Grade 8 Mathematics - Henry County Public Schools
|First Nine Weeks |Second Nine Weeks |Third Nine Weeks |Fourth Nine Weeks |
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|SOL Estimated Time | | | |
| |SOL Estimated Time |SOL Estimated Time |SOL Estimated Time |
|SOL 8.2 4 days | | | |
| |SOL 8.3 |SOL 8.7 13 days |SOL 8.12 9 days |
|SOL 8.5 1 day |(Banking problems) 5 days | | |
| | |SOL 8.9 6 days |Review for 9 Weeks Test 1 day |
|SOL 8.1(b) 3 days |SOL 8.15 | | |
| |(Solving Equations) 7 days |SOL 8.6 6 days |9 Weeks Test 1 day |
|Review converting fractions, | | | |
|decimals, percents 3 days |SOL 8.15 |SOL 8.8 6 days |SOL Review 6 days |
| |(Solving Inequalities) 5 days | | |
|SOL 8.1(c) 5 days | |SOL 8.11 7 days |Flanagan Posttest 2 day |
| |SOL 8.10 5 days | | |
|SOL 8.1(a) (Properties) 5 days | |SOL 8.13 3 days |SOL Review 11 days |
| |SOL 8.18 3 days | | |
|SOL 8.1(a) | |Review for 9 Weeks Test 3 days |SOL Testing Week 5 days |
|(Order of Operations) 4 days |SOL 8.14 5 days | | |
| | |9 Weeks Test 1 day |Enrichment |
|SOL 8.4 2 days |SOL 8.16 8 days | |10 days |
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|SOL 8.3 |SOL 8.17 3 days | | |
|(Percent problems) 5 days | | | |
| |Review for 9 Weeks Test 3 days | | |
|SOL 8.3 | | | |
|(Proportion problems) 8 days |9 Weeks Test 1 day | | |
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|Review for 9 Weeks Test 2 days | | | |
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|9 Weeks Test 1 day | | | |
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BIG IDEA – Number Sense and Computation
STRAND – Number and Number Sense
SOL – 8.1: The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers;
b) recognize, represent, compare, and order rational numbers expressed in scientific notation; and
c) compare and order decimals, fractions, percents, and numbers written in scientific notation.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Expressions are simplified |Students will… |“Ordering Numbers” - ESS –|Tests for Higher |*Glencoe Pre-Algebra - Chapter |Create a Word Wall with Essential |
|Expression |using the order of operations| |page 3 |Standards (TfHS – |1-2, pages 11-15; Student |Vocabulary |
|Exponent |and the properties for |Simplify numerical | |Flanagan) SAB – 8.1 |Workbook – Section 1-2. | |
|Rational Number |operations with real numbers,|expressions containing |“Round Robin” – ESS – page| | |Properties need to include, but are not |
|Order of Operations |i.e., associative, |exponents where the |30 |Check for Understanding|Chapter 1-4 and 1-5, pages |limited to the following: |
|Properties of operations |commutative, and distributive|base is a rational | |- Released SOL Test |22-29: Student Workbook – |Additive Identity Property |
|Scientific Notation |properties. |number and the exponent|“Formula Stations” – ESS –|Items – 8.1 |Sections 1-4 and 1-5. |Multiplicative Identity Property |
|Decimal | |is a positive whole |pages 31 – 33 | | |Additive Inverse Property |
|Fraction | |number, using the order| |SOL Coach – 8.1 |Chapter 5-1, pages 224-228; |Multiplicative Inverse Property |
|Percent | |of operations and |Comparing - | |Student Workbook – Section 5-1. |Multiplicative Property of Zero |
| | |properties of | released SOL | |Commutative Property |
| | |operations with real |6_52_x1.htm#section2 |Test Items –ESS – page |Chapter 6-1, pages 274-278; |Associative Property |
| | |numbers. | |44 |Student Workbook – Section 6-1. |Distributive Property. |
|Continued … | | | | | | |
SOL 8.1 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Facts |A number written in |Recognize, represent, |Comparing - |Jefferson Lab |Chapter 6-1, pages 274-278; |The order of operations is as follows: |
|The order of operations |scientific notation is the |compare, and order | and Number Sense |Student Workbook – Section 6-1. |Complete all operations within grouping |
|defines the order in which |product of two factors: a |rational numbers |mlinecomp.html |Strand | |symbols. If there are grouping symbols |
|operations are performed to |decimal greater than or |expressed in scientific | | |Chapter 6-9, pages 317-319; |within other grouping symbols, do the |
|simplify an expression. |equal to one but less than |notation, using both |Order of Operations - | |Student Workbook – Section- 6-9. |innermost operation first. |
|Scientific notation is used |10 multiplied by a power of|positive and negative | | |Evaluate all exponential expressions. |
|to represent very large or |10. |exponents. |Regents/math/orderop/orderP| |Chapter 9-7, pages 458-461; |Multiply and/or divide in order from |
|very small numbers. | | |rac.htm; | |Student Workbook – Section- 9-7. |left to right. (i.e. [pic] |
| |Numbers can be represented |Compare and order | | |Add and/or subtract in order from left |
| |as decimals, fractions, |fractions, decimals, |orderofoperations.html | | |to right. (i.e. [pic] |
| |percents, and in scientific|percents, and numbers | | |*Curriculum Framework (CF) - | |
|Continued … |notation. |written in scientific | | |pen.k12.va.us | |
| | |notation. | | | | |
| | | | | |*Enhanced Scope & Sequence (ESS)-| |
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SOL 8.1 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | |Scientific Notation – Whole| |Manipulatives – | |
| | | |numbers: | |Number line | |
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| | | |_71fx1.htm; | |Technology – | |
| | | | |Ordering – Smart notebook: | |
| | | |_71gx1.htm | |Gallery: Essentials for | |
| | | |Comparing: | |Educators: Mathematics: Number | |
| | | | |Concept and Operations: Number | |
| | | |_71hx1.htm | |Lines | |
| | | |Decimals: | | | |
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| | | |_71ix1.htm; | | | |
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| | | |_71jx1.htm | | | |
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| | | |“Properties Drill” | | | |
| | | |(PowerPoint) - | | | |
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| | | |math.html#6-12math | | | |
Check for Understanding – Released SOL Test Items – 8.1
1.
[pic]
2.
[pic]
3.
[pic]
4.
[pic]
5.
[pic]
Check for Understanding – Released SOL Test Items – 8.1 CONTINUED …
6.
[pic]
7.
[pic]
8.
Which of the following numbers is the largest ?
A 9.5 x 106
B 8.5 x 106
C 9.2 x 107
D 4.5 x 108
9.
The average distance of Saturn from the Sun is 1,503,000,000 miles. How is this distance expressed in scientific notation?
A 1.503 ( 10-9
B 15.03 ( 108
C 1.503 ( 106
D 1.503 ( 109
Check for Understanding – Released SOL Test Items – 8.1 CONTINUED …
10.
Arrange 50%, [pic], 0.74, from least to greatest.
A 50%, [pic], 0.74
B [pic], 50%, 0.74
C 0.74, 50%, [pic]
D 50%, 0.74, [pic]
BIG IDEA – Number Sense and Computation
STRAND – Number and Number Sense
SOL – 8.2 The student will describe orally and in writing the relationship between the subsets of the real number system.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |All real numbers are either |Students will… |“Organizing Numbers” – ESS-|Tests for Higher |*Glencoe Pre-Algebra – Chapter |Create a Word Wall with Essential |
|real numbers |rational or irrational but | |pages 4-8 |Standards (TfHS – |5-1, pages 224-228; Chapter |Vocabulary |
|rational numbers |not both. |Identify the subsets of | |Flanagan) SAB – 8.2 |13-3, pages 672-675: | |
|irrational numbers | |the real number system to|Practice Identifying - | |Student Workbook – Section 5-1 |CF –A visual representation of the |
|integers |The set of rational numbers |which a given number | for Understanding |and 13-3 - |relationships between the subsets of the |
|whole numbers |includes decimals that repeat|belongs. |.uk/interactive/ttaaudits/s|- Released SOL Test | |real number system is essential to |
|natural numbers |or terminate, fractions, | |ect_a1/default.htm |Items – 8.2 | |understanding. |
|Facts |mixed numbers, natural |Describe each subset of | | |*Curriculum Framework (CF) - | |
| |numbers, whole numbers, and |the set of real numbers. | |SOL Coach – 8.2 |pen.k12.va.us | |
|The set of real numbers is |integers. | | | | | |
|the set of all rational and| |Illustrate the | |Jefferson Lab – Number |*Enhanced Scope & Sequence (ESS)-| |
|irrational numbers. |The set of irrational numbers|relationships among the | |and Number Sense Strand | | |
| |includes only decimals that |subsets of the real | | |pen.k12.va.us | |
|Continued … |are nonrepeating and |number system by using | | | | |
| |nonterminating. |graphic organizers. | | | – | |
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| | | | | |Manipulatives –graphic organizers| |
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SOL 8.2 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|An irrational number cannot | | | | | | |
|be expressed as an integer or| | | | | | |
|the quotient of integers. | | | | | | |
Check for Understanding – Released SOL Test Items – 8.2
1.
[pic]
2.
[pic]
3.
[pic]
BIG IDEA – Number Sense and Computation
STRAND – Computation and Estimation
SOL – 8.3: The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such a finding a discount and discount prices and balancing a checkbook.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A percent is a special |Students will… |“Playground Problem” - ESS – |Tests for Higher |*Glencoe Pre-Algebra - |Create a Word Wall with Essential |
|Percent |ratio in which the | |pages 9 - 13 |Standards (TfHS – |Chapter 9-9, pages 467 - |Vocabulary |
|Discount |denominator is 100. |Select an appropriate method | |Flanagan) SAB – 8.3 |471; Student Workbook – | |
|Discount Price | |or methods for computing with|“Dividing Fractions, Using | |Section 9-9 |CF - Solving multistep problems in|
|Sales Tax |Common uses of percents in |rational numbers and percents|Pattern Blocks” – ESS – pages|Check for Understanding | |the context of real-life |
|Gratuity |everyday life include |according to the context of |17 – 19 |- Released SOL Test |Chapter 9-4, pages 444 – 447;|situations enhances |
|Simple Interest |discounts, sales tax, and |the problem. | |Items – 8.3 |Student Workbook – Section |interconnectedness and proficiency|
|Installment Buying |simple interest. | |“Ratio, Proportion, and | |9-4 |with calculating percents of |
|Checkbook | |Compute a discount and the |Percent” – ESS – pages 20 – |SOL Coach – 8.3 | |numbers. |
|Checkbook Registry |A checkbook registry is a |resulting (sale) price for |23 | |Chapter 9-5, pages 449 – 453;| |
|Ratio |record of daily financial |one discount. | |Jefferson Lab |Student Workbook – Section | |
|Proportion |transactions. | |“Spending Money” – ESS – |Number and Number Sense |9-5 | |
|Similar Figures | |Compute the cost of an item |pages 24 – 26 |Strand | | |
|Scale |A proportion is a statement|including sales tax. | | |Chapter 11-6; pages 578 – | |
| |of equality of two or more | |Simple interest - |Sample Released SOL Test|583; Student Workbook – | |
|Continued … |ratios. |Compute the amount of a | – ESS – page 122 -|Section 11-6 - | |
| | |paycheck after deductions. |mple-interest-prin.html |124 | | |
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SOL 8.3 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Facts |Given the relationship |Compute the gratuity |F/D/P - | |*Curriculum Framework (CF) - |CF - Examples of real-life situations |
|Mathema-tics relates to |between two items, a |amount and the total | |pen.k12.va.us |may include, but not be limited to, |
|problems in daily life. |proportion can be set up to|amount of a bill at a |lessons/vol4/challenge_vol4| | |those related to economics, sports, |
| |solve many real-life |restaurant. |.html | |*Enhanced Scope & Sequence (ESS)-|science, social sciences, |
| |problems. | | | | |transportation, and health. Some |
| | |Compute simple interest |Real-life problem - | |pen.k12.va.us |examples include problems involving the |
| | |on a savings account or | | |amount of a paycheck per month, the |
| | |on an installment loan. |h/pizza.html | |Manipulatives – checkbook |discount price on a product, |
| | | | | |register, checks, deposit slips, |temperature, simple interest, sales tax,|
| | |Maintain a checkbook and |Proportions - | |maps, sale fliers |and installment buying. |
| | |check registry for five | | | |
| | |or fewer transactions. |proportions/proportions.htm| |Technology – | |
| | | | | |F/D/P - | |
| | |Determine if two ratios | – | |Smart Notebook: Gallery: | |
| | |form a proportion. | |Essential for Educators: | |
| | | |nmatthews | |Mathematics: Number Concepts and | |
| | |Set up a proportion and | | |Operations: Fractions; | |
| | |solve for the missing | | | | |
| | |variable. | | |Proportions – Smart Notebook: | |
| | | | | |Gallery: Essentials for | |
| | | | | |Educators: Mathematics: Shapes, | |
| | | | | |Space, and Measure: Maps and | |
| | | | | |plans | |
Check for Understanding – Released SOL Test Items – 8.3
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[pic]
2.
[pic]
3.
[pic]
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[pic]
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[pic]
Check for Understanding – Released SOL Test Items – 8.3 – CONTINUED …
6.
[pic]
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[pic]
8.
[pic]
Check for Understanding – Released SOL Test Items – 8.3 - CONTINUED …
9.
If the regular price is $900 and the discount rate is 30%, what is the sale price?
A $630
B $870
C $873
D $897
10.
If the principal is $4,500 and the rate of interest is 8% (compounded annually), what is the amount of interest after one year?
A $1,800
B $800
C $720
D $360
BIG IDEA – Number Sense and Computation
STRAND – Computation and Estimation
SOL – 8.4: The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Problems will be limited to positive exponents.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Algebraic expressions are |Students will… |“Patterns on Powers” - ESS|Tests for Higher |*Glencoe Pre-Algebra - Chapter |Create a Word Wall with Essential |
| |evaluated by replacing the | |– pages 27-28 |Standards (TfHS – |1-3, pages 16-20; Student |Vocabulary |
|Variable |variables with numbers and |Substitute given numbers| |Flanagan) SAB – 8.4 |Workbook – Section 1-3 | |
|Replacement Value |applying the order of |for variables in an |“The Language of Algebra: | | |Refer back to SOL 8.1 Order of |
|Facts |operations to simplify the |algebraic expression and|Order of Operations” – ESS|Check for Understanding| |Operations. |
| |resulting expression. |simplify the expression |– page 29 |- Released SOL Test |*Curriculum Framework (CF) - | |
|Algebraic expressions use | |by using the order of | |Items – 8.4 |pen.k12.va.us |Emphasize the following concept: |
|operations with algebraic |The replacement values are |operations. |“Round Robin” – ESS – page| | |If a = 2 and b = 4, |
|symbols (variables). |the numbers that replace the | |30 |SOL Coach – 8.4 |*Enhanced Scope & Sequence |then ab = [pic], |
| |variables in an algebraic | | | |(ESS)- |NOT the number 24. |
| |expression. | |“Formula Stations” – ESS –|Jefferson Lab – |pen.k12.va.us | |
| | | |pages 31 - 33 |Computation and | | |
| | | | |Estimation Strand | – | |
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Check for Understanding - Released SOL Test Items – 8.4
1.
Evaluate: a + 4(b ( 3)
if a=15, b=12
A 51
B 60
C 75
D 171
2.
Let s=12 and t=6. What is [pic] ?
A 6
B 8
C 24
D 32
3.
[pic]
4.
[pic]
5.
[pic]
Check for Understanding – Released SOL Test Items – 8.4 – CONTINUED …
6.
[pic]
BIG IDEA – Number Sense and Computation
STRAND – Computation and Estimation
SOL – 8.5 – The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A perfect square is a squared |Students will… |“Perfectly Squared” – ESS|Tests for Higher |Glencoe Pre-Algebra – |Create a Word Wall with Essential |
| |whole number whose square root| | |Standards (TfHS) – |Chapter 13-1, pages 664 – 668; |Vocabulary. |
|Whole Number |is a whole number. |Identify the perfect |Pages 34 – 36 |Flanagan) |Student Workbook– Section 13-1 | |
|Square of a number | |squares from 0 to 100. | |SAB 8.5 | | |
|Square Root |Any whole number that is not a| | | | |
|Consecutive |perfect square has a square |When given a whole number |h_help/games/numbercop/nu|Check for Understanding|Curriculum Framework (CF) – | |
|Irrational Number |root that lies between two |between 0 and 100 that is |mbercop_hotmath.swf |- Released SOL Test |pen.k12.va.us | |
|Perfect Square |consecutive whole numbers. |not a perfect square, | |Items – 8.5 | | |
| | |identify the two |Glencoe Pre-Algebra – TE | |Enhanced Scope & Sequence (ESS) –| |
|Facts | |consecutive whole numbers |Alternative Learning |SOL Coach – 8.5 | | |
| | |between which the square |Styles – page 664 | |pen.k12.va.us | |
|If a whole number is not a | |root of that whole number | |Jefferson Lab – | | |
|perfect square, then its square| |lies. |Glencoe Pre-Algebra – TE |Computation and | – | |
|root is an irrational number. | | |Group Activity Card – |Estimation Strand | |
| | | |page 667 | |nmatthews | |
| | | | |Sample Released SOL | | |
|Continued … | | | |Test Items – ESS – page|Perfect Squares Chart | |
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| | | | | |tiles, spinners, grid paper, | |
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SOL 8.5 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | | | |Technology – | |
| | | | | |Smart Notebook: Gallery: | |
| | | | | |Essentials for Educators: | |
| | | | | |Mathematics: Number Concept and | |
| | | | | |Operations: Number Lines | |
Check for Understanding - Released SOL Test Items – 8.5
1.
[pic]
2.
[pic]
3.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Measurement
SOL – 8.6 – The student will verify by measuring and describe the relationships among vertical angles, supplementary angles, and complementary angles and will measure and draw angles of less than 360°.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Angles are named by their |Students will… |“What Does a Name Measure |Tests for Higher |*Glencoe Pre-Algebra- Chapter |Create a Word Wall with |
|Angle |defining attributes. | |Up To?” - ESS – pages 47 |Standards (TfHS – |11-3, pages 561 - 566; Student |Essential Vocabulary |
|Degree | |Measure angles of less | |Flanagan) SAB – 8.6 |Workbook – Section 11-3 - | |
|Vertical angles |Two intersecting lines form |than [pic]to the nearest |“What’s Your Angle?” – ESS| | |CF - Estimation skills are |
|Complementary angles |angles that have |degree, using appropriate|– pages 48 – 51 |Check for Understanding -| |developed in determining angle |
|Supplementary angles |relationships. |tools. | |Released SOL Test Items –|*Curriculum Framework (CF) - |measure. |
|Facts | | |Measuring Angles: |8.6 |pen.k12.va.us | |
| | |Identify and describe the| | | |
|The rays and vertex of an angle are| |relationships between the|11.xml |SOL Coach – 8.6 |*Enhanced Scope & Sequence (ESS)-| |
|used to name that angle. | |angles formed by two | | | | |
| | |intersecting lines. |Measuring Angles: |Jefferson Lab – |pen.k12.va.us | |
| | | | Strand | | |
| | |Identify and describe |de7/Math/MeasureGeo/Measur| |* – | |
| | |pairs of angles that are |ingAngles.htm |Sample Released SOL Test | |
| | |vertical. | |Items – ESS – page 55-56 |nmatthews | |
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| | | | | |Manipulatives –protractor, ruler | |
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|Continued … | | | | | | |
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SOL 8.6 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | |Identify and describe |AAA Math – Complementary/ | |Technology – | |
| | |pairs of angles that are |Supplementary Angles: | |SMART Notebook – Gallery: | |
| | |complementary. | |Essentials for Educators: | |
| | | |aaamath/geo-comp-or-sup.htm| |Mathematics: Shapes, Space and | |
| | |Identify and describe | | |Measure: Angles | |
| | |pairs of angles that are |Complementary Angles | | | |
| | |supplementary. |(3 activities): | | | |
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| | | |8.html | | | |
Check for Understanding - Released SOL Test Items – 8.6
1.
[pic]
2.
[pic]
3.
[pic]
4.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Measurement
SOL – 8.7 - The student will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones, and pyramids.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Volume and surface area are|Students will… |“Pyramids, Prisms, and |Tests for Higher |*Glencoe Pre-Algebra |Create a Word Wall with Essential |
|Square |found on 3-D figures. | |Cones – Oh, My!” - ESS – |Standards (TfHS – |S.A. Prisms – Ch. 12-5, pgs. 632 |Vocabulary |
|Rectangle | |Compute the perimeter and|pages 52 – 54 |Flanagan) SAB – 8.7 |– 637; Student Workbook 12-5; | |
|Triangle |Volume and surface area are|area of squares and | | |V. Prisms – Ch. 12-7, pgs. 644 – |CF – Physical experiences in measuring |
|Circle |different; volume involves |rectangles. |“Formula Stations” – ESS – |Check for Understanding |648; Student Workbook 12-7; |various objects promote the long-term |
|Area |filling a container, while | |pages 31 - 33 |- Released SOL Test | |retention and understanding of |
|Perimeter |surface area involves the |Compute the area of | |Items – 8.7 |S.A. Cylinders – Ch. 12-5. pgs. |measurement. |
|Radius |total area of the surfaces |triangles and circles. |Glencoe Pre-Algebra – | |634 – 637; | |
|Diameter |of the figure. | |Lesson 12-7A Volume, page |SOL Coach – 8.7 |Student Workbook 12-5; |Student should be able to find the |
|Height | |Compute the surface area |643 | |V. Cylinders – Ch. 12-7, pgs. 645|surface area and volume of square, |
|Slant Height | |of a pyramid by finding | |Jefferson Lab – |– 648; Student Workbook 12-7; |rectangular, and triangular pyramids. |
|Base | |the sum of the areas of |Surface Area and Volume of |Measurement Strand | | |
|Face | |the triangular faces and |Rectangular Prisms - | |S.A. Cones – Ch. 12-6, pgs. 640 –| |
|Pi | |the base. | Released SOL Test|642; Student Workbook 12-6; | |
|Volume | | |activate/activities/Surface|Items – ESS – page 56 - |V. Cones – Ch. 12-8, pgs. 650 – | |
|Surface Area | | |AreaAndVolume/ |58 |653; Student Workbook 12-8; | |
|Prism | | | | | | |
|Cone | | | | | | |
|Cylinder | | | | | | |
|Pyramid | | | | | | |
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|Continued … | | | | | | |
SOL 8.7 - CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Facts |Understanding the |Compute the volume and |Glencoe Pre-Algebra TE – | |S.A. Pyramids – Ch. 12-6, pgs. | |
|A polyhedron is a solid |derivation of formulas for |surface area of |S.A. of cylinders - | |638 – 642; Student Workbook 12-6;| |
|figure whose faces are all |volume and surface area of |rectangular solids |Alternative Learning Styles| |V. Pyramids – Ch. 12-8, pgs. 649 | |
|polygons. |prisms, cylinders, cones, |(prisms), cylinders, |– page 632 | |– 653; Student Workbook 12-8 | |
| |and pyramids enhances |cones and square | | | | |
| |ability to use the |pyramids, using formulas.| | | | |
| |formulas. | | | |*Curriculum Framework (CF) - | |
| | |Investigate and solve | | |pen.k12.va.us | |
| | |problems involving volume| | | | |
| | |and surface area of | | |*Enhanced Scope & Sequence (ESS)-| |
| | |rectangular solids | | | | |
| | |(prisms), cylinders, | | |pen.k12.va.us | |
| | |cones and pyramids. | | | | |
| | | | | | – | |
| | | | | | |
| | | | | |nmatthews | |
| | | | | | | |
| | | | | |Manipulatives – net patterns, | |
| | | | | |solid figures, real life examples| |
| | | | | |e.g. soup can = cylinder | |
| | | | | | | |
| | | | | | | |
|Continued … | | | | | | |
SOL 8.7 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | | | |Technology – | |
| | | | | |SMART Notebook – Gallery: | |
| | | | | |Essentials for Educators: | |
| | | | | |Mathematics: Shapes, Space, | |
| | | | | |Measure: Shapes: Solid Shapes | |
Check for Understanding - Released SOL Test Items – 8.7
1.
[pic]
2.
[pic]
3.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Geometry
SOL – 8.8 - The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art, and scaling.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |The rotation of a figure |Students will… |“Transformation-ally |Tests for Higher |*Glencoe Pre-Algebra |Create a Word Wall with Essential |
|Transfor-mation |can be made clockwise or | |Speaking” - ESS – pages 60 |Standards (TfHS – |- Translations, Reflections, |Vocabulary |
|Translation |counterclockwise around a |Identify the geometric |- 63 |Flanagan) SAB – 8.8 |Rotations Chapter 11-9, pages 595| |
|Reflection |fixed point. |transformations | | |- 599; Student Workbook – Section|CF - Real-life applications may include |
|Rotation | |(translation, reflection,|Glencoe Pre-Algebra TE – |Check for Understanding |11-9; |the following: |
|Dilation |Each point on a reflected |rotation or dilation) by |Group Activity Card – page |- Released SOL Test |Dilations – Chapter 11-6, page |- A rotation of the hour hand of a clock|
|Scale |figure is the same distance|using a variety of |598 |Items – 8.8 |578; |from 2:00 to 3:00 shows a turn of [pic] |
| |from the line of reflection|real-life examples. | | | |clockwise. |
|Facts |as the corresponding point | |Natural Library of Virtual |SOL Coach – 8.8 | |- A reflection of a boat in water shows |
| |on the original figure. |Demonstrate the |Manipulatives - | |*Curriculum Framework (CF) - |an image of the boat flipped upside down|
|The fixed point about which a| |reflection of a figure |Composition, Dilation, |Jefferson Lab – Geometry|pen.k12.va.us |with the water line being the line of |
|figure is rotated is called |All the points in a |over a vertical or |Reflection, Rotation, |Strand | |reflection. |
|the center of rotation. |translation move exactly |horizontal line on a |Translation: | |*Enhanced Scope & Sequence (ESS)-|- A translation of a shape on a |
| |the same distance in the |coordinate grid. | Released SOL Test| |wallpaper pattern shows the same shape |
| |same direction. | |category_g_3_t_3.html |Items – ESS – page 66 - |pen.k12.va.us |slid the same distance in the same |
| | | | |67 | |direction. |
| | | | | | – |- A dilation of a model airplane is the |
|Continued … | | | | | model of the airplane. |
| | | | | |nmatthews | |
| | | | | | | |
| | | | | |Manipulatives – graph paper, | |
| | | | | |geomirrors | |
SOL 8.8 - CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| |A dilation changes the size|Demonstrate [pic], [pic],|Dilations – | |Technology – | |
|The line across which a |of a figure by a scale |[pic], and [pic]rotations| |SMART Notebook – graph paper – | |
|figure is reflected is called|factor and creates a |of a figure on a |WebLessons/SamsSim| |Gallery: Essentials for | |
|the line of reflection. |similar figure. |coordinate grid. |ilarShapes/default.htm | |Educators: Mathematics: General | |
| | | | | |Resources: Paper Backgrounds | |
| |A relationship exists |Demonstrate the |Transmographer - | | | |
| |between transformations in |translation of a figure | | | |
| |a coordinate plane and |on a coordinate grid. |activate/activities/Transmo| | | |
| |their applications in | |grapher/ | | | |
| |real-life. |Demonstrate the dilation | | | | |
| | |of a figure from a fixed |Transmographer 2 | | | |
| | |point on a coordinate | | | |
| | |grid. |activate/activities/Transmo| | | |
| | | |grapherTwo/ | | | |
| | | | | | | |
Check for Understanding - Released SOL Test Items – 8.8
1.
[pic]
2.
[pic]
3.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Geometry
SOL – 8.9 - The student will construct a three-dimensional model, given the top, side, and/or bottom views.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A three-dimensional object |Students will… |“2-D to 3-D and Back Again”|Tests for Higher |*Curriculum Framework (CF) - |Create a Word Wall with Essential |
|Three-dimensional |can be represented as a | |- ESS – pages 64 - 65 |Standards (TfHS – |pen.k12.va.us |Vocabulary |
|View |two-dimensional model that |Construct | |Flanagan) SAB – 8.9 | | |
| |represents views of the |three-dimensional |3-D Object Viewer- | |*Enhanced Scope & Sequence (ESS)-|CF – Three-dimensional models of |
|Facts |object from different |models, given top, side| for Understanding | |geometric solids can be used to |
| |perspectives. |and/or front or bottom |ingen/00200/toepassing_wisw|- Released SOL Test |pen.k12.va.us |understand perspective and provide |
|Three-dimensional models of | |views. |eb.en.html |Items – 8.9 | |tactile experiences in determining |
|geometric solids can be | | | | | – |two-dimensional perspectives. |
|represented on isometric | |Identify a |Colouring sides 1- |SOL Coach – 8.9 | |
|paper. | |three-dimensional | |nmatthews | |
| | |figure given top, side |ingen/00207/toepassing_wisw|Jefferson Lab – Geometry| | |
| | |and front views of the |eb.en.html |Strand |Manipulatives – | |
| | |figure. | | |Isometric paper,cubes (paper, | |
| | | |Colouring sides 2- | |wooden, or plastic) | |
| | | | | | |
| | | |ingen/00208/toepassing_wisw| |Technology – | |
| | | |eb.en.html | |SMART Notebook – isometric paper | |
| | | | | |- Gallery: Essentials for | |
| | | | | |Educators: Mathematics: General | |
| | | | | |Resources: Paper Backgrounds | |
|Continued … | | | | | | |
SOL 8.9 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | |Rotating houses – | | |. |
| | | | | | |
| | | |ingen/00247/toepassing_wisw| | | |
| | | |eb.en.html | | | |
| | | | | | | |
| | | |Guess the view – | | | |
| | | | | | |
| | | |ingen/00198/toepassing_wisw| | | |
| | | |eb.en.html | | | |
| | | | | | | |
| | | |Plot Plans and Silhouettes | | | |
| | | |– | | | |
| | | | | | |
| | | |herslab/math/geometry/space| | | |
| | | |/plotplan/index.html | | | |
Check for Understanding - Released SOL Test Items – 8.9
1.
[pic]
2.
[pic]
3.
Which solid is represented by these views?
A
B
C
D
BIG IDEA – Algebra and Functions
STRAND – Geometry
SOL – 8.10: The student will
a) verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement; and
b) apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |In a right triangle, the |Students will… |“The Pythagorean Theorem” -|Tests for Higher |*Glencoe Pre-Algebra-- Chapter |Create a Word Wall with Essential |
| |square of the length of the | |ESS – pages 37 - 39 |Standards (TfHS – |13-4, pages 676 - 681; Student |Vocabulary |
|right angle |hypotenuse equals the sum of |Identify the parts | |Flanagan) SAB – 8.10 |Workbook – Section – 13-4 | |
|right triangle |the squares of the legs |of a right triangle |“Pythagoras of Samos” – ESS| | |CF - Examples of real-life situations |
|legs (altitude and base) |(altitude and base). |(the hypotenuse and |– pages 40 - 42 |Check for Understanding | |solved by using the Pythagorean Theorem |
|hypotenuse | |the legs). | |- Released SOL Test |*Curriculum Framework (CF) - |enhance proficiency with this skill. |
|Pythagorean Theorem |Whole number triples that are| | – 8.10 |pen.k12.va.us | |
|Pythagorean triples |the measures of the sides of |Verify the |activate/activities/Pythago| | |An effective visual proof of the |
| |right triangles, such as |Pythagorean Theorem,|reanExplorer/ |SOL Coach – 8.10 |*Enhanced Scope & Sequence (ESS)-|Pythagorean Theorem involves using |
|Facts |(3,4,5), (6,8,10), |using diagrams, | | | |post-it notes as the unit blocks of the |
|The square of the measure of the |(9,12,15), and (5, 12, 13), |concrete materials, | |Jefferson Lab – |pen.k12.va.us |squares of each side of the right |
|hypotenuse equals the sum of the |are commonly known as |and measurement. | |Geometry Strand | |triangle. The post-it notes from the |
|squares of the measures of the |Pythagorean triples. | | | | – |legs are placed over the post-it notes |
|base and altitude. | | | |Sample Released SOL Test| the hypotenuse to show the sum of the|
| | | | |Items – ESS – page 45 |nmatthews |squares of the legs is equal to the |
|Continued … | | | | | |square of the hypotenuse. |
| | | | | |Manipulatives – | |
| | | | | |Post-it notes, geoboards, rubber | |
| | | | | |bands | |
| | | | | | | |
SOL 8.10 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|The Pythagorean Theorem is a | |Find the measure of a | | |Technology - Smart Notebook: | |
|tool to find the measure of | |side of a right | | |Gallery: Essentials for | |
|any side of a right triangle, | |triangle, given the | | |Educators: Mathematics: Shapes, | |
|given the measures of the | |measures of the other | | |Space and Measure: Area | |
|other two sides. | |two sides. The | | | | |
| | |measures of the sides | | | | |
| | |of the triangle may be | | | | |
| | |whole numbers no larger| | | | |
| | |than 15 or decimals in | | | | |
| | |tenths. | | | | |
| | | | | | | |
| | |Solve real-life | | | | |
| | |problems involving | | | | |
| | |right triangles by | | | | |
| | |using the Pythagorean | | | | |
| | |Theorem. | | | | |
Check for Understanding – Released SOL Test Items – 8.10
1.
[pic]
2.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Probability and Statistics
SOL – 8.11 - The student will analyze problem situations, including games of chance, board games, or grading scales, and make predictions, using knowledge of probability.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Choices that involve chance |Students will… |“The Game Show Problem” - |Tests for Higher |*Glencoe Pre-Algebra- Chapter |Create a Word Wall with Essential |
|Sample Space |are based on an understanding| |ESS – pages 71 - 72 |Standards (TfHS – |9-3, pages 440 - 443; Student |Vocabulary |
|Outcome |of the reasonableness of |Analyze a problem | |Flanagan) SAB – 8.11 |Workbook – Section 9-3; | |
|Event |obtaining a specific outcome.|situation, and |“Well, What Did You | |Lesson 9-3A, page 439; |CF - Exploring experimental and |
|Prediction | |determine the |Expect?” – ESS – pages 73 -|Check for Understanding | |theoretical probability is enhanced |
|Probability | |likelihood of an event |74 |- Released SOL Test | |through experiments and simulations with|
|Theoretical probability |Predictions may be made based|occurring, using | |Items – 8.11 |*Curriculum Framework (CF) - |concrete, active learning activities. |
|Experimental Probability |on knowledge of probability. |knowledge of |“Making Predictions” – | |pen.k12.va.us | |
|Impossible | |probability. |Glencoe Pre-Algebra – |SOL Coach – 8.11 | |CF – The knowledge of probability can be|
|Less Likely | | |Lesson 10-8B, page 529 | |*Enhanced Scope & Sequence (ESS)-|used to determine the likelihood of |
|Equally Likely | |Predict the outcome of | |Jefferson Lab – | |winning such events as contests. |
|More Likely | |an event by analyzing |Basic Probability Video - |Probability and |pen.k12.va.us | |
|Certain | |its probability. | Strand | |If time permits, the concepts of |
| | | |com/Media/education/basicpr| | – |Independent and Dependent Events may be |
|Facts | |Explain the |obability.html | | to further the students’ |
| | |consequences of making | | |nmatthews |knowledge of the skill: |
|The probability that an event is | |different choices, | | | |Glencoe Pre-Algebra – Chapter 10-9, |
|likely to occur is close to one. | |using knowledge of | | |Manipulatives – dice, deck of |pages 530 – 534. |
| | |probability. | | |cards, spinners, marbles, coins | |
|Continued … | | | | | | |
SOL 8.11 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|The probability that an event| |Make predictions about |Adjustable Spinner - | |Technology – | |
|is not likely to occur is | |the outcomes of games of | |SMART Notebook – manipulatives – | |
|close to zero. | |chance, board games, and |activate/activities/Adjusta| |Gallery: Essentials for | |
|The probability that an event| |grading scales by using |bleSpinner/ | |Educators: Mathematics: | |
|is as likely to occur as it | |knowledge of probability.| | |Statistics and Probability AND | |
|is not to occur is close to | | |Spinner - | |Currency | |
|one-half. | | | | | |
| | | |urces.co.uk/mathspack2/pspi| | | |
| | | |n/pspin1.html | | | |
| | | | | | | |
| | | |Marbles – | | | |
| | | | | | |
| | | |activate/activities/marbles| | | |
| | | |/ | | | |
| | | | | | | |
| | | |The Winning Edge: | | | |
| | | |Probability in Basketball -| | | |
| | | | | | |
| | | |s/lessons/robin/winedge2.ht| | | |
| | | |ml | | | |
Check for Understanding - Released SOL Test Items – 8.11
1.
[pic]
2.
[pic]
3.
[pic]
4.
[pic]
5.
[pic]
BIG IDEA – Statistics
STRAND – Probability and Statistics
SOL – 8.12 - The student will make comparisons, predictions, and inferences, using information displayed in frequency
distributions; box-and-whisker plots; scattergrams; line, bar, circle, and picture graphs; and histograms.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Comparisons, predictions, and|Students will… |“Data Mania” - ESS – pages 75|Tests for Higher |*Glencoe Pre-Algebra- |Create a Word Wall with Essential |
|Comparison |inferences are made by | |- 78 |Standards (TfHS – |Frequency distributions – Chapter |Vocabulary |
|Prediction |examining characteristics of |Make comparisons, | |Flanagan) SAB – 8.12 |1-10, pages 51 – 55; Student | |
|Inference |a data set displayed in a |predictions, and |“Vashon-Maury Island Soil | |Workbook – Section 1-10; |CF – The information displayed in |
|Frequency distribution |variety of graphical |inferences, given data |Study” – ESS – pages 80 - 88 |Check for Understanding| |different graphs may be examined to |
|Box-and-Whisker Plot |representations in order to |sets of no more than 20| |- Released SOL Test |Box and Whisker Plots – Chapter |determine how data are or are not |
|Scattergram (scatterplot) |draw conclusions. |items that are |Glencoe Pre-Algebra – |Items –8.12 |10-3, pages 495 – 501; Student |related, ascertaining differences |
|Line graph | |displayed in frequency |“Send-A-Problem”, page 51 | |Workbook – Section 10-3; |between characteristics (comparisons),|
|Bar graph | |distributions; | |SOL Coach – 8.12 | |trends that suggest what new data |
|Circle graph | |box-and-whisker plots; |Glencoe Pre-Algebra – | |Scattergrams - |might be like (predictions), and/or |
|Picture graph | |scattergrams; line, |“Jigsaw”, page 499 |Jefferson Lab – |Chapter 8-2, pages 379 - 383; |“what could happen if” (inferences). |
|Histogram | |bar, circle, and | |Probability and |Student Workbook – Section 8-2; | |
| | |picture graphs; and |Create a Graph – |Statistics Strand | |CF – Scattergrams can be used to |
| | |histograms. | |Line graphs – |predict trends and estimate a line of |
| | | |reateagraph/default.aspx?ID=5|Sample Released SOL |Chapter 10-3, pages 497 – 498; |best fit. |
| | | |b2318af41224d0cb99d73aa9b5148|Test Items – ESS – page| | |
|Continued … | | |77 |91 | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
SOL 8.12 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Facts | | |Practice Graph Problems – | |Bar graphs – | |
| | | | |Chapter 1-10, pages 52 – 55; | |
|The line of best fit for a | | |ra/readtext.asp?txtfile=com| | | |
|scattergram describes the trend | | |munications/charts/exercise| |Circle graphs – | |
|of the data. | | |03.txt | |Chapter 10-3, page 497; Chapter | |
|A box-and-whisker plot divides | | | | |11-2, pages 556 – 559; Student | |
|the data into 4 sections, each | | |Understanding and | |Workbook – Section 11-2; | |
|section containing 25% of the | | |Interpreting Graphs: Lesson| | | |
|data. | | |10 - | |Picture graphs – | |
| | | | |Chapter 10-3, pages 497, 500; | |
| | | |Launch.aspx?content=%2fcont| | | |
| | | |ent%2fmesg%2fhtml%2fmath6we| |Histograms – | |
| | | |b%2fmath6shell.html | |Chapter 10-3B, pages 502 – 503; | |
| | | | | | | |
| | | |Box and Whisker Plots – | | | |
| | | | | | |
| | | |activate/activities/boxplot| |*Curriculum Framework (CF) - | |
| | | |/ | |pen.k12.va.us | |
|Continued … | | | | | | |
| | | | | |*Enhanced Scope & Sequence (ESS)-| |
| | | | | | | |
| | | | | |pen.k12.va.us | |
SOL 8.12 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | |Scatter Plots – | |Manipulatives – graph paper, | |
| | | | |ruler | |
| | | |activate/activities/Scatter| | | |
| | | |Plot/ | |Technology – | |
| | | | | |SMART Notebook – Line, Bar and | |
| | | | – | |Circle Graphs examples - Gallery:| |
| | | | |Essentials for Educators: | |
| | | |nmatthews | |Mathematics: Statistics and | |
| | | | | |Probability: Graphing; | |
| | | | | | | |
| | | | | |SMART Notebook – making graphs | |
| | | | | |-Gallery: Essentials for | |
| | | | | |Educators: Mathematics: General | |
| | | | | |Resources: Tools: Mathematical | |
| | | | | |Toolkit Coordinates and Graphing | |
Check for Understanding - Released SOL Test Items – 8.12
1.
[pic]
2.
[pic]
3.
[pic]
Check for Understanding – Released SOL Test Items – 8.12 – CONTINUED …
4.
[pic]
5.
[pic]
6.
[pic]
BIG IDEA – Geometry and Probability
STRAND – Probability and Statistics
SOL – 8.13 - The student will use a matrix to organize and describe data.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A matrix is a rectangular |Students will… |“Homework, TV, and Sleep” -|Tests for Higher |*Curriculum Framework (CF) - |Create a Word Wall with Essential |
| |array of numbers in rows | |ESS – page 79 |Standards (TfHS – |pen.k12.va.us |Vocabulary |
|Matrix |and columns that organizes |Describe the | |Flanagan) SAB – 8.13 | | |
|Row |a data set visually. |characteristics of a |“The Matrix” – ESS – pages | |*Enhanced Scope & Sequence (ESS)-|CF - Matrices are used to sort, list and|
|Column | |matrix, including |89 - 90 |Check for Understanding | |organize data, such as sorting by gender|
|Entry | |designating labels for | |- Released SOL Test |pen.k12.va.us |the number of soccer, football, |
|Dimension | |rows and columns. |PowerPoint presentation - |Items – 8.13 | |basketball, and softball players in a |
|Order | | | | – |set. |
| | |Use a matrix of no more |math.html#6-12math |SOL Coach – 8.13 | |
|Facts | |than 12 entries to |(scroll to “Grades 6- 12”) | |nmatthews |The size (order) of a matrix is |
| | |organize and describe a | |Jefferson Lab – | |expressed in a specific format, rows by |
|The size of a matrix is | |data set. | |Probability and |Lesson on Matrices – |columns. For example, the size of a “3 |
|identified by its dimensions,| | | |Statistics Strand | 4” matrix is written as |
|rows by columns. | |Identify the position of | | |/matrices-lessons.html |3 X 4 and indicates that the matrix has |
|Matrices are enclosed with | |an element by row and | | | |3 rows and 4 columns. |
|brackets. | |column. | | | | |
| | | | | | | |
| | |Transfer data from a | | | | |
| | |chart to a matrix. | | | | |
Check for Understanding - Released SOL Test Items – 8.13
1.
[pic]
2.
[pic]
3.
[pic]
BIG IDEA – Algebra and Functions
STRAND – Patterns, Functions, and Algebra
SOL – 8.14: The student will
a) describe and represent relations and functions, using tables, graphs, and rules; and
b) relate and compare tables, graphs, and rules as different forms of representation for relationships.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A relation is any set of |Students will… |“Graphing Equations and |Tests for Higher Standards |*Glencoe Pre-Algebra - Chapter |Create a Word Wall with Essential |
| |ordered pairs. For each | |Inequalities” - ESS – |(TfHS – Flanagan) SAB – |8-1, pages 372 - 377; Student |Vocabulary |
|Relation |first member (domain), there |Graph in a coordinate |page 99 |8.14 |Workbook – Section -8-1 | |
|Function |may be many second members |plane ordered pairs | | | |Encourage students to relate the x|
|Domain |(range). |that represent a |PowerPoint introduction -|Check for Understanding - |Chapter 8-4, pages - 392 – |value with a move to the right or |
|Range | |relation. | SOL Test Items – |394; Student Workbook – Section|left and the y value with a move |
|Table |A function is a relation in | |s-math.html#6-12math |8.14 |– 8.4 |up or down. |
|Graph |which there is one and only |Write a rule that | | | | |
|Rule |one second member (range) for|represents a relation |Plotting coordinates - |SOL Coach – 8.14 | | |
|Coordinate plane |each first member (domain). |from a table of values.| |*Curriculum Framework (CF) - | |
| | | |eractivate/activities/Gen|Jefferson Lab – Patterns, |pen.k12.va.us | |
|Facts | |Write a table of values|eralCoordinates/ |Functions, and Algebra | | |
| | |from a rule that | |Strand |*Enhanced Scope & Sequence | |
|Different representations, such as | |represents a relation. | | |(ESS)- | |
|tables, graphs, and rules, can be | | | |Sample Released SOL Test |pen.k12.va.us | |
|used to illustrate the same | | | |Items – ESS – page 125 - | | |
|relation. | | | |130 | – | |
|Continued … | | | | | |
| | | | | |m/nmatthews | |
SOL 8.14 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|A function is a one-to-one |As a graph, a function is |Write a table of values |Writing Expressions - | |Manipulatives – | |
|relationship between the |any curve (including |from the graph of ordered| |Graph paper, ruler | |
|domain and range. |straight lines) such that |pairs of a relation. |il/; | | | |
| |any vertical line would | | |Technology – | |
|Some relations are functions;|pass through the curve only|Describe and represent |odules/translat.htm | |Smart Notebook: Gallery: | |
|all functions are relations. |once. |relations and functions, | | |Essentials for Educators: | |
| | |using tables, graphs, and|“Battlegraph” - | |Mathematics: Patterns and | |
| |As a table of values, a |rules. | |Relations: Algebra | |
| |function has a unique value| |math.html#6-12math | | | |
| |assigned to the second |Relate and compare | | |Smart Notebook: Gallery: | |
| |variable (range) for each |different representations| | |Essentials for Educators: | |
| |value of the first variable|of the same relation. | | |Mathematics: Statistics and | |
| |(domain). | | | |Probability: Maps and plans: | |
| | | | | |graphing | |
Check for Understanding – Released SOL Test Items – 8.14
1.
[pic]
2.
[pic]
Check for Understanding – Released SOL Test Items – 8.14 – CONTINUED …
3.
[pic]
4.
[pic]
5.
[pic]
6.
[pic]
BIG IDEA – Algebra and Functions
STRAND – Patterns, Functions, and Algebra
SOL – 8.15 The student will solve two-step equations and inequalities in one variable, using concrete materials, pictorial representations, and paper and pencil.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |To maintain equality, an |Students will… |“Algeblocks and Equation |Tests for Higher |*Glencoe Pre-Algebra - Chapter |Create a Word Wall with Essential |
|Equation |operation that is performed| |Solving” - ESS – page 94 |Standards (TfHS – |7-2, pages 333 - 337; Student |Vocabulary |
|Inequality |on one side of an equation |Solve two-step linear | |Flanagan) SAB – 8.15 |Workbook – Section - 7-2 | |
|Variable |must be performed on the |equations by showing the|“Algeblocks: Solving | | | |
| |other side. |steps and using |Inequalities” – ESS – page |Check for Understanding|Chapter 1-9, pages 46 – 49; | |
|Facts | |algebraic sentences. |95 |- Released SOL Test |Student Workbook – Section – 1-9| |
|In an equation, the equal sign |When both expressions of an| | |Items – 8.15 | | |
|indicates that the value on the |inequality are multiplied |Solve two-step |“Cover-up Problems” – ESS –| |Chapter 3-6, pages 146 – 150; | |
|left is the same as the value on|or divided by a negative |inequalities by showing |pages 96 – 97 |SOL Coach – 8.15 |Student Workbook – Section – 3-6| |
|the right. |number, the inequality sign|the steps and using | | | | |
| |reverses. |algebraic sentences. |“Equations and |Jefferson Lab – |Chapter 3-7, pages 151 – 155; | |
|The same procedures that work | | |Inequalities” – ESS – page |Patterns, Functions, |Student Workbook – Section – 3-7| |
|for equations work for | | |98 |and Algebra Strand | | |
|inequalities. | | | | |Chapter 3-8, pages 156 – 159; | |
| | | |Solving Equations | |Student Workbook – Section – 3-8| |
| | | | | | |
|Continued … | | |Launch.aspx?content=%2fcont| | | |
| | | |ent%2fmesg%2fhtml%2fmath6we| | | |
| | | |b%2fmath6shell.html | | | |
SOL 8.15 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | |Solving Inequalities - | |Chapter 7-6, pages 351 – 354; | |
| | | | |Student Workbook – Section – 7-6 | |
| | | |subject2/practice/S2U3L4/S2| | | |
| | | |U3L4Pract.html | | | |
| | | | | |*Curriculum Framework (CF) - | |
| | | |Equation Buster - | |pen.k12.va.us | |
| | | | | | |
| | | |equations.html | |*Enhanced Scope & Sequence (ESS)-| |
| | | | | | | |
| | | | | |pen.k12.va.us | |
| | | | | | | |
| | | | | | – | |
| | | | | | |
| | | | | |nmatthews | |
| | | | | | | |
| | | | | |Manipulatives – | |
| | | | | |Cups, counters, and equation | |
| | | | | |mats (see Glencoe Pre-Algebra | |
| | | | | |page 333), balance scale | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
|Continued … | | | | | | |
SOL 8.15 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | | | | |Technology – | |
| | | | | |Inequality signs - Smart | |
| | | | | |Notebook: Gallery: Essentials for| |
| | | | | |Educators: Mathematics: General | |
| | | | | |Resources: Symbols | |
| | | | | | | |
| | | | | |Balanced scale – | |
| | | | | |Smart Notebook: Gallery: | |
| | | | | |Essentials for Educators: | |
| | | | | |Mathematics: General Resources: | |
| | | | | |Tools | |
Check for Understanding – Released SOL Test Items – 8.15
1.
[pic]
2.
[pic]
3.
[pic]
4.
[pic]
Check for Understanding – Released SOL Test Items – 8.15 – CONTINUED …
5.
Solve: [pic] + 5 > 17
A t > 120
B t < 120
C t > 220
D t < 220
6.
Solve the following inequality:
-9h + 8 < 80
A h > 8
B h < 8
C h > -8
D h < -8
BIG IDEA – Algebra and Functions
STRAND – Patterns, Function, and Algebra
SOL – 8.16: The student will graph a linear equation in two variables, in the coordinate plane, using a table of ordered pairs.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |A linear equation is an |Students will… |“Graphing Equations and |Tests for Higher |*Glencoe Pre-Algebra- Chapter|Create a Word Wall with Essential |
| |equation in two variables | |Inequalities: The |Standards (TfHS – |8-3, pages 385 - 390; Student|Vocabulary |
|Linear Equation |whose graph is a straight |Construct a table of |Coordinate Plane ” - ESS –|Flanagan) SAB – 8.16 |Workbook – Section – 8-3 | |
|Variable |line. |ordered pairs by |page 99 | | | |
|Ordered pairs | |substituting values for x| |Check for Understanding| | |
|Coordinate plane |Graphing a linear equation |in a linear equation to |Completing x/y tables and |- Released SOL Test |*Curriculum Framework (CF) - | |
|X-axis |requires determining a table|find values for y. |graphing - |Items – 8.16 |pen.k12.va.us | |
|Y-axis |of ordered pairs by | | | | |
|Origin |substituting into the |Plot in the coordinate |Algebra/lines%20and%20dist|SOL Coach – 8.16 |*Enhanced Scope & Sequence | |
|Quadrants |equation values for one |plane pairs (x, y) from |ances/lines.htm | |(ESS)- | |
|Coordinates |variable and solving for the|the table. | |Jefferson Lab – |pen.k12.va.us | |
| |other variable, plotting the| |All types of graph paper -|Patterns, Functions, | | |
| |ordered pairs in the |Connect the ordered pairs| Algebra Strand | – | |
| |coordinate plane, and |to form a straight line. |graph_paper.ht| | |
| |connecting the points to | |m | |com/nmatthews | |
| |form a straight line. | | | | | |
| | | | | |Manipulatives – | |
| | | | | |Graph paper, coordinate plane| |
| | | | | |mats, ruler | |
| | | | | | | |
|Continued … | | | | | | |
SOL 8.16 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| Facts |The axes of a coordinate | |Graphing Linear Equations | |Technology – | |
| |plane are generally labeled| |video - | |Smart Notebook: Gallery: | |
|The graph of a linear |x and y; however, any | | |Essentials for Educators: | |
|equation in two variables is |letters may be used that | |h/dataanalysisandprobabilit| |Mathematics: Statistics and | |
|the set of all ordered pairs |are appropriate for the | |y/graphinglinearequations/ | |Probability: Graphing; | |
|that satisfy the equation. |function. | | | | | |
| | | | | |Smart Notebook: Gallery: | |
| | | | | |Essentials for Educators: | |
| | | | | |Mathematics: Patterns and | |
| | | | | |Relations: Algebra: Maps and | |
| | | | | |plans; | |
| | | | | | | |
| | | | | |Smart Notebook: Gallery: | |
| | | | | |Essentials for Educators: | |
| | | | | |Mathematics: General Resources: | |
| | | | | |Tools | |
Check for Understanding – Released SOL Test Items – 8.16
1.
[pic]
2.
[pic]
BIG IDEA – Algebra and Functions
STRAND – Patterns, Functions, and Algebra
SOL – 8.17 - The student will create and solve problems, using proportions, formulas, and functions.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |Proportions, formulas, and |Students will… |“Ratio, Proportion, and |Tests for Higher Standards|*Glencoe Pre-Algebra |Create a Word Wall with Essential |
|Function |functions are ways to express| |Percent” - ESS – pages 20 |(TfHS – Flanagan) SAB – |- Proportions: Chapter 9-4, |Vocabulary |
|Proportion |relationships mathematically |Write problems that |– 23; |8.17 |pages 444 - 448; Student | |
|Formula |and are tools for solving |require establishing a | | |Workbook – Section 9-4; |CF - Proportional situations are based|
| |problems. |relationship between |“The Scoop on Ice Cream” –|Check for Understanding - |Chapter 11-6, pages 582 – 583; |on multiplicative relationships. |
|Facts | |ratios. |ESS – pages 103 – 106; |Released SOL Test Items – |Student Workbook – Section |Equal ratios result from |
| | | | |8.17 |11-6; |multiplication or division, not from |
|A formula is a statement based on| |Solve problems by using|“Animals Count” - ESS – | |Functions: Chapter 8-1, pages |addition or subtraction. |
|logical mathematical conclusions | |proportions. |pages 107 – 108; |SOL Coach – 8.17 |376 – 377; | |
|or observation and experimental | | | | |Chapter 8-4, pages 392 – 395; |SOLs 8.3, 8.10, and 8.14 introduce and|
|evidence. | |Create problems that |“Snowy Egrets” – ESS – |Jefferson Lab – Patterns, |Student Workbook – Section 8-4;|SOL 8.7 reinforces this SOL 8.17. |
| | |require the use of a |pages 109 – 110; |Functions, and Algebra |Formulas: Chapter 3-4, pages | |
| | |formula. | |Strand |134 – 137; Student Workbook – | |
| | | |“Population Density” – ESS| |Section 3-4; | |
| | |Substitute known values|– pages 111; |Sample Released SOL Test | | |
| | |for variables in a | |Items – ESS – page 121 - | | |
| | |formula. |“Virginia Population |130 | | |
| | | |Density” – ESS – pages 112| |*Curriculum Framework (CF) - | |
| | |Solve a formula by |– 115; | |pen.k12.va.us | |
|Continued … | |using algebraic | | | | |
| | |procedures. | | | | |
| | | | | | | |
SOL 8.17 – CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
| | |Create problems that |“Gridlock” – ESS – pages | |*Enhanced Scope & Sequence (ESS)-| |
| | |involve a functional |116 – 118; | | | |
| | |relationship. | | |pen.k12.va.us | |
| | | |“Waste Paper” – ESS – pages| | | |
| | |Solve problems that |119 – 120; | | – | |
| | |involve functions. | | | |
| | | |Glencoe Pre-Algebra - | |nmatthews | |
| | | |Capture – Recapture - | | | |
| | | |Lesson 9-4 B, page 448 | |Manipulatives – | |
| | | | | |real-life objects, graph paper | |
| | | | | | | |
| | | | | |Technology – | |
| | | | | |Formulas - SMART Notebook – | |
| | | | | |Gallery: Essentials for | |
| | | | | |Educators: Mathematics: Shapes, | |
| | | | | |Space and Measure: Area | |
Check for Understanding - Released SOL Test Items – 8.17
1.
[pic]
2.
[pic]
3.
[pic]
4.
[pic]
BIG IDEA – Algebra and Functions
STRAND – Patterns, Functions, and Algebra
SOL – 8.18: The student will use the following algebraic terms appropriately: domain, range, independent variable, and dependent variable.
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|Vocabulary |The domain is the possible |Students will… |“Independent and Dependent |Tests for Higher |*Glencoe Pre-Algebra- Chapter |Create a Word Wall with Essential |
| |set of all the input values | |Variables” - ESS – pages |Standards (TfHS – |8-1, pages 372 - 376; Student |Vocabulary |
|Domain |for the independent variable|Apply the following |100 - 102 |Flanagan) SAB – 8.18 |Workbook – Section – 8-1 | |
|Range |in a given situation. |algebraic terms | | | | |
|Independent variable | |appropriately: domain,| |Check for Understanding| | |
|Dependent variable |The range is the possible |range, independent | |- Released SOL Test |*Curriculum Framework (CF) - | |
| |set of all the output values|variable, and dependent| |Items – 8.18 |pen.k12.va.us | |
|Facts |for the dependent variable |variable. | | | | |
| |in a given situation. | | |SOL Coach – 8.18 |*Enhanced Scope & Sequence | |
|The domain represents all the | |Identify examples of | | |(ESS)- | |
|values for the independent |The independent variable is |domain, range, | |Jefferson Lab – |pen.k12.va.us | |
|variables and the range |the input value. |independent variable, | |Patterns, Functions, | | |
|represents all the values for | |and dependent variable.| |and Algebra Strand | – | |
|the dependent variables. | | | | | |
| | |Determine the domain of| | |/nmatthews | |
| | |a function. | | | | |
|Continued … | | | | | | |
| | |Determine the range of | | | | |
| | |a function. | | | | |
SOL 8.18 CONTINUED …
|Essential Knowledge |Essential Understandings |Essential |Activities |Assessments |Resources |Teaching Notes |
| | |Skills | | | | |
|The independent variable is |The dependent variable |Determine the | | | | |
|the value that causes the |depends on the independent |independent variable of| | | | |
|change in the dependent |variable and is the output |a relationship. | | | | |
|variable and the dependent |value. | | | | | |
|variable is affected by the | |Determine the dependent| | | | |
|independent variable. | |variable of a | | | | |
| | |relationship. | | | | |
| | | | | | | |
Check for Understanding - Released SOL Test Items – 8.18
Use the relation (5 ,7) , (6, 8) , (0, 2), (9, 11) for questions 1-2.
1. What is the domain of the relation?
A {5,7,6,8,}
B {5,6,0,9}
C {7,8,2,11}
D {0,3,9,11}
2. What is the range of the relation?
A {0,2,9,11}
B {7,8,2,11}
C {5,6,2,11}
D {5,6,0,9}
3.
Jill sold boxes of cookies for $4.00 each. The number of boxes sold is represented by x and the money earned is represented by. She wrote this equation to represent this situation:
y = 4x
Which of the following would be true about the relationship between x and y?
A y is an independent variable.
B x is an independent variable.
C y is NOT a function of x.
D If y is a function of x, the domain can only be positive real numbers
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