Download Math 8 (Pre-Algebra) Curriculum Map 2011-2012

Math 8 (Pre-Algebra) Curriculum Map 2011-2012
Quarter 1 Big Ideas
1. The real number system includes both rational and irrational numbers, each of which has distinguishing characteristics when expressed in decimal form.
2. Irrational numbers can be approximated by rational numbers.
3. There are laws that govern the use of integer exponents.
4. There is an inverse relationship between squares and square roots.
5. The Pythagorean Theorem is an historically and practically important application of squares and square roots.
Textbook
/Resource
Correlation
August
Textbook
Correlation for
all of Q1
Smart Start
Lesson 2, 3
Chapter 1
Lesson 1A-D
Lesson 2A,B
Standards
Vocabulary
Math Standards:
 Operations with rational
numbers (integers, fractions,
decimals, then integrate all
three) 8.2.1
 Conversions between and
comparing fractions,
decimals, and percents
imbedded in 8.2.3, 8.2.4
 Mental computation with
rational numbers 8.2.4
Rational
number,
integer,
inverse
relationship,
order of
operations,
reciprocal,
terminating
decimal,
repeating
decimal,
absolute value,
opposite
Common Core Standards:
CC8.NS.1
September
Continue August Curriculum
Chapter 2
Lesson 1A-C
Lesson 2A-C
Lesson 3A-D
Chapter 9
Lesson 2A,D
“Supplement”
indicated that textbook
does not sufficiently
cover standard
Math Standards:
 Positive exponents and
square roots 8.1.6, 8.1.7
 Number Sets (Rational and
Irrational #s) 8.1.2, 8.1.3
 Simplify and evaluate
expressions that include
exponents 8.3.4
 Exponent laws 8.1.4, 8.1.5,
8.3.3
Common Core Standards:
CC8.EE.1, CC8.EE.2
Exponent, laws
of integer
exponents,
base, power,
irrational
number, real
numbers,
square, square
root, radical,
radicand
Skills/Indicators of Success
8.2.1 Supplement Compute the solution to multi-step
problems involving addition, subtraction, multiplication and
division of integers, terminating decimals, fractions, and
a combination of the three.
8.2.3 Decide whether answers to computations involving
integers, fractions, decimals, and percents on a calculator
are reasonable and justify your response using estimation
techniques. (Classroom only, not ISTEP)
8.2.4 Compute with common fractions, decimals, powers,
and percents using mental arithmetic. (Classroom only, not
ISTEP)
8.1.6a Describe and provide an example of the inverse
relationship between squaring and finding the square root
involving a perfect square integer.
8.1.6b Supplement Simplify a problem involving a perfect
square root squared, i.e. 144 2  144 (State suggests relating
to Pythagorean Theorem, but PT will be covered in Q3)
8.1.7 Supplement Calculate the square root of a given
number to the precision requested or required by the context.
8.1.2c Identify a given decimal as either rational or irrational
and provide justification.
8.1.3 Determine and analyze the results of using addition,
subtraction, multiplication, and division on rational and
irrational numbers (other than zero) by doing the following:
operating on two rationals, operating on one rational and one
irrational, and operating on two irrationals. State and justify,
in words, any generalizations that you can make.
8.3.4a Simplify algebraic expressions involving powers by
using the correct order of operations.
8.3.4b Evaluate algebraic expressions involving powers by
substitution.
8.1.4a Supplement Evaluate an exponential expression
involving negative exponents without a calculator.
8.1.4b Simplify powers with variables as the base, the
exponent, or both that involve negative exponents.
Notes for
Instruction and
Pacing
Suggested
Formative and
Summative
Assessments
Mental
computation
should be
emphasized
throughout
Teach rules for
computation of
rational numbers
with integers first,
then fractions,
decimals, and a
combination.
To be filled in by
PLCs
8.1.3 assessed in
classroom only,
not ISTEP.
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.
To be filled in by
PLCs
8.1.4c & 8.3.3 Supplement Expand whole number powers
involving negative exponents into multiplicative inverse
(repeated division).
8.1.5a Describe the laws of exponents and explain how to
use each one in a given scenario.
8.1.5b Evaluate division of same base expressions that have
both positive and negative integer exponents by using the
law of exponents.
8.1.5c Evaluate multiplication of same base expressions that
have both positive and negative integer exponents by using
the law of exponents.
8.3.3a Recognize the difference between a negative number
raised to an exponent and the opposite of a positive number
raised to an exponent.
8.3.3b Rewrite an exponential expression in expanded form.
Textbook
Correlation for
all of Q1
Smart Start
Lesson 2, 3
Chapter 1
Lesson 1A-D
Lesson 2A,B
October (Q1)
Chapter 2
Lesson 1A-C
Lesson 2A-C
Lesson 3A-D
Chapter 9
Lesson 2A,D
“Supplement”
indicated that textbook
does not sufficiently
cover standard
Math Standards:
 Continue exponent laws with
scientific notation application
8.1.1
 Convert common
measurements within the
same system 8.5.1
Common Core Standards:
CC8.EE.3, CC8.EE.4
Exponent,
scientific
notation,
standard
notation,
dimensional
analysis,
proportion
8.1.1a Read orally decimals in scientific notation.
8.1.1b Write conversions of decimals from scientific notation
to standard form.
8.1.1c Write conversions of decimals from standard form to
scientific notation.
8.1.1d Use <, >, greater than or equal to, less than or equal
to, and = to compare decimals in scientific notation.
8.1.1e Evaluate problems including +, -, x, and / of scientific
notation.
8.1.1f Use scientific notation to solve word problems
involving decimals.
8.5.1 Convert common measurements for length, area,
volume, weight, capacity, and time to equivalent
measurements within the same system.
Discuss scientific
notation with
grade level
science teachers
to align instruction.
If you
teach conversions
as a series of
proportions, it is
suggested that
you teach
conversions using
dimensional
analysis. (State
suggests teaching
conversions in the
context of
perimeter and
area problems, but
this will be
covered more in
Q3)
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.
To be filled in by
PLCs
Quarter 2 Big Ideas
1. Relationships can be described and generalizations made for mathematical situations that repeat in a predictable way. These generalizations can then
be represented in a variety of forms including tables, graphs, equations, and in words.
2. Relations can be used to assign members of one set to members of another set. A function, a specific type of relation, assigns each member of one set
to a unique number of another set.
3. If a correlation exists within data plotted on a scatterplot, a line of best fit can be drawn and a linear equation formulated.
4. If two quantities vary proportionally, the relationship can be represented as a linear function.
5. Rules for arithmetic and algebra can be used together with notations of equivalence to transform equations and inequalities.
6. Nonlinear functions within families of functions have commonalities among their different representations.
Textbook
/Resource
Correlation
October (Q2)
Textbook
Correlation
for all of Q2
November
Chapter 3
Lesson 1 BCD
Lesson 2 ABC
Lesson 3 ABC
Lesson 4 A
Chapter 4
Lesson 1 ABC
Lesson 2 ABCD
December
Chapter 5
Lesson 2 CD
Lesson 3 BC
Lesson 4 AB
Chapter 6
Lesson 1 ABC
Lesson 2 A
Lesson 3 CD
Chapter 9
Lesson 1 AB
Additional Lesson
#7 (Back of Book)
Chapter 10
Lesson 3 B – F
“Supplement”
indicated that
textbook does not
sufficiently cover
standard
Standards
Math Standards:
 Properties and algebraic
expressions 8.3.4, imbedded
in 8.3.1
 One –step equations and
inequalities 8.3.1
Common Core Standards:
CC8.EE.7ab
Math Standards:
 Two-step equations and
inequalities 8.3.1
 Multi-step equations 8.3.1
Vocabulary
Commutative,
associative,
identity,
distributive,
coefficient,
term, constant,
expression,
equation,
inequality
Common Core Standards:
CC8.EE.7ab
Math Standards:
 Relationship between tables,
equations and linear graphs
8.3.5, 8.3.8
 Linear vs. Non-linear
functions 8.3.5, 8.3.8, 8.3.9,
8.3.10
 Slope/Rate of Change 8.3.5,
8.3.6, 8.3.7
(If time allows, begin systems
of equations)
Common Core Standards:
CC8.EE.5, CC8.EE.6,
CC8.F.1, CC8.F.2, CC8.F.3,
CC8.F.4, CC8.F.5, CC8.SP.3
Linear,
parabola,
quadratic,
cubic,
coordinate,
function,
relation,
domain, range,
independent,
dependent,
slope, rate of
change,
intercept,
vertical
change,
horizontal
change, input,
evaluate,
quadrant
Skills/Indicators of Success
8.3.1a Define unknowns for a real-world problem.
8.3.1bcf Solve a linear equation or inequality for a given
variable and verify solution.
8.3.1eg Write a linear equation or inequality to model a
real-world problem.
8.3.1a Define unknowns for a real-world problem.
8.3.1bcf Solve a linear equation or inequality for a given
variable and verify solution.
8.3.1eg Write a linear equation or inequality to model a
real-world problem.
8.3.1d Find ordered pairs that are solutions to a linear
equation and justify your reasoning.
8.3.5e Describe the change in y versus the change in x in
terms of a table, a graph, an equation, or a written
statement.
8.3.6a Calculate slope as rise/run and using the slope
formula.
8.3.6b Determine the slope of a linear function given an
equation, not necessarily in slope-intercept form.
8.3.6c Find the equation of a line given a graph or given the
slope and a point on the line.
8.3.7a Explain in written form the relationship between one
quantity with another quantity in terms of rate.
8.3.7b Write rates as the comparison of two quantities with
appropriate labels.
8.3.7c Draw a graph of one quantity with respect to another
quantity, i.e., time vs. distance.
8.3.10 Graph and compare functions of the form y  nx 2
and y  nx 3 , explain similarities and differences.
8.3.5a Identify linear functions from their graph.
Description: Discuss with students the domain and range
and which is allowed to have numbers repeat and still form
a function (a good technique to use is the "vertical-line
Notes for
Instruction and
Pacing
Continue to
emphasize word
problems that can
be solved by
equations and
inequalities.
Continue to
emphasize word
problems that can
be solved by
equations and
inequalities.
Suggested Formative
and Summative
Assessments
To be filled in by PLCs
To be filled in by PLCs
8.3.10 Assessed
in classroom only,
not on ISTEP
Make connections
between tables,
equations, and
graphs.
Emphasize
translating
equations into
slope intercept
form.
Continue to spiral
review these
topics during
bellringers and
other assessments
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.
To be filled in by PLCs
December
(continued)
test").
8.3.5b Identify linear functions from their table.
Description: Discuss with students the domain and range
and which is allowed to have numbers or variables repeat
and still form a function.
8.3.5c Identify linear functions from their equation.
8.3.5d Identify the slope of a line as positive or negative
from a graph.
8.3.6b Determine the slope of a linear function given an
equation, not necessarily in slope-intercept form.
8.3.8 Translate between a table, equation (using y= or
f(x)=), situation of words, and graph of a linear function
given at least one of the representations.
8.3.9a Recognize and state in words what makes a
quadratic function a quadratic in terms of its table,
equation, and graph.
8.3.9bcd Produce a table, equation, or graph of a quadratic
function, given a verbal description, graph, equation, or
table.
Quarter 3 Big Ideas
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.
1. Some attributes of objects are measurable and can be quantified using unit amounts.
2. Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes. These attributes are
useful in solving problems involving or modeled by these objects.
3. Objects in space can be transformed in an infinite number of ways, and those transformations can be described and analyzed mathematically.
4. The Pythagorean Theorem and its converse can be used to calculate lengths of line segments in 2- and 3-dimensional geometric objects.
Math Standards:
 Systems of equations 8.3.2
 Pythagorean Theorem 8.4.5
 Measurement (perimeter, area,
volume, surface area) 8.5.4
January
Common Core Standards:
CC8.EE.8abc, CC8.G.6,
CC8.G.7, CC8.G.8, CC8.G.9
Chapter 1
Lesson 1C
Chapter 3
Lesson 1B,C
February
Chapter 7
Lesson 4B
Chapter 8
Lesson 1B
Lesson 2B,C
Lesson 3A,B,D,E
Chapter 9
Lesson 1A
Lesson 2A
Math Standards:
 Irregular 2D and 3D shapes
8.5.5
 Scale factors 8.5.3
 Convert common
measurements 8.5.1
Common Core Standards:
CC8.G.4, CC8.G.9
Chapter 12
Lesson 1B,C,E
Lesson 2A,B
Lesson 3B,C,D
Scatter plot,
line of best fit,
correlation,
systems of
equations, no
solution, one
solution,
infinitely many
solutions,
substitution,
radius,
diameter,
surface area,
volume,
circumference,
slant, height,
cylinder, cone,
cube, pyramid,
sphere, face,
area, right
triangle,
rectangular
prism, right
prism, similar,
Pythagorean
theorem, leg,
hypotenuse,
proportion
Smart Start 5
March (Q3)
Math Standards:
 Derived measurements 8.5.2
 Simple and compound interest
8.2.2
 Transformations 8.4.4
Common Core Standards:
CC8.G.1, CC8.G.2, CC8.G.3,
CC8.G.4
Transformation
s, translation,
rotation,
reflection,
dilation, simple
and compound
interest
8.3.2b Solve a system algebraically using substitution.
8.3.2c Write solutions to a system as intersection points or
ordered pairs.
8.3.2d Determine the reasonableness of answers to realworld problems involving systems of equations and check
solutions.
8.4.5ab Explain and use the converse of the Pythagorean
Theorem to determine if a triangle is a right triangle, given
three side lengths. 8.4.5c Solve problems in two and three
dimensions using the Pythagorean Theorem and its
converse. Description: Use the Pythagorean Theorem to
determine if three side lengths form a right triangle as well
as finding the length of a missing side when given two side
lengths.
8.5.1 Convert common measurements for length, area,
volume, weight, capacity, and time to equivalent
measurements within the same system. Description: Note:
To prepare students for Algebra I, if you teach conversions
as a series of proportions, we also suggest that you teach
conversions using dimensional analysis.
8.5.3 Solve problems involving scale factors, area, and
volume using ratio and proportion. 8.5.4a Solve problems
involving perimeter and area of basic two-dimensional
shapes, including rectangles, parallelograms, trapezoids,
triangles, and circles
8.5.4b Solve problems involving surface area and volume
of basic three-dimensional shapes including prisms,
cylinders, spheres, cones, and pyramids. Description:
Problems involving cones, pyramids and spheres are first
found in 8th grade.
8.5.5a Compute and estimate the area of irregular twodimensional shapes.
8.5.5b Compute and estimate the volume of irregular threedimensional shapes.
8.5.2 & 8.2.2 Solve problems involving rates and derived
measurements (e.g., simple and compound interest,
velocity and density).
8.2.2 & 8.5.2 Solve problems involving simple and
compound interest.
8.4.4 Draw the translation (slide), rotation (turn), reflection
(flip), and dilation (stretch or shrink) of any given figure.
Description: This is the only transformation that is
introduced in 8th grade.
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.
Quarter 4 Big Ideas
1. The chance of an event occurring can be described numerically by a number between 0 and 1 inclusive and used to make predictions about other
events.
2. There are special numerical measures that describe the center and spread of numerical data sets.
3. Data can be represented visually using tables, charts, and graphs. The type of data determines the best choice of visual representation.
4. Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and
how best to collect it.
Math Standards:
 Populations and samples
8.6.1, 8.6.2
 Data displays (scatter plots
and line of best fit) 8.6.3, 8.6.4,
8.6.5
March (Q4)
Common Core Standards:
CC8.SP.1, CC8.SP.2,
CC8.SP.3, CC8.SP.4
Measure of
central
tendencies,
outlier,
quartiles,
scatter plot,
correlation,
sample, bias
Chapter 10
Lesson 1A,B,C
Lesson 2A,B,C
Lesson 3A-G
April
Chapter 11
Lesson 1A
Lesson 3D,E
Math Standards:
 Equally likely events 8.6.6
 Counting principle 8.6.7
 Geometric vocabulary and
properties 8.4.1, 8.4.3
May
Common Core Standards:
CC8.G.5
Math Standards:
 Constructions 8.4.2
Common Core Standards:
Probability,
dependent,
disjoint, equally
likely, counting
principle, tree
diagram,
bivariate data,
supplementary,
complementary
, congruent,
corresponding,
altitude,
bisector,
midpoint, edge,
compass,
perpendicular
8.6.1a Identify claims based on statistical data. 8.6.1ac
Identify possible sources of bias in selecting samples or in
an existing sample.
8.6.1b Evaluate the reasonableness of the claims based on
statistical data and design a study to investigate the claim.
8.6.2b Describe different methods of selecting samples,
analyzing the strengths and weaknesses of each method.
8.6.3 Identify or compute the minimum value, the lower
quartile, the median, the upper quartile, the interquartile
range, and the maximum value of a data set, explaining
what each represents in a data set and why each is useful
8.6.4ab Analyze, interpret, and display single-variable and
two-variable data in appropriate bar, line, and circle
graphs; stem-and-leaf plots; and box-and-whisker plots and
explain which types of display are appropriate for various
data sets.
8.6.5a Represent two-variable data with a scatterplot on
the coordinate plane and describe how the data points are
distributed. 8.6.5b Draw a line that appears to best fit the
data in a scatterplot (if the pattern appears to be linear),
and write the equation of that line.
8.6.6 Recognize and define equally likely events.
8.6.7 Find the number of possible arrangements of several
objects by using the Basic Counting Principle
8.4.1 Identify and define basic properties of geometric
shapes including altitudes, diagonals, angle and
perpendicular bisectors, central angles, radii, diameters,
and chords
8.4.3b Describe the results of the intersection of two or
more geometric figures in a plane or space.
8.4.2 Using appropriate tools, accurately construct and
justify the construction of: copies of segments and angles,
bisectors of segments and angles, and perpendicular
segments.
8.4.2, 8.4.3 are
assessed in
classroom only,
not ISTEP
** Incorporate problem solving standards (Mathematical Practices) in each unit. Standards are attached to Curriculum Map.