem Solving Investigation- Guess and Check.doc
1-8 Algebra-Equations.doc
1-9 Algebra- Area Formulas.doc
algebra_missing_numbers_in_equations_blanks_001.pdf
Assignment Verbal Expressions + Order of Operations + Distributive Property.ipa
Geometry
(Week 21, 10 Weeks) / Geometry stands for:
geo which means earth and metria which means measure.(Greek)
A major contributor to the field of geometry wasEuclid - 325 BC1who is typically known as the Father of Geometry and is famous for his works called The Elements. As one progresses through the grades, Euclidian geometry (Plane Geometry) is a big part of what is studied. However, non-Eucledian geometry will become a focus in the later grades and college math.
Simply put, geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. However, geometry is used daily by almost everyone. In geometry, one explores spatial sense and geometric reasoning. Geometry is found everywhere: in art, architecture, engineering, robotics, land surveys, astronomy, sculptures, space, nature, sports, machines, cars and much more.
When taking geometry, spatial reasoning and problem solving skills will be developed. Geometry is linked to many other topics in math, specifically measurement and is used daily by architects, engineers, architects, physicists and land surveyors just to name a few. In the early years of geometry the focus tends to be onshapes and solids,2then moves to properties and relationships of shapes and solids and as abstract thinking progresses, geometry becomes much more about analysis and reasoning.
Geometry is in every part of thecurriculum K-123and through to college and university. Since most educational jurisdictions use a spiraling curriculum, the concepts are re-visited throughout the grades advancing in level of difficulty. Typically in the early years, learners identify shapes and solids, use problem solving skills, deductive reasoning, understand transformations, symmetry and use spatial reasoning. Throughout high school there is a focus on analyzing properties of two and three dimensional shapes, reasoning about geometric relationships and using the coordinate system. Studying geometry provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, analytical reasoning andproblem solving4to name just a few.
Some of the tools often used in geometry include: Compass,protractors,5squares,graphing calculators,6Geometer's Sketchpad,7rulers etc.
Thegrade by grade goals section (scroll down)8will give more specific details of the geometry concepts expected in grades Pre-K to 12. / Geometry stands for:
geo which means earth and metria which means measure.(Greek)
A major contributor to the field of geometry wasEuclid - 325 BC1who is typically known as the Father of Geometry and is famous for his works called The Elements. As one progresses through the grades, Euclidian geometry (Plane Geometry) is a big part of what is studied. However, non-Eucledian geometry will become a focus in the later grades and college math.
Simply put, geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. However, geometry is used daily by almost everyone. In geometry, one explores spatial sense and geometric reasoning. Geometry is found everywhere: in art, architecture, engineering, robotics, land surveys, astronomy, sculptures, space, nature, sports, machines, cars and much more.
When taking geometry, spatial reasoning and problem solving skills will be developed. Geometry is linked to many other topics in math, specifically measurement and is used daily by architects, engineers, architects, physicists and land surveyors just to name a few. In the early years of geometry the focus tends to be onshapes and solids,2then moves to properties and relationships of shapes and solids and as abstract thinking progresses, geometry becomes much more about analysis and reasoning.
Geometry is in every part of thecurriculum K-123and through to college and university. Since most educational jurisdictions use a spiraling curriculum, the concepts are re-visited throughout the grades advancing in level of difficulty. Typically in the early years, learners identify shapes and solids, use problem solving skills, deductive reasoning, understand transformations, symmetry and use spatial reasoning. Throughout high school there is a focus on analyzing properties of two and three dimensional shapes, reasoning about geometric relationships and using the coordinate system. Studying geometry provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, analytical reasoning andproblem solving4to name just a few.
Some of the tools often used in geometry include: Compass,protractors,5squares,graphing calculators,6Geometer's Sketchpad,7rulers etc.
Thegrade by grade goals section (scroll down)8will give more specific details of the geometry concepts expected in grades Pre-K to 12. / spatial reasoning
problem solving
coordinate graph/coordinate system
logic
deductive reasoning
analytical reasoning / size
shape
position
2DD
3D
Spatial Sense
Geometric reasoning
1. Polygon – A simple closed figure in a plane formed by three or more line segments.
2. Quadrilateral – A polygon with four sides.
3. Rectangle – A quadrilateral with opposite sides congruent and parallel and all angles are right.
4. Parallelogram – A quadrilateral with both pairs of opposite sides parallel and congruent.
5. Square - A parallelogram with four congruent sides and four right angles.
6. Triangle - A polygon with three sides.
7. Trapezoid - A quadrilateral with exactly one pair of parallel opposite sides.
8. Area – The measure of the inside of a closed figure, expressed in square units.
9. Perimeter – The measure of the distance around the outside of a closed figure.
10. Ratio – A comparison of two numbers by division.
11. Scale – The ratio of a given length on a drawing or model to its corresponding length in reality.
12. Scale Drawing - A drawing that is similar, but either larger or smaller than the actual object.
13. Scale Factor – the ratio of the lengths of two corresponding sides of two similar polygons
14. Scale Model – A replica of an original object that is too large or too small to be built at actual size. / Personal Project
Habitat for Humanity House: Area and Perimeter of 3D solids
Raise the Roof Project: Surface Area and Volume/ Design Dream Spaces/ /Budget-cost extention
Geometry Vocabulary
Other written assessments
word search
Geometry Vocabulary
Other written assessments
Crossword Puzzle
Geometry Vocabulary
Other written assessments
Vocabulary Matching
Geometry Unit Summative Assessment
Standardized Test
Using 7th Grade NYState Math test questions from prior years
Short and Extended Responses
Geometry Vocabulary
crossword puzzle medial assessment / Raise the Proof(see links)
Habitat House(see links)
(see links)
Geometry
§ Hypothesize, sketch, identify, sort, classify, construct, measure, and apply a variety of geometric shapes and figures and problems
§ Sketch and construct a variety of shapes given the dimensions
§ Create and solve a variety of geometric problems
§ Analyze and identify shapes that have been rotated, reflected, translated and describe those that are congruent
§ Determine if shapes/figures will tile a plane (tessellate)
§ Analyze tiling patterns
One Week Project: in and out of class room
Area and Perimeter practice: kinesthetic activity
Dream Space Design: Free Write
Coordinate Geometry 2011 01 04.docx
Coordinate Points Who Am I 2011 01 06.doc
Coordinate_Geometry.ppt
Identify Coordinate Points 2011 01 07.doc
Who am I.doc
Assignment Verbal Expressions + Order of Operations + Distributive Property.pdf
Statistics and Probability
(Week 31, 10 Weeks) / What are the chances of that?
How will I find simple probabilities and odds?
How will I use probability to make predictions?
What is the difference between probabilty and odds?
How can knowing the probability or odds of winning a game help you determine whether or not it is fair?
How do statistics and probability relate to medicine? to weather? to business? to games (cards), to sports? to science?
How can statistics and probability save time, man-power and money?
How can statistics be used to inform?
How can statistics be used to distort/misinform? / Probability
§ Design surveys, collect and organize more complex data and identify and explain patterns and trends in data
§ Construct a variety of graphs and label them appropriately and state the difference between selecting one graph over another
§ Defend your choices of graphs
§ Make more accurate predictions
§ Understand the importance of statistics on decision making and provide real life scenarios
§ Describe collected data in terms of mean, median and the mode and be able to analyze any bias
§ Make inferences, predictions and evaluations based on interpretations of data collection results
§ Be able to predict possible outcomes based on background information
§ Apply the rules of probability to games of chance and sports / working with ratios
understanding percents
multiplying fractions
probability of simple events
calculating probability of simple events
writing fractions as percents
multiplying whole numbers
working with ratios
rounding decimals
working with proportions / probability
outcomes
equally likely
eveny
odds
fair
compliment
certain
impossible
percents
independent
dependent
sample
simulations
trial
experimental probability
random
permeatation
combination
central tendency
range
Atlas Version 7.2.2
© Rubicon International 2011. All rights reserved