Download Grade 7 - Harrison County Schools

Harrison County Schools
Curriculum Guide for Math Department
Course Name: ___General Math________ Grade Level Targeted: 7th Grade Unit (s): ___________
Essential Questions
How is coordinate
geometry used in the
real world?
Kentucky
Core Content
Version 4.1
MA-07-3.3.1
Students will identify
and graph ordered
pairs on a coordinate
system, correctly
identifying the origin,
axes and ordered pairs;
and will apply graphing
in the coordinate
system to solve realworld and mathematical
problems.
DOK 2
Key Vocabulary
1.
2.
3.
4.
5.
6.
7.
Ordered Pairs
X-Axis
Y-Axis
Vertical
Horizontal
Origin
Four Quadrants
Activities
and
Assessments
Week One: Review axes, identify
components of ordered pairs.
Identify and label all four quadrants,
plot points and label in all four
quadrants.
Essential Questions
How do you use
properties and order
of operations to solve
problems?
How do you use order
of operations with
fractions, decimals,
and percents?
How do you use
properties to solve
problems?
Kentucky
Core Content
Version 4.1
MA-07-1.3.1
Students will add,
subtract, multiply and
divide whole numbers,
fractions and decimals
to solve real-world
problems and apply
order of operations
(including positive
whole number
exponents) to simplify
numerical expressions.
DOK 2
MA-07-1.5.1
Students will identify
and apply prime
numbers, composite
numbers, prime
factorization, factors,
multiples and
divisibility to solve realworld and mathematical
problems (e.g., prime
factorization to
determine a least
common multiple [LCM]
or greatest common
factor [GCF]). DOK 2
Key Vocabulary
1. Divisibility Rules
(2,3,4,5,6,9,10,12)
2. Prime and Composite
3. Exponent
4. Square Root
5. Order of Operations
6. Properties
7. Factor
8. Multiple
9. Prime Factorization
10. Greatest Common
Factor
11. Least Common
Multiple
Activities
and
Assessments
Week Two: Define and apply
divisibility rules, identify prime and
composite numbers, review exponents
and introduce square roots.
Week Three: Review order of
operations, factors, and multiples.
Use the L-Method to complete prime
factorization.
Week Four: Review GCF and LCM,
review for comprehensive unit test.
http://www.saab.org/mathdrills/fraction
_a.html
http://argyll.epsb.ca/jreed/math7/strand1
/1106.htm
http://www.mindspring.com/~alanh/frac
s.html
http://www.bbc.co.uk/skillswise/number
s/wholenumbers/multiplication/mental/
http://www.bbc.co.uk/skillswise/number
s/wholenumbers/division/mental/
http://mathforum.org/k12/mathtips/divis
ion.tips.html
http://www.aaamath.com/B/sub39_x2.ht
m
http://www.aaamath.com/mul.html
http://www.skoool.ie/content/skoool_lea
rning/junior/lessons/maths/factors_1/int
erface.html?id=f1
Essential Questions
Kentucky
Core Content
Version 4.1
Key Vocabulary
Activities
and
Assessments
http://library.thinkquest.org/20991/alg/f
actoring.html
http://www.purplemath.com/modules/fa
ctnumb.htm
http://sf.factmonster.com/ipka/A093346
9.html
http://mathforum.org/dr.math/faq/faq.le
arn.factor.html
http://amby.com/educate/math/21_GCF.html
http://amby.com/educate/math/21_LCM.html
http://www.eduplace.com/cgibin/schtemplate.cgi?template=/kids/mw/
help/eh_popup.thtml&grade=6&chapter
=3&lesson=3&title=Prime+Factorizatio
n&tm=tmfg0303e
Essential Questions
How do you convert
fractions to decimals
and percentages and
vice versa?
Kentucky
Core Content
Version 4.1
MA-07-1.1.1
Students will provide
examples of and
describe integers,
fractions, decimals,
percents, and π. DOK - 1
MA-07-1.1.2
Students will describe
and provide examples
of representations of
numbers (whole
numbers, fractions,
decimals, percents,
integers, square roots
and π) and operations
in a variety of
equivalent forms using
models, diagrams and
symbols (e.g., number
lines, 10 by 10 grids,
rectangular arrays,
number sentences)
based on real-world
and mathematical
MA-07-1.2.1
MA-07-1.3.1
How do you estimate
percentages?
MA-07-1.1.1
MA-07-1.1.2
Key Vocabulary
1.
2.
3.
4.
5.
6.
7.
8.
Simplest Form
Comparing Fractions
Ordering Fractions
Equivalent Fractions
Mixed Numerals
Improper Fractions
Cancellation
Reciprocal
Activities
and
Assessments
Week Five: Review reducing fractions
and forming equivalent fractions.
Review conversions between mixed
and improper fractions.
Week Six: Review addition and
subtraction of fractions, including
mixed numbers and renaming.
Week Seven: Review multiplying
with cross canceling and division of
fractions, including mixed numbers.
Week Eight: Review all operations
and content with fractions to date,
prepare for unit assessment.
http://www.themathpage.com/ARITH/d
ecimals.htm
http://www.ricksmath.com/fractions.ht
ml
http://www.purplemath.com/modules/fr
action.htm
http://www.mcwdn.org/FRACTIONS/F
ractionsMain.html
http://www.kidsolr.com/math/fractions.
html
1. Fraction Bar (as
symbol for division)
Week Nine: Review place value and
rounding. Introduce conversions
Essential Questions
Using proportions,
how do you solve
problems involving
percents, ratios, and
sales tax?
Kentucky
Core Content
Version 4.1
MA-07-1.2.1
Students will estimate
to solve real-world
and/or mathematical
problems with
fractions, decimals, and
percents, checking for
reasonable and
appropriate
computational results.
DOK - 2
MA-07-1.3.1
Students will add,
subtract, multiply and
divide whole numbers,
fractions and decimals
to solve real-world
problems and apply
order of operations
(including positive
whole number
exponents) to simplify
numerical expressions.
DOK 2
MA-07-1.4.1
Students will apply
ratios and proportional
reasoning to solve realworld problems (e.g.,
percents, sales tax,
discounts, rate).
DOK - 3
Key Vocabulary
2. Percent
3. “Of”
4. Place Value
Activities
and
Assessments
from fractions to decimals and
percents.
Week Ten: Introduce converting
decimals to fractions and percents, as
well as percents to fractions and
decimals.
Week Eleven: Focus on real-world
applications of conversions.
http://www.saab.org/mathdrills/fraction
_a.html
http://argyll.epsb.ca/jreed/math7/strand1
/1106.htm
http://www.mindspring.com/~alanh/frac
s.html
http://www.bbc.co.uk/skillswise/number
s/wholenumbers/multiplication/mental/
http://www.bbc.co.uk/skillswise/number
s/wholenumbers/division/mental/
http://mathforum.org/k12/mathtips/divis
ion.tips.html
http://www.aaamath.com/B/sub39_x2.ht
m
http://www.aaamath.com/mul.html
Essential Questions
How do you use
properties to solve
problems?
Kentucky
Core Content
Version 4.1
MA-07-1.5.2
Students will identify
the use of properties
(commutative
properties of addition
and multiplication, the
associative properties
of addition and
multiplication and the
identity properties for
addition and
multiplication) to justify
a given step in solving
problems.
DOK 1
Key Vocabulary
1.
2.
3.
4.
5.
6.
Commutative
Associative
Additive Identity
Multiplicative Identity
Zero Property
Substitution
MA-07-1.5.2
What is an integer?
MA-07-1.1.1
MA-07-1.1.2
1.
2.
3.
4.
Integer
Opposites
Positive
Negative
Activities
and
Assessments
Week Twelve: Introduce KCCT
reference guide for properties. Define
and identify properties and use to
justify steps in a given order of
operations problem.
http://www.skoool.ie/content/skoool_lea
rning/junior/lessons/maths/factors_1/int
erface.html?id=f1
http://library.thinkquest.org/20991/alg/f
actoring.html
http://www.purplemath.com/modules/fa
ctnumb.htm
http://sf.factmonster.com/ipka/A093346
9.html
http://mathforum.org/dr.math/faq/faq.le
arn.factor.html
http://amby.com/educate/math/21_GCF.html
http://amby.com/educate/math/21_LCM.html
http://www.eduplace.com/cgibin/schtemplate.cgi?template=/kids/mw/
help/eh_popup.thtml&grade=6&chapter
=3&lesson=3&title=Prime+Factorizatio
n&tm=tmfg0303e
Week Thirteen: Introduce integers
and number lines to compare and
order. Define all vocabulary terms,
discuss applications of integers for the
Essential Questions
Kentucky
Core Content
Version 4.1
Key Vocabulary
5. Neutral Number
Activities
and
Assessments
real world.
Week Fourteen: Introduce adding
integers.
Week Fifteen: Introduce subtracting
integers.
Essential Questions
How can you use
equations and/or
formulas to represent
real life situations?
Does change in one
variable affect the
change in another,
and if so, does it
always and why?
Are you limited in the
numbers of variables
you may use to
express an everyday
situation in an
algebraic expression?
How do you use
inequalities to
represent real-life
situations?
Kentucky
Core Content
Version 4.1
MA-07-5.1.2
MA-07-5.1.2
Students will represent,
analyze and generalize
first degree
relationships using
tables, graphs and
words and will apply
the relationships to
solve real-world and
mathematical problems.
DOK 2
MA-07-5.1.5
MA-07-5.1.5
Students will explain
how the change in one
quantity affects the
change in another
quantity (e.g., in tables
or graphs). DOK 2
MA-07-5.2.1
MA-07-5.2.1
Students will substitute
values for variables (up
to three different
variables) and evaluate
algebraic expressions.
DOK 2
MA-07-5.3.1
Students will model and
solve real-world and
mathematical problems
with one- or two-step
single variable, first
Key Vocabulary
1. Variable
2. Expression
3. Terms found in
translating
4. Equation
5. Inverse Operation
6. Substitution
7. Inequality
8. Inequality Symbols
9. Open Circle
10. Closed Circle
Activities
and
Assessments
Week Sixteen: Define variable and
expression, practice solving
expressions through substitution.
Discuss terms used in translating
expressions/equations.
Week Seventeen: Introduce solving
basic equations with addition and
subtraction of positive whole
numbers.
http://www.skoool.ie/content/skoool_lea
rning/junior/lessons/maths/addition_sub
traction/index.htm
http://www.purplemath.com/modules/ex
ponent.htm
Week Eighteen: Introduce solving
basic equation with multiplication
and division of whole numbers.
Week Nineteen: Begin
comprehensive review of Algebraic
expressions and equations for midunit test.
Week Twenty: Introduce
inequalities, symbols, and circles used
for graphing. Identify graphs of
inequalities. Apply equation rules to
solve, translate, and graph positive
whole number inequalities.
Essential Questions
Kentucky
Core Content
Version 4.1
degree equations or
inequalities (e.g., 2x+1
= 9, 3x+3 < 9).
(Statements and
solutions use only nonnegative numbers.)
DOK 2
Key Vocabulary
Activities
and
Assessments
Essential Questions
Using proportions,
how do you solve
problems involving
percents, rates and
sales tax?
How do you find
percentages using
proportions?
Name the difference
between congruent
and similar figures.
How do you graph
data in a variety of
ways?
How do you decide
which graph to use to
display data?
When using
probability is it
beneficial to use
counting techniques,
tree diagrams, charts,
and tables?
What is the difference
in mean, median, and
mode?
What is the difference
in cluster, gaps, and
outliers?
Kentucky
Core Content
Version 4.1
MA-07-1.4.1
MA-07-3.1.4
Students will describe
and provide examples
of congruent and
similar figures and will
apply congruent and
similar figures to solve
real-world and
mathematical problems.
DOK 2
MA-07-4.1.1
Students will analyze
and make inferences
from data displays
(drawings,
tables/charts,
pictographs, bar
graphs, circle graphs,
line plots, Venn
diagrams, line graphs,
stem-and-leaf plots,
scatter plots).
DOK 3
MA-07-4.1.2
Students will explain how
different representations
of data (e.g., tables,
graphs, diagrams, plots)
are related.
MA-07-4.2.1
Students will determine
Key Vocabulary
1.
2.
3.
4.
5.
6.
7.
8.
9.
Ratio
Equivalent Ratio
Cross Product
Rate
Unit Rate
Proportion
“is/of = %/100”
Congruent Figures
Similar Figures
1. Data
2. Measures of Central
Tendency
3. Frequency Chart
4. Bar Graph
5. Histogram
6. Interval
7. Circle Graph
8. Sector
9. Line Graph
10. Key
11. Stem-and-Leaf Plot
12. Line Plot
13. Outlier
14. Cluster
15. Gap
16. Scatterplot
17. Positive Correlation
Activities
and
Assessments
Week Twenty-One: Define ratio;
write ratios and reduce to lowest
terms. Define and discuss rate and
unit rate, find unit rates using
division. Introduce proportions,
practice solving.
Week Twenty-Two: Using
proportions to set up real-world
applications, including basic
variables, percents, and similar
figures.
Week Twenty-Three: Review and
create frequency charts and stemand-leaf charts, review measures of
central tendency. Review bar graphs,
define interval, apply frequency
tables to create histograms.
Week Twenty-Four: Review circle
graph, sectors, make inferences using
the circle graph. Review and
construct line graphs. Unit Test.
Essential Questions
Kentucky
Core Content
Version 4.1
the mean, median,
mode and range of a
set of data and will
identify clusters, gaps
and outliers within the
data.
DOK 2
MA-07-4.1.4
Students will determine
and construct
appropriate data
displays (bar graphs,
line plots, Venn
diagrams, tables, line
graphs, stem-and-leaf
plots) and will explain
why the type of display
is appropriate for the
data.
DOK 2
Key Vocabulary
18. Negative Correlation
19. No Correlation
Activities
and
Assessments
Essential Questions
What are the
differences in random
sampling, stratified
sampling, and
systematic sampling,
and give
characteristics of
each?
What makes
theoretical
probability different
from experimental
probability?
Using the data that
you tabulated, explain
how theoretical and
experimental
probabilities are
related?
How do you
determine the area
and perimeter of a
rectangle?
How do you
determine the area
and perimeter of a
Kentucky
Core Content
Version 4.1
MA-07-4.4.1
Students will apply
counting techniques
to determine the size
of a sample space for
a real-world or
mathematical
situation.
DOK 2
MA-07-4.4.2
Students will:
determine theoretical
probabilities of simple
events; determine
probabilities based on
the results of an
experiment and make
inferences from
probability data.
DOK 3
MA-07-2.1.1
MA-07-2.1.1
Students will measure
lengths (to the nearest
eighth of an inch or the
nearest centimeter) and
will determine and use
in real-world and
Key Vocabulary
1. Probability
2. Experiment
3. Outcome
4. Theoretical Probability
5. Certain
6. Likely
7. Equally Likely
8. Unlikely
9. Impossible
10. Experimental
Probability
11. Tree Diagram
12. Fundamental Counting
Principle
1. Sides
2. Vertices
3. Angles (Acute, Obtuse,
Right)
4. Perpendicular
5. Parallel
6. Intersecting
Activities
and
Assessments
Week Twenty-Five: Introduce
vocabulary, determine theoretical
probabilities and compare results of
experiment in class.
Week Twenty-Six: Introduce tree
diagrams and the fundamental
counting principle.
Week Twenty-Seven: Begin review of
identification of basic geometry
elements, describe, and identify their
applications to real-world problems.
Introduce KCCT Reference sheet.
Week Twenty-Eight: Review similar
Essential Questions
Kentucky
Core Content
Version 4.1
Key Vocabulary
triangle?
How do you
determine the area
and circumference of
a circle?
What are the
characteristic
properties of two
dimensional figures?
What re the
differences between
and right, acute, and
isosceles triangle?
What are the
differences in
congruent and similar
figures?
mathematical
problems:
 area and
perimeter of
triangles;
 area and
perimeter of
quadrilaterals
(rectangles,
squares,
trapezoids)
(using the
Pythagorean
theorem will not
be required as a
strategy);
 area and
circumference
of circles and
 area and
perimeter of
compound
figures
composed of
triangles,
quadrilaterals
and circles.
DOK 2
7. Congruent Parts
8. Two-Dimensional
Figures
9. Acute Triangle
10. Obtuse Triangle
11. Scalene Triangle
12. Isosceles Triangle
13. Equilateral Triangle
14. Congruent Figure
15. Similar Figure
16. Formula
17. Transformations
MA-07-3.1.2
MA-07-3.1.2
Students will describe
and provide examples
of the elements (e.g.,
sides, vertices, angles,
Activities
and
Assessments
and congruent figures, use in
applications to real-world geometry
and measurement.
Week Twenty-Nine: Review, identify,
and experiment with creating
transformations.
Week Thirty: Practice finding and
transforming figures based on the
coordinate plane. Discuss and create
tessellations for project grade.
Introduce symmetry as time allows.
http://www.ucl.ac.uk/Mathematics/geo
math/rev/aandv/MHavnb.html
http://www.bbc.co.uk/scotland/educatio
n/bitesize/standard/mathsI/area/index.sh
tml
http://www.bbc.co.uk/schools/gcsebitesi
ze/maths/shape/arearev1.shtml
http://www.bbc.co.uk/schools/gcsebitesi
ze/maths/shapeih/areaandvolumerev1.sh
tml
http://argyll.epsb.ca/jreed/math9/strand3
/3108.htm
http://www.aaamath.com/geo.html
http://www.mhhe.com/math/devmath/al
eks/wtbm/student/olc/graphics/common/media
Essential Questions
Kentucky
Core Content
Version 4.1
Key Vocabulary
congruent parts) of
two-dimensional
figures (circles,
triangles [acute, right,
obtuse, scalene,
isosceles, equilateral],
quadrilaterals [square,
rectangle, rhombus,
parallelogram,
trapezoid], regular
polygons) and will
apply these elements
and figures to solve
real-world and
mathematical problems.
DOK 2
Activities
and
Assessments
/content/main.htm#0108010129
http://www.mhhe.com/math/devmath/al
eks/wtbm/student/olc/graphics/common/media
/content/main.htm#0207010131
http://www.bbc.co.uk/schools/gcsebitesi
ze/maths/shapeh/circlepropertiesrev1.sh
tml
http://www.mste.uiuc.edu/dildine/heron/
triarea.html
http://www.learningwave.com/chapters/
tools/circle.html
MA-07-3.1.4
MA-07-3.1.4
Students will describe
and provide examples
of congruent and
similar figures and will
apply congruent and
similar figures to solve
real-world and
mathematical problems.
DOK 2
MA-07-3.3.1
REVIEW
Weeks Thirty-One through ThirtySix: Review concepts from the year
to date as preparation for state
assessment. Students will participate
in in-depth activities and applications
as review.