Grade 6 Mathematics

Correlation Between the California Content Standards and the eTAP Lessons

Number Sense | Algebra and Functions | Measurement and Geometry | Statistics, Data Analysis, and Probability |Mathematical Reasoning

Topics marked by yellow are accessible from the Demo. You need to become a subscribing Member to access other lessons. Below are the eTAP lessons covering each standard. Click on the eTAP lesson for access to the Q/A & video.

Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages:

1.1

Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

Compare and Order Positive and Negative Fractions, Decimals, Mixed Numbers

http://www.321know.com/cmp41bx2.htm

1.2

Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).

Interpret and Use Ratios

http://aaamath.com/B/rat62ax2.htm http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=ratio

1.3

Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

Use Proportions to Solve Problems
What is a Fraction?

http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=proport

1.4

Calculate Percentages and Solve Problems

http://aaamath.com/B/dec61ax2.htm http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=percent

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:

2.1

Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.

Addition of Fractions
Subtraction of Fractions
Multiplying and Dividing Fractions

http://nlvm.usu.edu/en/nav/frames_asid_105
_g_2_t _1.html
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=fractions

2.2

Explain the meaning of multiplication and division of positive fractions and perform the calculations
(e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 = 2/3).

Multiplying and Dividing Fractions
Tenths in Decimals and Fractions

http://www.aaamath.com/fra66o-divfract.html http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=fractions

2.3

Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

Problems Involving Addition, Subtraction, Multiplication, and Division

http://www.akgupta.com/Java/arithmetic.htm

2.4

Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

Using LCM to Solve Fraction Problems

http://www.purplemath.com/modules/lcm_gcf.htm

Algebra and Functions (top)
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results

1.1

Write and solve one-step linear equations in one variable.

Basic Equations

http://www.purplemath.com/modules/solvelin.htm http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=formulas

1.2

Write and evaluate an algebraic expression for a given situation, using up to three variables.

Changing Words into Math

http://www.themathpage.com/alg/algebraic-
expressions.htm
http://regentsprep.org/Rege
nts/math/orderop /evalPrac.htm

1.3

Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

Commutative and Associative Rules
Grouping Numbers

http://www.mathgoodies.com/lessons/vol7/orde
r_operations.html
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=orderop

1.4

Solve problems manually by using the correct order of operations or by using a scientific calculator.

Order of Operations and Combining Terms

http://amby.com/educate/ord-op/ http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=orderop

2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:

2.1

Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

Converting Measurements within a System
Volumes and Areas

http://hemsidor.torget.se/users/b/bohjohan
/convert/conv_e.htm
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=meteng

2.2

Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.

http://fp.uni.edu/mathcenter/ratios,_rate
| s,_a nd_percents.htm

2.3

Solve problems involving rates, average speed, distance, and time.

Speed and Velocity

http://www.physicsclassroom.com/m
media/kinema/trip.html

3.0 Students investigate geometric patterns and describe them algebraically:

3.1

Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

Geometric Formulas

http://www.purplemath.com/modules/geoform.htm http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=fperim
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=fsolid

3.2

Express in symbolic form simple relationships arising from geometry.

Geometric Formulas

http://mathforum.org/dr.math/faq/formulas/

Measurement and Geometry (top)
1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:

1.1

Understand the concept of a constant such as pi; know the formulas for the circumference and area of a circle.

Area of Circle
Circumference of Circle

http://www.mathgoodies.com/lessons/vol
2/circumference.html
http://regentsprep.org/ Regents/math/math-
topic.cfm?TopicCode=fperim

1.2

Know common estimates of

(3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.

Area of Circle
Circumference of Circle

http://www.1728.com/diamform.htm http://regentsprep.org/Regents/math/math
-topic.cfm?TopicCode=fperim

1.3

Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.

Volume Formulas

http://www.gomath.com/htdocs/ToGoSheet/G
eometry/volume.html
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=fsolid

2.0 Students identify and describe the properties of two-dimensional figures:

2.1

Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Lines and Angles

http://www.mcwdn.org/Geometry/Lines.html http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=angles

2.2

Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

http://www.geocities.com/kevinbisesser/ compsup.html http://www.mcwdn.org/Geometry/Lines.html http://regentsprep.org/Regents/math/math-topic.cfm?
TopicC ode=angles

2.3

Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Recognizing Figures

http://www.mathsteacher.com.au/year8/ch09 _geometry/07_quad/quad.htm

Statistics, Data Analysis, and Probability (top)
1.0 Students compute and analyze statistical measurements for data sets:

1.1

Compute the range, mean, median, and mode of data sets.

Data Calculations

http://library.thinkquest.org/6068/pages/rmmm.htm

1.2

Understand how additional data added to data sets may affect these computations of measures of central tendency.

Data Calculations

http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=mean

1.3

Understand how the inclusion or exclusion of outliers affects measures of central tendency.

Data Calculations

http://www.itl.nist.gov/div898/handbook/prc
/section1/prc16.htm

1.4

Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.

Data Calculations

http://ceds.vu.edu.au/studentlearni ng/CourseSpecific/PsychStatsTopics/Cen
tralTendency/CentralTendencyIntro.htm

2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:

2.1

Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.

Compare Samples

http://www.mrs.umn.edu/~sungurea/statle
ts/free/multsam.htm

2.2

Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Sample Selection Procedures

http://www.stats.gla.ac.uk/steps/glossary/ s
ampling.html

2.3

Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

Data Display Analysis

http://www.learner.org/channel/courses/lea
rningmath/data/session2/index.html
http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=venn

2.4

Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

http://en.wikipedia.org/wiki/Sampling_error

2.5

Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

Claims

3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:

3.1

Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

Possible Outcomes

http://regentsprep.org/Regents/math/math-
topic.cfm?TopicCode=events

3.2

Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).

Estimate Probability

http://www.mathgoodies.com/lessons/vol
6/intro_probability.htm

3.3

Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.

Probabilities as Ratios, Proportions, Decimals

http://mathforum.org/library/drmath/view/
56524.html

3.4

Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

Possible Outcomes of Compound Events

http://regentsprep.org/Regents/math/events
/LSimple.htm

3.5

Understand the difference between independent and dependent events.

Estimate Probability

http://library.thinkquest.org/20991/alg2
/prob.html#prob

Mathematical Reasoning (top)
1.0 Students make decisions about how to approach problems:

1.1

Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

1.2

Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.

1.3

Determine when and how to break a problem into simpler parts.

Basic Equations

http://www.studyzone.org/testprep/math4/d/prob
lempartl.cfm

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1

Use estimation to verify the reasonableness of calculated results.

2.2

Apply strategies and results from simpler problems to more complex problems.

2.3

Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

2.4

Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Graphs

http://www.rinkworks.com/brainfood/p/math1.shtml

2.5

Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.6

Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.7

Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1

Evaluate the reasonableness of the solution in the context of the original situation.

3.2

Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3

Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.