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Standard 4.1 (Number and Numerical Operations)
All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety or ways.A. Numerical operations and introduction to AlgebraObjectivesStandards1. Perform calculations involving addition, subtraction, multiplication, and division, and exponents with integers and all number types.
4.1.(8)B.1
2. Extend understanding of the number system by constructing meanings for the following:
a. Rational numbers and irrational numbers.
b. Exponents, extension negative exponents and scientific notation.
c. Roots including cube roots.
d. Absolute value.
4.1.(8)A.1,2,4,6,7; (8)C.2
4.3.(8)D.1
3. Use exponentiation to find whole number powers of numbers.
4.1.(8)B.24. Find square and cube roots of numbers and understand the inverse nature of powers and roots.
a. Estimate square and cube roots.
b. Recognize the limitations of estimation and assess the amount of error resulting from estimation.
4.1.(8)B.3; (8)C.1,3
5. Understand and apply the standard algebraic order of operations, including appropriate use of grouping symbols.
4.1.(8)B.5
6. Solve and graph simple linear equations with integer coefficients.
4.3.(8)D.1,27. Solve and graph simple linear inequalities with integer coefficients.
4.3.(8)D.1,3
8. Create, evaluate, and simplify algebraic expressions involving
variables:
a. Order of operations.
b. Distributive property.
c. Substitution of a number for a variable.
d. Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa.
4.3.(8)D.4
9. Understand and apply the properties of operations, numbers, equations, and inequalities including:
a. Additive inverse.
b. Multiplicative inverse.
c. Addition and multiplication properties of equality.
d. Addition and multiplication properties of inequalities.
4.3.(8)D.5
Standard 4.1 (Number and Numerical Operations) - Continued
All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety or ways.B. Problem solving with ratio, proportion and percentObjectivesStandards1. Develop a conceptual understanding and use ratios, proportions, unit rates and percents (including percents greater than 100 and less than 1).
4.1.(8)A.3,5
2. Illustrate, model, and solve problems involving ratios, proportions, unit rate, and percents in real-life word problems, including:
a. Discount and successive discount.
b. % increase and decrease.
c. Tax.
d. Simple interest.
e. Commission.
f. Compound interest
4.1.(8)B.4; (8)C
Suggested Strategies and Resources:
1. Construct meanings for common irrational numbers such as pi and square root of 2.
2. Graph all types of numbers and solutions on a number line.
3. Apply prime factorization to open-ended questions.
4. Create circle graphs with and without a protractor with %, create own percent games using word problems.
Standard 4.2 (Geometry and Measurement)
All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.A. Geometric PropertiesObjectivesStandards1. Understand and apply concepts involving lines, angles and planes
including:
a. Complementary and supplementary.
b. Vertical angles.
c. Bisectors and perpendicular bisectors.
d. Parallel, perpendicular, and intersecting planes.
e. Intersection of plane with cube, cylinder, cone, and sphere.
4.2.(8)A.1,5
2. Identify fundamental properties of triangles including:
a. Sum of angles = 180.
b. Base of angles of an isosceles triangle are equal.
c. Equilateral implies equiangular.
d. Triangle inequality.
4.2.(8)A.3
3. Apply simple algebraic equations to properties of geometry including lines, angles, and polygons.
4.2.(8)A.5; (8)D.2
4. Understand and apply Pythagorean Theorem.
4.2.(8)A.2
4.5.(8)C.55. Understand and apply properties of polygons including:
a. Quadrilaterals (squares, rectangles, parallelograms, trapezoids, rhombi).
b. Sums of measure of interior angles of a polygon.
c. Regular polygons.
4.2.(8)A.3
6. Understand concepts of similarity.
a. Create and interpret scale drawings.
b. Apply proportions to a variety of problems.
4.2.(8)A.4
7. Create and use models of 3-D objects from different perspectives and nets.
4.2.(8)A.4
B. TransformationsObjectivesStandards1. Understand, graph, and apply transformations.
a. Find the image, given the pre-image, and vice versa.
b. Determine the sequence of transformations needed to map one figure.
c. Create reflections, rotations, and translations that result in images congruent to the pre-image.
d. Explore why dilations (stretching/shrinking) result in images similar to the pre-image.
4.2.(8)B.1; (8)C.1,2
C. Measuring geometric objectsObjectives1. Develop and apply strategies for finding perimeter and area
including:
a. Geometric figures made by combining triangles, rectangles, circles or parts of circles.
b. Impact of a dilation on the perimeter and area of a 2-D figure.
4.2.(8)E.1
2. Recognize that the volume of a pyramid and a cone is one-third of
the volume of the prism or cylinder with the same base and height.
4.2.(8)E.2
3. Develop and apply strategies and formulas for finding the surface
area and volume of a 3-D figure including:
a. Volume prism, cone, pyramid.
b. Surface area prism (triangular or rectangular base), pyramid (triangular or rectangular base).
c. Impact of dilation on surface area and volume of a 3-D figure.
4.2.(8)E.3
4. Use formulas to find the volume and surface area of a sphere. 4.2.(8)E.4
Suggested Strategies and Resources:
1. Use geometry notebooks as a project to identify all geometric vocabulary words and diagrams See
NV EMath Site
2. Use 3-D models and nets to increase understanding of spatial sense.
3. Use and create fractals such as the Koch snowflake and Sierpinskis triangle. 4.2(8)B2
Standard 4.3 (Patterns and Algebra)
All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.ObjectivesStandards1. Recognize, describe, extend, and create patterns as they relate to:
a. Arithmetic and geometric sequences.
b. Repeating pattern.
c. Pictorial/geometric.
4.5.(8).C1; (8)E.1;
(8)D.3; (8)F.4
4.3.(8)A.1
2. Solve problems involving real-life situations
4.3.(8)B.2
4.5.(8)A.1-5; (8)C.3,4,63. Create and interpret function tables..
4.3.(8)B.1,2AlgebraObjectivesStandards1. Investigate Monomials
a. Identify monomial, binomial, trinomial and polynomial.
b. Combine like terms.
c. Multiply monomials including raising to a power.
d. Divide monomials.
e. Simplify using the distributive property.
f. Find the GCF & LCM of monomials.
4.5.(8)D.1; (8)E.2
2. Evaluate Equations
a. Solve two-step equations including rational coefficients.
b. Solve multiple step equations including the use of the distributive property.
c. Translate word problems into algebraic equations and vice versa.
4.3.(8)D.2
3. Evaluate Inequalities
a. Solve and graph two-step inequalities including rational coefficients.
b. Solve multiple step inequalities including the use of the distributive property.
c. Translate word problems into algebraic inequalities and vice versa.
4.3.(8)D.3
Suggested Strategies and Resources:
1. Graph multiple linear equations using a function table to recognize rates of changes (informal notation of slope)
Standard 4.4 (Data Analysis, Probability, and Discrete Mathematics)
All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.A. Data Analysis (Statistics)ObjectivesStandards1. Select and use appropriate representations for set of data, and measures of central tendency (mean, median, mode, and range).
a. Choose the type of display most appropriate for given data.
b. Develop and interpret box-and-whisker plot, upper quartile, lower quartile.
c. Develop and interpret scatter plot and estimating line of best fit.
4.4(8)A1,3
2. Make inferences and formulate and evaluate arguments based on displays and analysis of data.
4.4(8)A2
3. Use surveys and sampling techniques to generate data and draw conclusions about large groups.
4.4(8)A4
B. ProbabilityObjectivesStandards1. Interpret probabilities as ratios, percents, and decimals.
4.4.(8)B.12. Determine probabilities of compound events.
4.4.(8)B.23. Explore the probabilities of conditional events.
4.4.(8)B.3
4. Model situations involving probability with simulations.
4.4.(8)B.45. Estimate probabilities and make predictions based on experimental and theoretical probabilities.
4.4.(8)B.5
6. Employ systematic listing and counting.
a. Apply the multiplication principle of counting.
b. Explore permutations, factorials, and combinations.
c. Construct and interpret Venn diagrams
d. Apply systematic listing, counting, and reasoning in a variety of different contexts.
4.4.(8)C.1-3
7. Explore Vertex-edge graphs
a. Find the shortest network connecting specified sites.
b. Find the minimal route.
c. Find the shortest circuit on a map.
4.4(8)D1
Suggested Strategies and Resources:
1. Play and analyze probability-based games.
2. Discuss the concept of fairness and expected value. 4.4.(8)B.6
3. See NV EMath Site
At each grade level with respect to appropriate content, students will solve problems, communicate to clarify mathematical thinking, make connections, use reasoning skills, create and use mathematical representations, and use appropriate technology. For further clarification, see Standard 4.5.
Standard 4.5 (Mathematical Processes)
All students will use mathematical processes of problem solving, communication, connections, reasoning, representations and technology to solve problems and communicate mathematical ideas.ObjectivesStandardsA. Apply problem solving approaches to investigate and understand mathematical content.
4.5A.1
B. Solve problems that arise in mathematics and in other contexts using open-ended, non-routine, multiple solutions, and problems that can be solved in several ways.
4.5A.2
C.4
C. Formulate problems from everyday and mathematical situations.4.5A.1
4.1.(5)A.1
D. Develop and apply strategies to solve a wide variety of multi-step problems, using pencil and paper, mental math and calculators.
4.1.(5)A.3; (5)B.2,6
8.1.(8)B.6E. Verify and interpret results with respect to the original problem.4.1.(5)B.2
4.5E.2
8.1.(8)B.10F. Acquire confidence in communicating mathematical thinking coherently in written and oral form to peers and teachers.
4.5B.2; D.6
8.1.(8)A.8
9.2.(8)A.1; (8)C.2
G. Use a calculator and technology as an appropriate computational method in a given situation.4.1.(5)B.4
4.5F.1,4
H. Utilize real-life experiences, physical materials and technology to construct meanings for numbers.4.1.(5)A.1
4.5C.3
8.1.(8)B.8
Suggested Strategies, Resources and Activities:
You Can Bank on It
Decorate Your Dream Bedroom
Use book Problem Solving Experiences in Mathematics, by Randall Charles (Addison Wesley)
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