Harrison County Schools

Curriculum Guide for Math Department

Course Name: ___General Math______Grade Level Targeted: 7th Grade Unit (s): ______

Essential Questions / Kentucky
Core Content
Version 4.1 /

Key Vocabulary

/ Activities
and
Assessments /
How is coordinate geometry used in the real world? / 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 real-world and mathematical problems.
DOK 2 / 1.  Ordered Pairs
2.  X-Axis
3.  Y-Axis
4.  Vertical
5.  Horizontal
6.  Origin
7.  Four Quadrants / Week One: Review axes, identify components of ordered pairs. Identify and label all four quadrants, plot points and label in all four quadrants.

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? /

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 real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK 2 / 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 /
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/fracs.html
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/multiplication/mental/
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/division/mental/
http://mathforum.org/k12/mathtips/division.tips.html
http://www.aaamath.com/B/sub39_x2.htm
http://www.aaamath.com/mul.html
http://www.skoool.ie/content/skoool_learning/junior/lessons/maths/factors_1/interface.html?id=f1
http://library.thinkquest.org/20991/alg/factoring.html
http://www.purplemath.com/modules/factnumb.htm
http://sf.factmonster.com/ipka/A0933469.html
http://mathforum.org/dr.math/faq/faq.learn.factor.html
http://amby.com/educate/math/2-1_GCF.html
http://amby.com/educate/math/2-1_LCM.html
http://www.eduplace.com/cgi-bin/schtemplate.cgi?template=/kids/mw/help/eh_popup.thtml&grade=6&chapter=3&lesson=3&title=Prime+Factorization&tm=tmfg0303e

How do you convert fractions to decimals and percentages and vice versa?

/

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

/ 1.  Simplest Form
2.  Comparing Fractions
3.  Ordering Fractions
4.  Equivalent Fractions
5.  Mixed Numerals
6.  Improper Fractions
7.  Cancellation
8.  Reciprocal / 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/decimals.htm
http://www.ricksmath.com/fractions.html
http://www.purplemath.com/modules/fraction.htm
http://www.mcwdn.org/FRACTIONS/FractionsMain.html
http://www.kidsolr.com/math/fractions.html
How do you estimate percentages?
Using proportions, how do you solve problems involving percents, ratios, and sales tax? /
MA-07-1.1.1

MA-07-1.1.2

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 real-world problems (e.g., percents, sales tax, discounts, rate).
DOK - 3 / 1.  Fraction Bar (as symbol for division)
2.  Percent
3.  “Of”
4.  Place Value / Week Nine: Review place value and rounding. Introduce conversions 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/fracs.html
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/multiplication/mental/
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/division/mental/
http://mathforum.org/k12/mathtips/division.tips.html
http://www.aaamath.com/B/sub39_x2.htm
http://www.aaamath.com/mul.html
How do you use properties to solve problems?
/
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
MA-07-1.5.2 / 1.  Commutative
2.  Associative
3.  Additive Identity
4.  Multiplicative Identity
5.  Zero Property
6.  Substitution / 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_learning/junior/lessons/maths/factors_1/interface.html?id=f1
http://library.thinkquest.org/20991/alg/factoring.html
http://www.purplemath.com/modules/factnumb.htm
http://sf.factmonster.com/ipka/A0933469.html
http://mathforum.org/dr.math/faq/faq.learn.factor.html
http://amby.com/educate/math/2-1_GCF.html
http://amby.com/educate/math/2-1_LCM.html
http://www.eduplace.com/cgi-bin/schtemplate.cgi?template=/kids/mw/help/eh_popup.thtml&grade=6&chapter=3&lesson=3&title=Prime+Factorization&tm=tmfg0303e
What is an integer?
/
MA-07-1.1.1
MA-07-1.1.2 / 1.  Integer
2.  Opposites
3.  Positive
4.  Negative
5.  Neutral Number / Week Thirteen: Introduce integers and number lines to compare and order. Define all vocabulary terms, discuss applications of integers for the real world.
Week Fourteen: Introduce adding integers.
Week Fifteen: Introduce subtracting integers.
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? /
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 degree equations or inequalities (e.g., 2x+1 = 9, 3x+3 < 9). (Statements and solutions use only non-negative numbers.)
DOK 2 / 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 / 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_learning/junior/lessons/maths/addition_subtraction/index.htm
http://www.purplemath.com/modules/exponent.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 mid-unit 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.
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. /
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 / 1.  Ratio
2.  Equivalent Ratio
3.  Cross Product
4.  Rate
5.  Unit Rate
6.  Proportion
7.  “is/of = %/100”
8.  Congruent Figures
9.  Similar Figures / 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.
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? /

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 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 / 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
18.  Negative Correlation
19.  No Correlation / Week Twenty-Three: Review and create frequency charts and stem-and-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.

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? /

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 / 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 / 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.

How do you determine the area and perimeter of a rectangle?

How do you determine the area and perimeter of a 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? /

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 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

MA-07-3.1.2

MA-07-3.1.2
Students will describe and provide examples of the elements (e.g., sides, vertices, angles, 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
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 / 1.  Sides
2.  Vertices
3.  Angles (Acute, Obtuse, Right)
4.  Perpendicular
5.  Parallel
6.  Intersecting
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 / 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 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/geomath/rev/aandv/MHavnb.html
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/area/index.shtml
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/arearev1.shtml
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/areaandvolumerev1.shtml
http://argyll.epsb.ca/jreed/math9/strand3/3108.htm
http://www.aaamath.com/geo.html
http://www.mhhe.com/math/devmath/aleks/wt-bm/student/olc/graphics/common/media/content/main.htm#0108010129
http://www.mhhe.com/math/devmath/aleks/wt-bm/student/olc/graphics/common/media/content/main.htm#0207010131
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/circlepropertiesrev1.shtml
http://www.mste.uiuc.edu/dildine/heron/triarea.html
http://www.learningwave.com/chapters/tools/circle.html
/ / REVIEW / Weeks Thirty-One through Thirty-Six: Review concepts from the year to date as preparation for state assessment. Students will participate in in-depth activities and applications as review.