Download 7th grade Unit Mappingsept11 - GCS6

Unit
Standard(s)
Unit Title
Big Ideas and Understandings
Unit 1:
(4 wks)
7NS1a, 7NS1b, 7NS1c
7NS1d
7NS2a, 7NSb
7NSc, 7NSd
7NS3
Unit 2:
(7 wks)
7EE1
7EE2
7EE3
7EE4a, 7EE4b
Expressions and
Equations
Unit 3:
(9 wks)
7RP1
7RP2a
7RP2b, 7RP2c, 7RP2d
7RP3
7G1
Ratio and Proportional
Relationships
 Analyze proportional relationships and use them to
solve real-world and mathematical problems.
 Solve problems involving scale drawings of
geometric figures.
Unit 4:
(9 wks)
7G5
7G4
7G2
7G6
7G3
Geometry
 Draw, construct, and describe geometrical figures
and describe the relationships between them.
 Solve real-life and mathematical problems involving
angle measure, area, surface area, and volume.
Unit 5:
(4 wks)
7SP1
7SP2
7SP3
7SP4
7SP5
7SP6
7SP7a
7SP7b
7SP8a, 7SP8b,
7SP8c
Common Unit Assessments:
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ClassScape
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Benchmarks
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Unit Tests
Total Weeks :
33
The Number System

Apply and extend previous understandings of
addition and subtraction to add, subtract,
multiply, and divide rational numbers.

Use properties of operations to generate
equivalent expressions.
Solve real-life and mathematical problems
using numerical and algebraic expressions and
equations.
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Statistics and
Probability


Use random sampling to draw inferences
about a population.
Draw informal comparative inferences about
two populations.
Investigate chance processes and develop, use,
and evaluate probability models.
UNIT 1 INFORMATION
Unit Title:
Topic:
Unit 1: The Number System
Grade Level:
7
Rational Numbers
Length (in weeks / days):
4
% of Formal Assessment
7 – 12%
WHAT’S THE BIG IDEA(s)?
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
STANDARDS
7NS1 Apply and extend previous understandings of
addition and subtraction to add and subtract rational
numbers, represent addition and subtraction on a
horizontal or vertical number line diagram.
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Describe situations in which opposite quantities
combine to make 0. For example, a hydrogen
atom has 0 charge because its two constituents
are oppositely charged.
Understand p + q as the number located a
distance /q/ from p, in the positive or negative
direction depending on whether q is positive or
negative. Show that a number and its opposite
have a sum of 0 (are additive inverses). Interpret
sums of rational numbers by describing realworld contexts.
Understand subtraction of rational numbers as
adding the additive inverse, p – q = p + (-q).
Show that the distance between two rational
numbers on the number line is the absolute value
of their difference, and apply this principle in
real-world contexts.
Apply properties of operations as strategies to
add and subtract rational numbers.
7NS2 Apply and extend previous understandings of
multiplication and division and of fractions to multiply and
divide rational numbers.

Understand that multiplications is extended from
fractions to rational numbers by requiring that
operations continue to satisfy the properties of
operations, particularly the distributive property,
leading to products such as
(-1)(-1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers
by describing real-world contexts.

Understand that integers can be divided,
provided that the divisor is not zero, and every
quotient of integers (with non-zero divisor) is a
rational number. If p and q are integers, then
-(p/q) = (-p)/q = p/(-q). Interpret quotients of
rational numbers by describing real-world
contexts.

Apply properties of operations as strategies to
multiply and divide rational numbers.

Convert a rational number to a decimal using
long division; know that the decimal form of a
rational number terminates in 0’s or eventually
repeats.
7NS3 Solve real-world and mathematical problems
ENDURING UNDERSTANDINGS

To meet the standards, students
will need to:
MATHEMATICAL PRACTICES
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understand and identify opposites.
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describe situations in which
opposite quantities combine to
make zero (additive inverses).
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understand meaning of absolute
value.
compute and solve addition and
subtraction of integer math
problems.

solve real- world and
mathematical problems involving
integers (add and subtract).

compute and solve addition and
subtraction of fractions and
decimal numbers.

solve real-world and mathematical
problems involving fractions and
decimal numbers. (adding and
subtracting)

compute multiplication and
division of all fractions, decimals,
and integers.

convert a fraction to a decimal
using long division.

solve real world and mathematical
problems with fractions, decimals,
and integers.

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
Make sense of problem and
persevere in solving them.
Reason abstractly and
quantitatively.
Construct viable arguments and
critique the reasoning of others.
Model with mathematics
Use appropriate tools
strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity in
repeated reasoning.
involving the four operations with rational numbers.
(NOTE: Computations with rational numbers extend the
rules for manipulating fractions to complex fractions.)
Essential Vocabulary
Rational numbers
Integers
Opposites
Additive Inverse
Absolute Value
Artisan Big 6
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Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Corrections
21st Century Learning Skills
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Suggested Resources:
Practice Skills, Intervention, and Word Problem Prentice Hall workbooks
www.symbaloo.com (search concepts in gallery link)
www.brainpop.com
www.math.com
www.learn4good.com
www.amathsdictionaryforkids.com
www.discoveryed.com
www.readwritethink.org
www.Illustrativemathematics.org
Integers (+/-)
Course 1: pg. 294, 300, 304,
Course 2: pg. 106, 120, 128
Course 3: pg. 23, 28
Fractions and Decimals (+/-)
Course 1: pg. 310
Course 2: pg. 134
Course 3: pg. 88
Rationals (x, ÷)
Course 1: pg. 206, 316
Course 2: pg. 138, 210
Course 3: pg. 34, 62, 71 - 76
Word Problems
Course 1: pg. 333
Course 2: pg. 30
Course 1: Word Problem Workbook
Course 2: Word Problem Workbook pgs. 21 - 24
Course 3: Word problem Workbook
Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information
UNIT 2 INFORMATION
Unit Title:
Subject/Topic:
Unit 2: Expressions and Equations
7
Algebraic Reasoning
Length (in weeks / days):
7 weeks
% of Formal Assessment
18 – 23%


Grade Level:
WHAT’S THE BIG IDEA(s)?
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
STANDARDS
7EE1 Apply properties of operations and strategies to add,
subtract, factor, and expand linear expressions with rational
coefficients.
7EE2 Understand that rewriting an expression in different
forms in a problem can shed light on the problem and how
the quantities in it are related.
7EE3 Solve multistep and real-life mathematical problems
posed with positive and negative rational numbers in any
form using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental computation and
estimation strategies.
7EE4 Use variables to represent quantities in a real-world
or mathematical problem, and construct simple equations
and inequalities to solve problems by reasoning about the
quantities.
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:
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Essential Vocabulary:
MATHEMATICAL PRACTICES
combine like terms and apply
properties of operations and work
with rational numbers to write
equivalent expressions.
understand that various expressions
can be written from real world
situations that will result to the same
conclusion.
solve word problems using rational
numbers.
convert fractions, decimals and
percents to solve problems.
use estimation to justify their
solutions.
write an equation or inequality to
represent a situation.
explain how to determine if a situation
is represented with an equation or
inequality and the properties of the
number system used to determine
their solution.
define the variable and use
appropriate units from context.
Artisan Big 6
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Make sense of problem and
persevere in solving them.
Reason abstractly and
quantitatively.
Construct viable arguments and
critique the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity in
repeated reasoning.
21st Century Learning
Like Terms
Coefficient
Numeric Expression
Maximum/minimum
Equation
Variable
Distributive Property
Factor
Algebraic Expression
Estimation
Inequality
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Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Corrections
Suggested Resources:
Practice Skills, Intervention, and Word Problem Prentice Hall workbooks
www.symbaloo.com (search concepts in gallery link)
www.brainpop.com
www.math.com
www.learn4good.com
www.amathsdictionaryforkids.com
www.discoveryed.com
www.readwritethink.org
Like Terms/Equivalent Expressions
Course 3: pg. 472
Expressions from real world situations
Course 2: pg. 312
Course 3: pg. 210
Word problems with rational numbers
Course 2: pg. 166, 172
Course 3: pg. 474, 484, 492 – 500
Equations/Inequalities from word problems
Course 2: pg. 301
Course 3: pg. 548
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Teamwork and Collaboration
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Accessing and Analyzing Information
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
UNIT 3 INFORMATION
Unit 3: Ratio and Proportional Relationships
Unit Title:
Grade Level:
7
Proportional Reasoning
Subject/Topic:
Length (in weeks / days):
9 weeks
% of Formal Assessment
22 – 27%
WHAT’S THE BIG IDEA(s)?
Analyze proportional relationships and use them to solve real-world and mathematical problems.
STANDARDS
7RP1 Compute unit rates associated with ratios of fractions,
including ratios of lengths, areas and other quantities
measured in like or different units.
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:

work with unit rates including
proper or improper fractions
with like or different units.

determine if two quantities are
proportional from a table.
(including fractions and
decimals)

Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships.
graph relationships to determine
if two quantities are proportional
and to give meaning to the
ordered pairs.

Represent proportional relationships by
equations.
use ratio tables and unit rates to
solve word problems.

solve problems using crossmultiplication.
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use proportions to solve
multistep ratio and percent word
problems.
7RP3 Use proportional relationships to solve multistep
ratio and percent problems.

determine the dimensions of
figures when given a scale.
7G1 Solve problems involving scale drawings and geometric
figures including computing actual lengths and areas from a
scale drawing and reproducing a scale drawing at a
different scale.

identify the scale factor given two
figures.
7RP2 Recognize and represent proportional relationships
between quantities.
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Decide whether two quantities are in a
proportional relationship by testing for
equivalent ratios in a table or graphing on a
coordinate plane and observing whether the
graph is a straight line through the origin.
Explain what a point (x, y) on the graph of a
proportional relationship means in terms of the
situation, with special attention to the points (0,
0) and (1, r) where r is the unit rate.
MATHEMATICAL PRACTICES

Make sense of problem and
persevere in solving them.

Reason abstractly and
quantitatively.

Construct viable arguments and
critique the reasoning of others.

Model with mathematics

Use appropriate tools strategically.

Attend to precision.

Look for and make use of
structure.

Look for and express regularity in
repeated reasoning.

reproduce a drawing at a
different scale when given the
scale factor.

understand the impact that the
scale factor has on perimeter and
area of two similar figures.
Essential Vocabulary:
Artisan Big 6
21st Century Learning
Scale
Scale Factor
Scale drawing
Perimeter
Area
Ratio
Rate
Unit rate
Proportion
Proportional relationships
Constant of proportionality
Complex fractions
Ordered Pairs/coordinates
Cross-multiplication
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Teamwork and Collaboration
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Accessing and Analyzing Information
Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Corrections
Suggested Resources:
Navigation Series:
Navigating through Geometry “Exploring Similar Figures” pg. 19
Similarity and the Coordinate Plane “Using Scale Factors pg. 48
Navigating through Number and Operations – (chapter 3)
Practice Skills, Intervention, and Word Problem Prentice Hall workbooks
www.symbaloo.com (search concepts in gallery link)
www.brainpop.com
www.math.com
www.learn4good.com
www.amathsdictionaryforkids.com
www.discoveryed.com
www.readwritethink.org
Unit Rates
Course 1: pg. 380, 386
Course 2: pg. 288 – 292, 297
Course 3: pg. 156 – 160
Proportional relationships in tables, graphs, coordinates, etc.
Course 2: pg. 292
Course 3: pg. 160 – 162, 170
Ratio and Percent problems
Course 1: pg. 409
Course 2: pg. 340, 350
Course 3: pg. 216 – 241
Word problem workbooks
Scale Drawings
Course 2: pg. 301, 440
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Course 3: pg. 184
UNIT 4 INFORMATION
Unit Title:
Subject/Topic:
Unit 4: Geometry
7
Angles/Circumference/Area/volume
Length (in weeks / days):
9 weeks
% of Formal Assessment
25 – 30%


Grade Level:
WHAT’S THE BIG IDEA(s)?
Draw, construct, and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
STANDARDS
ENDURING UNDERSTANDINGS
MATHEMATICAL PRACTICES
To meet the standards, students will need to:

7G5 Use facts about supplementary, complementary,
vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a
figure.
7G4 Know the formulas for the area and circumference of a
circle and use them to solve problems; give an informal
derivation of the relationship between the circumference
and area of a circle.
7G2 Draw geometric shapes (freehand with a ruler,
protractor, and technology) with given conditions. Focus
on constructing triangles from three measures of angles or
sides, noticing when the conditions determine a unique
triangle, more than one triangle, or no triangle.
7G6 Solve real world and mathematical problems involving
area, volume, and surface area of 2 and 3 dimensional
objects composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
7G3 Describe the two-dimensional figures that result from
slicing three-dimensional figures, as in plane sections of
right rectangular prisms and right rectangular pyramids.
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write equations to find missing
angle measures.
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understand the relationship
between the radius and diameter.
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understand the ratio of
circumference to diameter can be
expressed as pi.
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generate formulas for
circumference and area.
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draw geometric shapes when
given certain conditions (circles
and cylinders are not included)
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recognize that finding the area of
each face of a three dimensional
figure and adding the areas will
give the surface area.
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find the dimensions of a figure
given the area or volume.

describe the face shape made
from parallel and perpendicular
cuts to the base.
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Make sense of problem and
persevere in solving them.
Reason abstractly and
quantitatively.
Construct viable arguments and
critique the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity in
repeated reasoning.
Essential Vocabulary:
Artisan Big 6
21st Century Learning
Supplementary angles Complementary angles
Vertical angles
Adjacent angles
Radius
Diameter
Circumference
Pi
Face
Base
Volume
Area
Surface area
Right rectangular prism
Right rectangular pyramid
Parallel
Perpendicular
Plane sections
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Teamwork and Collaboration
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Accessing and Analyzing Information
Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Corrections
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Suggested Resources:
Navigation Series:
Navigating through Geometry “Cross Sections of 3-Dimensional Shapes pg. 67
Practice Skills, Intervention, and Word Problem Prentice Hall workbooks
www.symbaloo.com (search concepts in gallery link)
www.brainpop.com
www.math.com
www.learn4good.com
www.amathsdictionaryforkids.com
www.discoveryed.com
www.readwritethink.org
Angles
Course 1: pg. 506
Course 2: pg. 413
Course 3: pg. 256
Circumference
Course 1: pg. 556
Course 2: pg. 493
Course 3: pg. 319
Read Aloud:
Sir Circumference and the Dragon of Pi
Triangles
Course 2: pg. 428, 432
Area/Volume/Surface Area
Course 1: pg. 546, 551, 555, 564, 570, 575
Course 2: pg. 483, 489, 498, 520, 524, 532, 538
Course 3: pg. 314 – 357
Plane Sections
Course 3: pg. 351
UNIT 5 INFORMATION
Unit Title:
Subject/Topic:
Unit 5: Statistics and Probability
7
Measures of Central Tendency/Variability
Length (in weeks / days):
4 weeks
% of Formal Assessment
15 – 20%
WHAT’S THE BIG IDEA(s)?

Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.

Investigate chance processes and develop, use, and evaluate probability models.
STANDARDS
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:
7SP1 Understand that statistics can be used to gain

use a random sample from a total
information about a population by examining a sample of
population to make valid
the population; generalizations about a population from a
predictions and draw inferences
sample are valid only if the sample is representative of that
about the population.
population. Understand that random sampling tends to
produce representative samples and support valid

collect and use multiple samples
inferences.
of data to make generalizations
about a population.
7SP2 Use data from a random sample to draw inferences
about a population with an unknown characteristic of

understand the interpretation of
interest. Generate multiple samples (or simulated samples)
data requires consideration of
of the same size to gauge the variation in estimates or
the measures of variability
predictions.
(range, inter-quartile range,
variance, standard deviation) as
7SP3 Informally assess the degree of visual overlap of two
well as mean or median.
numerical data distributions with similar variabilities,
measuring the difference between the centers by

compare and understand the
expressing it as a multiple of a measure of variability.
variability of two data sets.
7SP4 Use measures of center and measures of variability for
numerical data from random samples to draw informal
comparative inferences about two populations.
7SP5 Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood of
the event occurring.
7SP6 Approximate the probability of a chance event by
collecting data on the chance process that produces it, and
observing its long-run relative frequency, and predict the
approximate relative frequency given the probability.

understand that the median is
associated with the inter-quartile
range and mean associates with
the mean absolute deviation.

compare two sets of data using
measures of center (mean and
median) and variability (MAD
and IQR.)

determine the probability of any
single event expressed in terms
as impossible, unlikely, likely, or
certain as a number between 0
and 1.
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recognize that the sum of all
possible outcomes equals 1.

collect data from a probability
experiment and recognize that as
the number of trials increase the
experimental probability
approaches the theoretical
probability.
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use theoretical probabilities to
predict frequencies of outcomes.
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use tree diagrams, frequency
tables, organized lists, and
simulations to determine the
probability of compound events.
7SP7 Develop a probability model and use to find
probabilities of events.
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Compare probabilities from a model to observed
frequencies; if the agreement is not good, explain
possible sources of discrepancy.
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Develop a uniform probability model by
assigning equal probability to all outcomes, and
use the model to determine probabilities of
events.
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Develop a probability model (which may not be
uniform) by observing frequencies in data
generated from a chance process.
7SP8 Find probabilities of compound events using
organized lists, tables, tree diagrams and simulation.
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Grade Level:
Understand that, just as with simple events, the
probability of a compound event is a fraction of
outcomes in the sample space for which the
compound event occurs.
MATHEMATICAL PRACTICES








Make sense of problem and
persevere in solving them.
Reason abstractly and
quantitatively.
Construct viable arguments and
critique the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity in
repeated reasoning.

Represent for compound events using methods
such as organized lists, tables, and tree diagrams.
For an event described in everyday language,
(e.g., “rolling double sixes”), identify the
outcomes in the sample space which composed
the event.

Design and use a simulation to generate
frequencies for compound events. For example;
use random digits as a simulation tool to
approximate the answer to the question: If 40%
of donors have type A blood, what is the
probability that it will take at least 4 donors to
find one with type A blood?

Essential Vocabulary:
Random sample
Variation/variability
Random Sample
Population
Representative sample
Inference
survey
Measures of Variability
Measures of center
Distribution
Range
Inter-quartile range
Variance
Standard deviation
Mean
Median
Relative frequency
Mean Absolute Deviation
Chance event
Theoretical/Experimental probability
Sample spaces
Compound events
Artisan Big 6
21st Century Learning
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Teamwork and Collaboration
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Accessing and Analyzing Information
Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Corrections
Suggested Resources:
Navigation Series:
Navigating through Probability in Grades 6 – 8
Practice Skills, Intervention, and Word Problem Prentice Hall workbooks
www.symbaloo.com (search concepts in gallery link)
www.brainpop.com
www.math.com
www.learn4good.com
www.amathsdictionaryforkids.com
www.discoveryed.com
www.readwritethink.org
Random Samples
Course 1: pg. 438
Course 2: pg. 60, 345
Read aloud: If The World Were A Village
Variability
Course 2: pg. 64, 69, 71
Youtube video: z9AJk7TvdpQ
Mean/Median/MAD/IQR
Course 2: pg. 85
Course 3: pg. 442
Chance Events
Course 1: Chapter 11
Course 2: pg. 374
Experimental/Theoritical Probability
Course 1: Chapter 11
Course 3: Chapter 8
Compound Events
Course 1: pg. 434, 436
Course 2: pg. 381, 387
Course 3: pg. 384 - 391
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication