math (salgado) st quarter: week 1-2 timeframe: 10 days level/grade: 6 grade math 08-09.pdf ·...

Math (Salgado) 1st quarter: week 1-2 Timeframe: 10 days Level/Grade: 6

Unit 1: Pre-Pre-AlgebraObjectives:After completing this unit, the students will

evaluate an expression containing multiple operations, exponents and parentheses write and evaluate exponential expressions write and evaluate variable expressions from a given picture or situation solve a one step equation using inverse operations or mental math or identify the correct solution

Vocabulary: expression; evaluate; order of operations; exponent; base; powers; squared; cubed; equation; variable; parentheses; inverse operations

Lesson 1: My Dear Aunt SallyStudents will explore the natural order of operations when solving a multi-step problem and evaluate expressions with multiple operations.Lesson 2: ParenthesesStudents will discover the need to over-ride the natural order of operations then write and evaluate expressions using grouping symbols.Lesson 3: VariablesStudents will translate English expressions into mathematical expressions using variables and evaluate variable expressions once given the value of each variable.Lesson 4: ExponentsStudents will identify the function of exponents and evaluate exponential expressions.Lesson 5: Please Excuse My Dear Aunt SallyStudents will evaluate expressions using multiple operations, exponents and parentheses. Lesson 6: EquationsStudents will evaluate equations to determine whether possible solutions are correct and solve equations using inverse operations.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice; read story

TEKS:6.2B,C 6.4A 6.5 6.11A,B,C,D 6.12A,B 6.13A,B

7.1C 7.2E

Materials:Graphing calculators; pencil; math log; scissors; markers; index cards; tape; scissors; chart paper; “One Grain of Rice” (book)

SE Modifications:Extended time; shortened assignments; step-by-step outline; TLC;

Resources:Teacher-made worksheets; TAKS study guide; TAKS practice books

TA TEKS:1 A, B, E 2 A, C 3 D, E 6 B 7 J

GT Modifications:Benchmark problems; create problems

Evaluation Methods:Calculator check; self check; teacher check; oral question & answer; assignment; quiz; test; project

Math (Salgado) 1st quarter: week 3-5 Timeframe:15 days Level/Grade: 6

Unit 2: Multiples & FactorsObjectives:After completing this unit, the students will.

generate lists of multiples and identify common multiples. distinguish between prime and composite numbers and identify the properties of each. write the prime factorization of numbers using exponential notation. generate lists of factors and identify common factors. generate equivalent fractions and reduce fractions to lowest terms. compare and order fractions.

Vocabulary: multiple, LCM, factor, GCF, prime, composite, prime factorization, equivalent, reduce, simplify, lowest terms, common denominator

Lesson 1: LCMStudents will list multiples of various numbers, noting common multiples and the least common multiple.Lesson 2: Prime and CompositeStudents will classify numbers as prime, composite or neither using area models and factor lists.Lesson 3: Prime FactorizationStudents will find the prime factorization of a given number using either factor trees or “up-side-down division” and write using exponents.Lesson 4: GCFStudents will list all the factors of various numbers, noting common factors and the greatest common factor, then connect the prime factorizations of each number to the GCF.Lesson 5: Equivalent FractionsStudents will first model equivalent fractions and look for patterns in the fractions. Students will then use LCM to generate list of equivalent fractions and GCF to find equivalent fractions be simplifying (or reducing).Lesson 6: Compare and Order FractionsStudents will compare and order fractions by calculating a common denominator and using equivalent fractions.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice; power point presentation

TEKS:

6.1A,B,D,E 6.2C,D 6.11A,B,C,D 6.12A,B 6.13A,B

7.1A,B 7.2B,F,G

Materials:Graphing calculators; pencil; math log; scissors; markers; tape; scissors; chart paper; computer; aver key; TV; power point presentation




GT Modifications:Benchmark problems; research perfect, deficient, abundant numbers


Math 1st quarter: week 6-8 Timeframe: 15 days Level/Grade: 6

Unit 3: FractionsObjectives:After completing this unit, the students will

Convert mixed numbers to improper fractions and vice versa. Solve problems involving addition and subtraction of fractions and mixed numbers, in situations with

fractions having a common denominator and having different denominators.

Vocabulary: numerator, denominator, mixed number, improper fraction, common denominator, simplify, lowest terms

Lesson 1: Like DenominatorsStudents will add and subtract fractions and mixed numbers with like denominators, and check using a calculator.

Lesson 2: Mixed Numbers & Improper Fractions Students will convert improper fractions to mixed numbers (and vise versa) using manipulatives, models, and pencil & paper.

Lesson 3: Regrouping - Improper answersStudents will add fractions, regrouping improper answers to make mixed numbers.

Lesson 4: Regrouping – Borrowing from whole numbers Students will subtract fractions from whole numbers (ex. 8 – ½ ), regrouping a 1 whole as a fraction.

Lesson 5: Regrouping – Borrowing from mixed numbersStudents will subtraction fractions and mixed numbers, regrouping a 1 whole as a fraction when necessary.

Lesson 6: Unlike DenominatorsStudents will add and subtract fractions and mixed numbers with unlike denominators by finding equivalent fractions with a common denominator.

Activity Type: Teacher guided instruction; exploration; whole class (cooperative); individual practice; read story

TEKS:

6.2A,B,D 6.8A,B,D 6.11A,B,C,D 6.12A,B 6.13A,B

Materials:Graphing calculators; pencil; math log; fraction circles

Math (Salgado) 2nd quarter: week 1-3 Timeframe: 15 days Level/Grade: 6

Unit 4: Operations with decimalsObjectives:After completing this unit, the students will

solve problems by using addition, subtraction, multiplication and division of decimals. estimate solution to problems involving decimals. compare and order decimals numbers. generate decimal form of a number given as a fraction (with denominators of 10, 100, 1000 etc.) or in

written words. generate fraction form of a number when given as decimal or in written words. draw models of multiplication and division of decimals.

Vocabulary: place value, sum, difference, product, quotient, like terms, convert

Lesson 1: Add and Subtract DecimalsStudents will apply their knowledge of place value to addition and subtraction problems involving decimal numbers, making sure to only add or subtract like terms. Students will use addition and subtraction of decimalsO solve problems, including finding perimeter.Lesson 2: Estimating with DecimalsStudents will round decimal numbers and estimate the answer to problems involving decimals when an exact answer is not needed and to check the reasonableness of an exact answer.Lesson 3: Compare and OrderStudents will compare decimal numbers using place value, write inequality statements and ordered lists of decimals numbers.Lesson 4: Equivalent Fractions and DecimalsStudents will model equivalent fractions and decimals, and convert from fraction form (with denominators of 10, 100, 1000 etc.) to decimal form to word form and vice versa.Lesson 5: Multiply DecimalsStudents will first model multiplication of decimals by whole numbers then by decimals. Students will use multiplication of decimals to solve problems, including finding the area of rectangles.Lesson 6: Divide DecimalsStudents will divide decimal numbers by whole numbers, them by decimal numbers, checking the algorithm by estimation and reasonable answers.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice; read book

TEKS:

6.1A, B 6.2B, C, D 6.8A, B 6.11A, B, C, D 6.12A, B 6.13A, B

7.1A,B 7.2A,C,D,G 7.9

Materials:Graphing calculators; pencil; math log; scissors; markers; index cards; tape; scissors; chart paper; “Pigs Go To Market”




GT Modifications:Benchmark problems;


Math 2nd quarter: week 4-6 Timeframe: 15 days Level/Grade: 6

Unit 5: Fractions-Decimals-PercentsObjectives:After completing this unit, the students will

generate equivalent forms of fractions, decimals and percents. compare fractions, decimals and percents. sketch circle graphs. calculate the percent and fractional part of a given number.

Vocabulary: equivalent, decimal places (tenths, hundredths, etc.), percent, circle graph

Lesson 1: Fraction > DecimalStudents will convert fractions to decimal numbers mentally, with paper and pencil, and with the graphing calculator.Lesson 2: Fraction <> PercentStudents will convert fractions to percents and percents to fractions mentally and with paper and pencil, using equivalent fractions or by using the decimal form of the number. Lesson 3: Decimal <>PercentStudents will convert decimals to percents and percents to decimals mentally, with paper and pencil, and with the graphing calculator.Lesson 4: Compare Fractions, Decimals and PercentsStudents will compare and order fractions, decimals and percents (using models and conversions) when given a set of number in the same form or in different forms.Lesson 5: Sketch Circle GraphsStudents will sketch circle graphs using data obtained from the class and converted to percents, and compare those sketches to graphs generated by the graphing calculator.Lesson 6: Fraction of Number and Percent of NumberStudents will calculate a fractional part of a given number and a percentage of a given number in real-life problems.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice;

TEKS:

6.1A,B 6.2C,D 6.3A,B,C 6.8D 6.10C,D 6.11A, B, C, D

6.12A,B 6.13A,B

7.1A,B 7.2B,G 7.3A

Materials:Graphing calculators; pencil; math log; chart paper;


Resources:Teacher-made worksheets; TAKS study guide; TAKS practice books;

TA TEKS:1 A, B, E 2 A, C 3 B, D, E 6 B 7 J



Math 2nd quarter: week 7-8 Timeframe: 10 days Level/Grade: 6

Unit 6: Coordinate GraphingObjectives:After completing this unit, the students will

Use integers to express real life situations. Locate and name points of a coordinate grid (all four quadrants). Graph transformations on a coordinate plane.

Vocabulary: integer, positive, negative, x-axis, y-axis, origin, vertical, horizontal, ordered pair, coordinate, quadrant,

Lesson 1: Quadrant IStudents will examine the grid formed by two number lines, one vertical and one horizontal, which intersect at zero on each line, then will locate and name points on the grid using ordered pairs of coordinates.

Lesson 2: The Number Line Behind ZeroStudents will explore the number line behind zero, locate negative and positive numbers, and identify real life situations that use both types of numbers.

Lesson 3: Quadrants II, III, IVStudents will extend the number lines and grid to the negative side of the axes, discovering four quadrants, then will locate and name points in all four quadrants using ordered pairs of coordinates.

Lesson 4: Graphing TransformationsStudents will graph figures along with their reflections and translations, while noting and describing the changes in the coordinates of each point in the figures.


TEKS:

6.1C 6.2B, C 6.4A 6.7 6.8B 6.11A,D 6.12A 6.13A,B

7.6D 7.7A,B

Materials:Graphing calculators; pencil; math log; scissors; markers; ruler; scissors; grid paper; “A Fly on the Wall” (book)




GT Modifications:Benchmark problems; Create pictures


Math 3rd quarter: week 1-3 Timeframe: 15 days Level/Grade: 6

Unit 7: ProportionalityObjectives:After completing this unit, the students will

Describe situations using ratios Develop equivalent ratios using models, tables and scale factors. Demonstrate the concept of proportionality through both visual and numerical examples Make predictions in proportional situations. Solve problems using proportional situations.

Vocabulary:Ratio, rate, unit rate, proportional, proportion, survey, prediction

Lesson 1: Ratios and Unit RatesStudents will describe a given situation using several different ratios and unit rates when applicable.

Lesson 2: Restless RectanglesStudents will identify rectangles that “go together” or that grow proportionally, then discover the pattern of growth of the dimensions of the rectangles and the use of equivalent fractions in proportional situations.

Lesson 3: Proportional Coordinate Graph PicturesStudents will produce proportional pictures by graphing a set of original ordered pairs, using a scale factor to change the ordered pairs then graphing each again.

Lesson 4: Survey PredictionsStudents will predict the outcomes of a school-wide survey based on a classroom survey by using proportionality.

Lesson 5: Picture Frame proportionsStudents will use the old fashion method of solving proportions by setting up two equivalent ratios.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice

TEKS:

6.2C 6.3A,B,C 6.4A 6.7 6.8A,D 6.11A,B,C,D 6.12A,B 6.13A,B

7.2D 7.3B

Materials:Graphing calculators; pencils; math log; scissors; markers; index cards; tape; chart paper; grid paper; survey; grocery ads; food labels




GT Modifications:Benchmark problems; illustration or creation of proportional situation; check proportion answers with survey


Math 3rd quarter: week 4 Timeframe: 5 days Level/Grade: 6

Unit 8: Measurement SystemsObjectives:After completing this unit, the students will

Distinguish between the two measurement systems (customary and metric). Develop a working knowledge of the units in both systems. Convert measures within the same system

Vocabulary: length, volume, capacity, mass, weight, unit, meter, liter, gram, kilo-, centi-, milli-, convert

Lesson 1: Customary SystemStudents will choose the appropriate units when measuring in the customary system.

Lesson 2: Customary ConversionsStudents will convert between different units in the customary system using the measurement chart, Gallon Man, pictures and proportions.

Lesson 3: Metric SystemStudents will chose the appropriate units when measuring in the metric system and describe the relationships within the base-ten system. Lesson 4: Metric ConversionsStudents will convert between different units in the customary system using the measurement chart, King Henry, and proportions.


TEKS:

6.2C 6.8A,B,D 6.11A,B,C,D 6.12A,B 6.13A,B

Materials:Graphing calculators; pencil; math log; scissors; markers; index cards; tape; chart paper; ruler, measurement chart



TA TEKS:3 D, E 4 A, B

GT Modifications:Benchmark problems;


Math 3rd quarter: week 5-8 Timeframe: 20 days Level/Grade: 6

Unit 9: GeometryObjectives:After completing this unit, the students will

Analyze, classify and measure angles. Analyze angles in triangles and quadrilaterals. Generate perimeter, area and volume formulas. Explain the connections between radius, diameter and circumference. Solve application problems involving perimeter, circumference, area and volume.

Vocabulary: point, line, segment, ray, plane, parallel, perpendicular, intersecting, angle, protractor, acute, right, obtuse, straight, degrees, , polygon, triangle, scalene, isosceles, equilateral, quadrilateral, parallelogram, trapezoid, rhombus, rectangle, square, pentagon, hexagon, heptagon, octagon, nonagon, decagon, perimeter, area, square units, base, height, circle, diameter, radius, chord, circumference, volume, cubic units, rectangular prism

Lesson 1: Basics of GeometryStudents will identify the basic pieces of geometry and the attributes of each.

Lesson 2: AnglesStudents will identify the types of angles, classify angles, and measure angles using a protractor. Students will use the complementary and supplementary relationships of angles to solve problems.

Lesson 3: Polygons & TrianglesStudents will classify polygons and triangles according to the number of sides and the length of the sides. Students will solve problems involving the perimeter of polygons and the angles in a triangle.

Lesson 4: QuadrilateralsStudents will classify quadrilaterals according to the properties of each, and solve problems involving the relationship of the angles in a parallelogram.

Lesson 5: Area and Perimeter of Squares & RectanglesStudents will calculate area and perimeter of squares and rectangles, analyze the process, and develop formulas.

Lesson 6: Area of Triangles, Parallelograms, & TrapezoidsStudents will compare triangles and parallelograms to rectangles and develop formulas for calculating the areas of these shapes, then solve problems involving the area of these shapes. Students will compare trapezoids to triangles, find connections between the formulas for these shapes, and solve problems involving the area of trapezoids.

Lesson 7: Circles and PiStudents will explore circles, discover the relationship between the diameter, radius, circumference, and pi, then solve problems involving circles.

Lesson 8: Circumference & Area of CirclesStudents will solve problems using the circumference and area formulas, using both 3 and 3.14 for pi.

Lesson 9: Volume Students will compare prisms to the 2-dimensional base, develop a formula for volume, then solve problems involving volume of rectangular prisms.


TEKS:

6.2B,C,D 6.4A,B 6.5 6.6A,B,C 6.8A,B,C

7.2A,B,D,E,F,G 7.4A,B 7.6A,B 7.9

Materials:Graphing calculators; pencil; math log; scissors; markers; index cards; tape; scissors; chart paper; lids, rulers, measuring tape, formula chart, cm cubes, protractors, Sir Cumference books






Math 4th quarter: week 1-2 Timeframe: 10 days Level/Grade: 6

Unit 10: Data and GraphsObjectives:After completing this unit, the students will

Collect and analyze data. Construct different graphs with and without technology (including bar, picto-, line and circle graphs). Compare different graphs representing the same data. Choose the best graph for presenting data. Describe data using mean, median, mode and range.

Vocabulary: statistics, data, bar graph, pictograph, line graph, circle graph, measure of central tendency, average, mean, median, mode, range, outlier

Lesson 1: Data Collection, Organization and DisplayThe student will collect data from the classroom and through research, organize and analyze that data to find trends, and display the data in various forms including charts and graphs.

Lesson 2: Computer and Calculator GraphsThe students will use graphing calculators or online resources to create graphs of given data.

Lesson 3: Mean, Median, Mode, RangeThe students will calculate mean, median, mode and range to describe a set of data, both by hand and by using the built in functions on the graphing calculator, noting the difference an outlier can make.


TEKS:

6.1A,B 6.2B,C,D 6.10A,B,C,D 6.11A,B,C,D 6.12A,B 6.13A,B

7.1B 7.11A,B 7.12A,B

Materials:Graphing calculators; pencil; math log; rulers; markers; chart paper; computer w/internet access



TA TEKS:1 A, B, E, F,G 2 A, C 3 B, D, E 4 A, B 6 B 7 J

GT Modifications:Benchmark problems; create problems, gather data from outside sources



Unit 11: ProbabilityObjectives:After completing this unit, the students will

Assemble a set of all possible outcomes using lists, tree diagrams and the counting principle. Give examples of experimental and theoretical probability. Describe and calculate simple probability and its complement. Distinguish between simple probability and compound probability. Distinguish between dependent and independent events.

Vocabulary: event, outcome, experimental probability, theoretical probability, chances, complement, simple probability, compound probability, dependent events, independent events, tree diagram, counting principle, combinations

Lesson 1: Possible OutcomesThe student will list the possible outcomes of different experiments and calculate the probability of each event. (Lotto games)

Lesson 2: Experimental vs. Theoretical ProbabilityThe student will distinguish between the two and use the graphing calculator simulation application to compare the results of an experiment to the theoretical probability, noting that the more trials conducted will give results closer to the theoretical probability.

Lesson 3: Simple Probability and its ComplementThe student will calculate simple probability and the probability of the complementary event, and describe and apply the relationship between the two.

Lesson 4: Compound Probability and Dependent EventsThe students will differentiate between simple and compound events, analyze the outcomes of both types of experiments and distinguish between dependent and independent events in situations with compound probability.

Lesson 5: CombinationsThe student will generate all possible combinations for a given problem using lists and tree diagrams, and use the basic counting principle to calculate the total number of combinations possible in dependent and independent situations.


TEKS:

6.1B 6.2B,C 6.9A,B 6.11A,B,C,D 6.12A,B 6.13A,B

7.10A,B

Materials:Graphing calculators; pencil; math log; rulers; markers; chart paper; computer w/internet access, spinners, dice, cards, colored cubes



TA TEKS:1 B, E, F 3 D, E

GT Modifications:Benchmark problems; create problems;



Unit 12: Combining IntegersObjectives:After completing this unit, the students will

Model integers with paper and pencil, manipulatives and words. Compare and order integers. Solve problems by combining integers.

Vocabulary: integers, positive, negative, opposite, combining

Lesson 1: Exploring IntegersThe student will plot integers on a number line, model integers with manipulatives and write integers using numbers and symbols as well as words, connecting integers to real-life situations.

Lesson 2: Compare and OrderThe students will compare and order integers, first using a number line then with symbols (<,>).

Lesson 3: Combining Integers The student will combine integers (add and subtract) using manipulatives, models, then abstractly with symbols.

Activity Type:Teacher guided instruction; exploration; whole class (cooperative); individual practice; games

TEKS:

6.1C 6.11A,B,C,D 6.12A,B 6.13A,B

7.1A 7.2B,C

Materials:Graphing calculators; pencil; math log; chart paper; cards

SE Modifications:Extended time; shortened assignments; step-by-step outline; TLC


TA TEKS:1 A, B, E 2A, C 3 D, E, 6 B 7 J




Unit 13: Multiply and Divide Fractions Objectives:After completing this unit, the students will

Model multiplication and division of fractions. Solve problems by multiplying and dividing fractions.

Vocabulary: numerator, denominator, mixed number, improper fraction, KFC

Lesson 1: Modeling Multiplication and Division ProblemsThe students will construct and identify models of multiplication and division problems involving fractions anfd whole numbers.

Lesson 2: Solving Multiplication and Division ProblemsThe student will solve multiplication and division problems involving fractions and mixed numbers, both by hand and using a calculator.


TEKS:

6.2C,D 6.11A,B,C,D 6.12A,B 6.13A,B

7.2A,B,C

Materials:Graphing calculators; pencil; math log;



TA TEKS:1 A, B, E 2A, C 3 D, E, 6 B 7 J



Math 4th quarter: week 9 Timeframe: 5 days Level/Grade: 6

Unit 14: Great MathematiciansObjectives:After completing this unit, the students will

Compare the life and times of several famous mathematicians. Connect the mathematical discoveries of famous mathematicians to the material studied this year. Examine the patterns and properties of numbers discovered by famous mathematicians.

Note: These lessons vary from year to year depending on the time available and the interests of the students. Below are several examples of lessons, we may do some or all of the lessons any given year.

Vocabulary: Pythagorian theorem, regular solids, fulcrum, lever, pi, triangular numbers, series,

Lesson 1: PythagorasThe students will compare the life and school of Pythagoras to their own, construct the 5 regular solids discovered by Pythagoras, model the Pythagorian theorem, and explore Pythagorian triples. (regular figures, exponents)

Lesson 2: ArchimedesThe students will compare the life of Archimedes to their own, design levers to lift a given weight using the law of the lever, and compare his work with pi to that of other mathematicians. (pi, formulas)

Lesson 3: Carl Friedrich GaussThe students will compare the life of Gauss to their own, solve the problem of adding the numbers 1-100, calculate the sum of a given series of numbers, and explain and give examples of the entry in Gauss’ journal “Eurkea (num) = Δ+Δ+Δ.” (formulas, number patterns)

Lesson 4: Mary BooleThe students will compare the life of Mary Boole to their own, then compose and design pictures like those found on her Boole cards. (geometry, number patterns)

Lesson 5: Benjamin FranklinThe students will compare the life of Benjamin Franklin to their own, then decode the magic squares that Franklin found so entertaining. (number patterns)


TEKS:

6.1 A, D, E 6.2 B, C,1 6.5 6.6 B 6.8 B 6.11 A, B, C, D

Materials:Graphing calculators; pencil; math log; power point presentations; paper; scissors; reading passages; computers with internet access

SE Modifications:Extended time; shortened assignments; step-by-step outline; TLC; hand-on activities

Resources:Teacher-made worksheets; TAKS study guide; TAKS practice books; Mathematicians are People, Too; Famous Problems and Their Mathematicians

TA TEKS:1A, B, E, F, H 2A 3A, B, D, E 4A, B6A, B, C 7A, J 10A, D 11A,



math (salgado) st quarter: week 1-2 timeframe: 10 days level/grade: 6 grade math 08-09.pdf ·...

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