Middle Grades Curriculum Guide for Mathematics 6 ... * denotes a learning opportunity found at ....

The * denotes a learning opportunity found at http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/ .

Middle Grades Curriculum Guide for Mathematics 6

Curriculum Target Date

Instruction North Carolina Standard Course of Study Strategic Action Plan for Student Learning and Instruction

(Revised Bloom’s Taxonomy, Differentiation, and 21’st Century Skills)

Goal Objective Clarifying Objectives

Task Analysis Essential Question

Essential Vocabulary

Instructional Opportunity

Learning Opportunity

Resources

1 The learner will understand and compute with rational numbers.

1.01 Develop number sense for negative rational numbers.

Connect the model, number word, and number using a variety of representations, including the number line.

Compare and order.

Make estimates in appropriate situations.

The learner will: Demonstrate a knowledge of rational numbers by identifying positive and negative numbers. Demonstrate an under-standing of rational numbers by illustrating three different representations of a rational number. Compare and order negative rational numbers. Estimate rational

2nd 9-weeks

Represent numbers on the number line. Understand that an integer and its additive inverse are called opposites. Use rational numbers to represent real-life situations

What is a rational number? How are number lines used to display rational numbers? How are values of rational numbers compared and ordered? How can the principles of estimation be applied to rational numbers?

Additive

inverse

greater than

or equal to

opposites

compound

inequality

(ex. a < b <

c)

Negation

ascending

order

integers

descending

order

number line

rounding

equal

place value

less than or

Create a vocabulary square for the word ‘rational number.’ Display and analyze examples of number lines and picture representations of numbers. Assign each student a rational number and create a living number line with the rational numbers. Each student should explain why he/she chose his/her specific position on the number line.

Compose an essay from the perspective of any negative rational number. Explain why you are rational, where you are on a number line, how you are compared and ordered, and how you can be estimated. Provide students with a list of numbers. Students must determine which numbers from the list are negative rational numbers, and display those numbers on a number line.

A Cold Day in Fairbanks http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01a/1.01a-tasks/1.01a-fairbanks.pdf Classroom Number Line http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01b/1.01b-tasks/1.01b-numberline.pdf Checkbook Activity http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01c/1.01c-tasks/1.01c-checkbook.pdf

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01a/1.01a-tasks/1.01a-fairbanks.pdf





http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01b/1.01b-tasks/1.01b-numberline.pdf






http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.01c/1.01c-tasks/1.01c-checkbook.pdf















Resources

numbers in appropriate situations.

equal to

benchmark

values

1.02 Develop meaning for percents.

a. Connect the model, number word, and number using a variety of representations.

b. Make estimates in appropriate situations.

The learner will: Define percents. Demonstrate an under-standing of percents by illustrating three different representations of a percent. Estimate percents in appropriate situations.

3rd 9-weeks

Understand that an integer and its additive inverse are called opposites. Use rational numbers to represent real-life situations. Interpret absolute value as a distance from zero

What is a percentage? How are percentages represented? How can percentages be estimated?

part/whole

proportion

hundred grid

ratio

cross

product

circle graph

Color in different percentages of multiple circles and label each. Survey the class to determine how many students like each type of music. Create a pie graph that displays the percentages. Create a generic acrostic poem that explains percents.

Create a board game about shopping in which percents on sales are incorporated. Peruse the newspaper for sales advertisements. Calculate the sales prices of items with percentages reduced.

Fractions, Decimals, and Percent Hexagon Puzzle http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.02a/1.02a-tasks/1.02a-fractionhexpuzzle.pdf

Math Playground http://mathplayground.com/mathvideos.html

1.03 Compare and order rational numbers.

The learner will: Compare and

3rd 9-weeks

Recognize that a rational number could be represented

How do I compare and order rational numbers?

Fractions

greater than

Create a flow map that orders and ranks rational numbers. Illustrate each

Rational Benchmark Race http://www.dpi.state.nc.us/docs/curriculum/mathemati

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.02a/1.02a-tasks/1.02a-fractionhexpuzzle.pdf






http://mathplayground.com/mathvideos.html


http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.03/1.03-tasks/1.03-rationbenchrace.pdf

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.03/1.03-tasks/1.03-rationbenchrace.pdf











Resources

order rational numbers.

by a terminating or repeating decimal. Use −2, −1, −1, −, 0,, 1, 1, 2 and so on as benchmarks to estimate the values of other fractions. Graph, compare, and order positive and negative numbers (and 0).

or equal to

factor

Decimals

compound

inequality a

< b < c

numerator

Percents

ascending

order

denominator

number line

descending

order

improper

fraction

equal to

common

denominator

mixed

rational number with a picture. Provide a written explanation of how the order of the rational numbers was determined. Create individual squares of paper with a rational number written on each. Place all of the squares into a pile and draw two squares at a time. Determine the relationship between the two numbers (greater than, less than, or equal to)

cs/middlegrades/grade06/goal01/objective1.03/1.03-tasks/1.03-rationbenchrace.pdf











Resources

number

greater than

least

common

denominator

simplify

fraction

less than

multiple

less than or

equal to

least

common

multiple

(LCM)

1.04 Develop fluency in addition, subtraction, multiplication, and division of non-negative

The learner will: Identify non-negative rational

1st and 2

nd 9-

weeks

Identify non-negative rational numbers. Perform operations

How can you demonstrate the different ways to represent a non-

Decimals

least

common

multiple

Cooperative Learning: Create a list of rational numbers. Rank those numbers on a timeline.

Provide practice examples related to real-world examples of computations of non-negative rational

NCDPI Activities http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/tasks?subjectIn=

http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/tasks?subjectIn=mathematics&&gradeIn=06&&goalIn=01&&objectiveIn=1.04













Resources

rational numbers.

a. Analyze computational strategies.

b. Describe the effect of operations on size.

c. Estimate the results of computations.

d. Judge the reasonableness of solutions.

numbers. Perform operations with non-negative rational numbers. Analyze computational strategies with non-negative rational numbers. Describe the effect of operations on size with non-negative rational numbers. Estimate the results of computations with

with non-negative rational numbers. Analyze computational strategies with non-negative rational numbers. Describe the effect of operations on size with non-negative rational numbers. Estimate the results of computations with non-negative rational numbers. Judge the reasonableness of solutions with non-

negative rational number? How are basic mathematical operations performed on non-negative rational numbers? What strategies can be used to analyze non-negative rational numbers? How do the basic operations affect the size of an answer? How can I estimate the outcomes of

(LCM)

difference

Fractions

greatest

common

factor (GCF)

product

Numerator

like/unlike

quotient

Denominator

inverse

operation

improper

fractions

common

denominator

multiplicativ

e inverse

simplify

Create a Frayer model vocabulary graphic organizer for the word ‘rational numbers.’ Create a circle map that illustrates the relationships among different types of numbers (real, irrational rational, etc.).

numbers. Provide examples of computations that have been completed correctly and incorrectly. Determine whether each computation was completed correctly or incorrectly. Justify your determination. Create a monthly budget spreadsheet from perspective of a restaurant owner detailing a fictional monthly operating cost and illustrate the computations of non-negative rational numbers necessary to create that

mathematics&&gradeIn=06&&goalIn=01&&objectiveIn=1.04

Discovering Math: Computations http://school.discoveryeducation.com/lessonplans/programs/DM_computation/

http://school.discoveryeducation.com/lessonplans/programs/DM_computation/














Resources

non-negative rational numbers. Judge the reasonableness of solutions with non-negative rational numbers.

negative rational numbers.

mathematical operations performed on non-negative rational numbers? How can you evaluate that answers are reasonable to non-negative rational number problems?

fractions

least

common

denominator

rounding

factors

mixed

number

benchmark

numbers

products

sum

budget.

1.05 Develop fluency in the use of factors, multiples, exponential notation, and prime factorization.

The learner will: Produce factors of a number. Identify the GCF of a set of numbers.

1st and 2

nd 9-

weeks

Produce factors of a number. Identify the GCF of a set of numbers. Construct prime factorization.

How can divisibility rules be used to determine the factors of a number? What is GCF?

Exponent

order of

operations

Base

factor tree

Power

divisibility

Create a graphic organizer displaying examples of addition, multiplication, division, and subtraction operations performed on non-negative rational numbers.

Create logic problems that include finding GCF or LCM. Detail the solutions to the problems. Using each date on the calendar, use graph paper to make area models of

Calendar Factors http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.05/1.05-tasks/1.05-calendarfactors.pdf

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.05/1.05-tasks/1.05-calendarfactors.pdf
















Resources

Construct prime factorization. Understand exponential notation. Produce multiples of a number. Identify the LCM of a set of numbers.

Recognize prime and composite numbers. Understand exponential notation. Produce multiples of a number. Identify the LCM of a set of numbers.

How can prime factorization be used to find GCF? What are the steps to identify the GCF of two or more numbers? What is LCM? What are the steps to identify the LCM of two or more numbers? What is an exponent? How can you write In exponential notation to indicate the prime

rules

Square

greatest

common

factor

square root:

(of perfect

square) least

common

multiple

cube

prime

number

cube root: (of

perfect cube)

composite

number

operations:

with

exponents (x

Provide examples of estimations with non-negative rational numbers.

that number. List the factors of that number and tell whether the number is prime or composite.











Resources

factorization of a number?

and y)

1.06 Use exponential, scientific, and calculator notation to write very large and very small numbers.

The learner will: Define exponential, scientific, and calculator notation to write very large and very small numbers. Compare and contrast exponential, scientific, and calculator notation to write very large and very small numbers.

1st and 2nd 9-weeks

Relate positive powers of 10 as used in scientific notation to repeated multiplication of ten (e.g. 103= 10 ⋅ 10 ⋅ 10 = 1000) Relate negative powers of 10 as used in scientific notation to repeated multiplication of the fraction 10-3=0.1 ⋅ 0.1 ⋅0.1 = 0.001) Convert numbers written in scientific notation to standard

What is scientific notation? How are numbers expressed in scientific notation?

place value

powers of ten

base

standard

form

exponent

Create a vocabulary square with GCF and LCM. Create a Venn diagram that compares/contrasts aspects of GCF and LCM. Explore supplemental textbook and virtual interactive resources related to GCF and LCM. Create steps to use GCF and LCM.

Create a list of ten microscopic species and determine their approximate size in scientific notation. Create a list of the distances of planets from the sun and express those numbers in scientific notation.

NCDPI http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/tasks?subjectIn=mathematics&&gradeIn=06&&goalIn=01&&objectiveIn=1.06

















Resources

notation and numbers written in standard notation to scientific notation. (Move the decimal point to the right for positive exponents and to the left for negative exponents.) Use calculators to explore contexts in which numbers are expressed in scientific notation.

1.07 Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators

The learner will: Apply appropriate strategies for using mental computation,

1st 9-weeks

Use strategies such as: making a table or diagram, using guess-and-check,

How can rational numbers be used to solve problem?

Simplify

Extraneous

Information

Present a variety of large and small numbers and represent each in scientific notation. Domino Game*

Deli Dilemma*

Deli Delimma http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.07/1.07-tasks/1.07-delidilemma.pdf

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal01/objective1.07/1.07-tasks/1.07-delidilemma.pdf















Resources

or computers, and paper and pencil.

estimation, calculators or computers, and paper and pencil.

looking for patterns, simplifying the problem, working backwards to solve problems, knowledge of estimation.

Scientifico*

Evaluation & Assessment Target Date

Formative Common Benchmark Summative Note(s):











Resources

2 The learner will select and use appropriate tools to measure two- and three-dimensional figures.

2.01 Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.

The learner will: Identify two- and three-dimensional figures based on the characteristics. Understand the difference between area and perimeter. Classify angles. Estimate measurements. Understand the difference between the customary and metric system

1st and 4

th 9-

weeks

Estimate angle measures and find precise angle measures of two-dimensional figures using appropriate tools. Estimate length measures and find precise length measures of two-dimensional figures using appropriate tools. Estimate weight/mass measures and find precise weight/mass measures of three-dimensional objects

How can the length of an object be measured? How can the perimeter of an object be measured? How is the area of an object calculated? How can we differentiate between weight and mass? What tools are used to make these measurements?

protractor

meters miles

degree

centimeters

ounces vertex

kilometers

pounds acute angle

grams

square units

obtuse angle kilograms

parallelogram

right angle

customary system

triangle

complementa

Create a graphic organizer of two and three-dimensional shapes and illustrate equations used to calculate area and perimeter where appropriate. Create a Venn diagram that illustrates the difference between weight and mass. Use manipulatives to illustrate making measurements on two- and three-dimensional figures.

Estimate the amount of water it would take to fill a local swimming pool. Compare the estimate to the actual amount of water used to fill the pool. Find examples of two- and three-dimensional figures in your home. Measure the length, area, and/or perimeter of the objects where appropriate. Create a collage of objects that represent acute, obtuse, and right angles. Create a song about measuring different types of two- and three- dimensional shapes.

NCDPI – Look under tasks http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/grade06/

A Metric World http://school.discoveryeducation.com/lessonplans/programs/metricworld/ Measure for Measure: Lengths and Heights http://school.discoveryeducation.com/lessonplans/programs/measure_lengths/ Math Warehouse www.mathwarehouse.com/geometry

http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/grade06/



http://school.discoveryeducation.com/lessonplans/programs/metricworld/



http://school.discoveryeducation.com/lessonplans/programs/measure_lengths/




http://www.mathwarehouse.com/geometry












Resources

units. using appropriate tools. Understand and find perimeter and area of simple and composite two-dimensional figures.

ry angles

feet trapezoid

supplementar

y angles

inches height

balance scale

yards altitude

metric system

2.02 Solve problems

involving

perimeter/circumferenc

e and area of plane

figures.

The learner will: Determine the differences between regular and irregular figures. Label and define parts of a circle.

1st and 4th 9-weeks

Determine the differences between regular and irregular figures. Label and define parts of a circle. Apply appropriate

formulas for

How is perimeter used to solve problems? How is circumference used to solve problems? How is the area of plane figures

pi

triangle

nonagon

radius

quadrilateral

decagon

diameter

pentagon

square units

Use a string to measure the circumference, diameter, and perimeter of different coins. Using a multi-flow map, illustrate the steps in solving problems that deal

Research and celebrate Pi Day. Compose an essay from the perspective of pi that explains pi’s importance in math. Bean Pi* Create a multimedia

Bean Pi http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal02/objective2.02/2.02-tasks/2.02-beanpi.pdf

Discovery Math: Exploring Geometry http://school.discoveryed

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal02/objective2.02/2.02-tasks/2.02-beanpi.pdf





http://school.discoveryeducation.com/lessonplans/programs/DM_exploring_geometry/











Resources

Apply appropriate formulas for determining perimeter, circumference, and area of plane figures.

determining

perimeter,

circumference, and

area of plane figures,

as well as solve for

any unknown variable within the

formula.

used to solve problems?

circle

hexagon

height

polygon

octagon

altitude

with perimeter, circumference, and area. Use graph paper to illustrate the calculation of perimeter, area, and circumference. Create a venn diagram or double bubble map comparing/contrasting perimeter, area, and circumference.

presentation that examines and illustrates examples of real-world situations where determining circumference, perimeter, and area are relevant.

ucation.com/lessonplans/programs/DM_exploring_geometry/ Math Warehouse www.mathwarehouse.com/geometry















Resources

3 The learner will understand and use properties and relationships of geometric figures in the coordinate plan.

3.01 Identify and

describe the intersection

of figures in a plane.

The learner will: Identify and describe the intersection of figures in a plane.

4th 9-weeks

Recognize parallel and intersecting lines in a plane. Recognize perpendicular lines. Identify all pairs of angles and their relationships. Understand and identify common points, line segments, rays, angles, lines, and areas that two intersecting plane figures create. Draw and describe a path of shortest length between

What types of relationships can be formed when two lines intersect in a plane? What is the difference between interior and exterior angles?

vertex

interior angles

parallel

interior

region exterior

angles

perpendicular

exterior region

Create vocabulary squares (characteristics, definition, examples, non-examples, drawings) for each of the following words: ray, line, intersection, vertical angles, supplementary angles, line segments, rays.

Stir Crazy Geometry*

Stir Crazy Geometry http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal03/objective3.01/3.01-tasks/3.01-stircrazygeom.pdf

Math Warehouse www.mathwarehouse.com/geometry

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal03/objective3.01/3.01-tasks/3.01-stircrazygeom.pdf


















Resources

points to solve problems in context. Understand and know that the intersection of figures and/or lines in a plane create interior and exterior regions and/or angles.

3.02 Identify the

radius, diameter, chord, center, and circumference of a circle; determine the relationships among them.

The learner will: Label and define parts of a circle. Analyze the relationships among the parts of a circle.

1st

9-weeks

Determine the relationship between circumference and diameter of a circle. Understand that the circumference is greater than the diameter (C = Πd).

What is the radius of a circle? How is the radius of a circle related to the circle of the diameter?

Pi

ratio

proportion

Use a hula hoop to illustrate the measurements of a circle. Draw trace circles of various classroom objects. Illustrate and calculate determining the radius, diameter, chord, and

Round and Round * Draw circles that illustrate the sizes of the planets based on their circumferences or diameters. Create artwork with various circle sizes in a clear covering. One side

Round and Round http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal03/objective3.02/3.02-tasks/3.02-roundandround.pdf

Math Warehouse www.mathwarehouse.co

http://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade06/goal03/objective3.02/3.02-tasks/3.02-roundandround.pdf

















Resources

Understand that the diameter is greater than the radius (d = 2r). Model and understand the formula for circumference of a circle. (Discover that it takes slightly more than three (Π) diameters to equal the circumference of a circle.) Explain why the diameter is the longest chord in a circle.

circumference of the circle.

of the display should be artistic; the other side should include the radius, diameter, circumference, and area of each circle.

m/geometry Math Playground http://mathplayground.com/mathvideos.html

3.03 Transform

figures in the coordinate plane and

The learner will:

4th 9-weeks

Identify the four quadrants of the coordinate plane.

What impact does translation have on an

reflection

(flip)

Create a coordinate plane on a large area. Create shapes and

Slammin’ Sammy * Draw It Again, Sam*

NCDPI Activities http://www.dpi.state.nc.us/














Resources

describe the transformation.

Compare and contrast the differences between reflection, translation, and rotation.

Transform figures within the coordinate plane using reflections, translations, and rotations.

object? What impact does rotation have on an object? How do we represent a reflected object in the coordinate plane?

x-axis

notation translation

(slide)

y-axis

rotation (turn) quadrants

line of

reflection Quadrant I

center of

rotation

1st Quadrant angle of

rotation

Quadrant II

pre-image 2nd Quadrant

mirrors

image

move them around on the coordinate plane. Note changes in the coordinates of the vertices of the objects. Create a drawing that illustrates translation, reflection, rotation, shifts in shapes.

curriculum/mathematics/middlegrades/tasks?subjectIn=mathematics&&gradeIn=06&&goalIn=03&&objectiveIn=3.03














Resources

Quadrant III

patty paper clockwise

3rd Quadrant

counterclock

wise Quadrant IV

4th Quadrant 3.04 Solve

problems involving geometric figures in the coordinate plane.

The learner will: Construct and identify all parts of the coordinate plane. Solve problems involving geometric figures in the coordinate plane.

4th 9-weeks

Understand that the rectangular coordinate plane consists of two axes (number lines) of infinite length and four quadrants of infinite area. Demonstrate the graphing of ordered pairs.

How can I solve problems related to geometric shapes in the coordinate plane?

reflection

(flip)

x-axis

clockwise translation

(slide)

y-axis counterclock

wise

rotation (turn)

quadrants notation:

Geometry In The Coordinate Plane Draw a coordinate plane on a write-on/wipe-off surface. Draw shapes in the coordinate plane and experiment with solving problems with those shapes.

Constructing Geometric Figures* Create a living coordinate plane. Have students stand on plots in the coordinate plane, create shapes, etc.

NCDPI Activities http://www.dpi.state.nc.us/curriculum/mathematics/middlegrades/tasks?subjectIn=mathematics&&gradeIn=06&&goalIn=03&&objectiveIn=3.04




















Resources

line of

reflection Quadrants

I ,II, III, IV













Resources

4 The learner will understand and determine probabilities.

4.01 Develop

fluency with counting strategies to determine the sample space for an event. Include lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle.

The learner will: Develop fluency with counting strategies to determine the sample space for an event. Create and interpret lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle.

3rd

9-weeks

Determine sample space for events. Distinguish between fair, unfair, compound, and simple events. Determine strategy to solve for possible outcomes (including lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle).

How do you determine possible outcomes? What counting strategies can be utilized to determine the sampling space for an event? How are tree diagrams, frequency tables, permutations, and the Fundamental Counting Principle related to probability?

sample space

favorable outcome

possible outcome

Generate a list of examples of events that deal with probability. Recreate one of those events and determine probability. Flip a coin and create a frequency table that illustrates the number of times the coin lands on heads Create a double bubble map that illustrates the relationship between permutations and combinations.

Create a multimedia presentation on a real-world example in which probability has relevance (the probability of a sports team winning, etc.). Create a frequency table in MS Excel that exemplifies using frequency to solve a real-world problem.



4.02 Use a sample

space to determine

The learner will:

3

rd 9-

weeks

Determine the probability of

How is a sample space used to

possible

outcome

Present a Venn diagram, tree diagram,

Create a board game that illustrates

NCDPI – Look under DPI Resources
















Resources

the probability of an event.

Determine the probability of specific events.

specific events once the possible outcomes have been concluded. Define theoretical and experimental probability.

determine probability? How can the probability of an event be written?

favorable

outcome

geometric probability

or some other type of graphic organizer that represents a sample space that displays a probability event. Create a number wheel spinner and use it to determine the probability of landing on certain numbers.

probability events. Create a color spinner and use it to determine the probability of landing on certain colors.


4.03 Conduct

experiments involving simple and compound events.

The learner will: Conduct experiments involving simple and compound events.

3rd

9-weeks

Apply knowledge of probability events Determine trials and outcomes of experiments. Deduce the experimental probability of the event.

How can the theoretical and experimental probabilities be determined for an event? How can experiments be designed to determine probability?

experimental results

sample space

outcomes

favorable outcomes

possible

outcomes tree diagrams

organized lists

Create a Venn diagram that compares/contrasts simple and compound events. Cooperative learning: Conduct a series of simple experiments with coins that involve simple and compound events.

Design an experiment that involves simple and compound events. Compose a report or give an oral presentation that outlines the experiment.


















Resources

Fundamental Counting Principle

4.04 Determine

and compare experimental and theoretical probabilities for simple and compound events.

The learner will: Determine and compare experimental and theoretical probabilities for simple and compound events.

Determine the processes needed to conclude experimental and theoretical probability. Compare and contrast theoretical and experimental probability.

How are experimental probabilities determined for simple and compound events? How are theoretical probabilities determined for simple and compound events?

experimental

results

sample space outcomes

favorable

outcomes

possible outcomes

tree diagrams

geometric probability

Fundamental Counting Principle organized lists

Create a double bubble map that illustrates the relationship between probabilities for simple and compound events.

Use statistical data to create a display that compares experimental and theoretical probabilities for simple and compound events.


Understanding Probability http://school.discoveryeducation.com/lessonplans/programs/probability/




http://school.discoveryeducation.com/lessonplans/programs/probability/













Resources

4.05 Determine and

compare experimental

and theoretical

probabilities for

independent and

dependent events.

The learner will: Determine and compare experimental and theoretical probabilities for independent events. Determine and compare experimental and theoretical probabilities for dependent events.

3rd

9-weeks

Define the differences between independent and dependent events. Determine and compare experimental and theoretical probabilities for independent events in which the second outcome does not depend on the first outcome. Determine and compare experimental and theoretical probabilities for dependent events in

What is the difference between independent and dependent events? How is the outcome of one event affected by the outcome of another event in independent or dependent events?

experimental

results sample space

favorable

outcomes

possible outcomes

with

replacement and without

replacement

Create scenarios for independent and dependent events. Brainstorm and design an experiment that exemplifies an independent and dependent event.

Brainstorm and design an experiment that exemplifies an independent or dependent event and create a spreadsheet of the outcomes probabilities of the events.















Resources

which the second outcome depends on the first.

4.06 Design and

conduct experiments or

surveys to solve

problems; report and

analyze results.

The learner will: Distinguish between biased and random sampling. Design and conduct experiments or surveys to solve problems. Report and analyze results for experiment.

1st 9-

weeks Discuss the differences between biased and random samples. Develop unbiased questions, collect data, and make interpretations. Report and analyze results for experiment through various methods, such as visual representations and/or oral reports.

What determines if a sample is biased or random? How can you conduct an experiment to solve a problem, while reporting and analyzing the results?

sample space

representative sample

theoretical

probability

experimental results

Brainstorm and design a class experiment that exemplifies probability. Conduct the experiment and analyze the results. Planet Collector Cards*

Compose a song that describes a probability experiment, how that experiment would be conducted, and how to analyze the results of that experiment. Design a game using different colored marbles or beans that exemplifies a probability experiment.


Evaluation & Assessment














Resources

Target Date












Resources

5 The learner will demonstrate an understanding of simple algebraic expressions.

5.01 Simplify

algebraic expressions

and verify the results

using the basic

properties of rational

numbers.

a. Identity.

b. Commutative.

c. Associative.

d. Distributive.

e. Order of

operations.

The learner will: Identify the properties of addition and multiplication, as well as distributive and order of operations. Apply the properties of rational numbers to algebraic expressions.

1st and

3rd

9-weeks

Understand how to rewrite problems by grouping like terms. Rewrite expressions using the distributive property. Solve problems with order of operations.

How can various mathematical properties be defined and used? How can you simplify expressions using the order of operations?

term

multiplicative identity

braces

like terms

additive identity

combining

like terms multiplicative

inverse

equivalent

expressions additive

inverse

coefficient

grouping symbols

variable

order of

Create a bridge map for identity, commutative, associative, distributive, and order of operations. Create a vocabulary square with characteristics, examples, non-examples, paraphrase definition of each of the basic properties. Mental Math Using Properties* Order of Operations Square Puzzle*

Compose a story about a neighborhood that narrates relationships among the neighbors that parallel each of the basic properties of rational numbers. Create an informational brochure that identifies, explains, and describes each of the basic properties. Alien Math* Property Concentration* Property Matching Game*


Discovering Math: Computations http://school.discoveryeducation.com/lessonplans/programs/DM_computation/ Math Warehouse www.mathwarehouse.com/algebra








http://www.mathwarehouse.com/algebra












Resources

operations

exponents parentheses

brackets

5.02 Use and

evaluate algebraic

expressions.

The learner will: Evaluate or simplify algebraic expressions. Construct algebraic expressions.

1st and 2nd 9-weeks

Determine whether expressions are equivalent. Perform substitutions in order to evaluate expressions Apply algebraic concepts to problem-solving solutions.

How can clue words be used to write algebraic expressions? How can algebraic expressions be used in real-life situations?

combining

like terms

exponents coefficient

variable

order of

operations

equivalent expressions

Create a gallery walk of algebraic equations solved correctly and incorrectly. Determine which equations are solved correctly. Justify your reasoning for why they are solved correctly. Evaluate the problems that are solved incorrectly and determine the correct solution. Create a multi-flow map that illustrates the steps in the order of

Create a poster of “clue words” used to create expressions. Formulate a plan for a small business. Create a plan for that business that illustrates your monthly expenditures. Compose an informative report that details your plan and describes how you used algebraic expressions to complete the plan. Exponents Experts Game*


Math Warehouse www.mathwarehouse.com/algebra



















Resources

operations and details an application of the order of operations. Using Variables* X in the mix*

Expression War* Ordered Pairs and Patterns* Using Models for Algebraic Expressions*

5.03 Solve simple (one- and two-step) equations or inequalities.

The learner will: Compare and contrast equations and inequalities. Solve one-step equations. Solve two-step equations. Solve one-step

1st and

3rd

9-weeks

Define inequality symbols, coefficients, and variables. Solve equations and inequalities by applying the properties and inverse operations.

How can “guess and check” be used to solve equations? How does increase operation help to solve the unknown in an equation or inequality?

variable order of

operations

additive

inverse less than

inequalities,

multiplicative

inverse greater than

distributive

property

Model simple expressions with counting blocks, tiles, or other manipulatives. Create a multi-flow map that illustrates the steps of “Guess and Check” used to solve an equation. Model various strategies and examples of solving

Create an acronym that can be used as a memory aid for solving one- and two- step equations or inequalities. Showcase problems based on real-world situations in which the guess and check strategy must be applied.


Math Warehouse www.mathwarehouse.com/algebra
















Resources

inequalities. Solve two-step inequalities.

less than or

equal to equivalent

expressions

greater than or equal to

one- and two- step equations and/or inequalities. Inequality Race*

5.04 Use graphs,

tables, and symbols to

model and solve

problems involving

rates of change and

ratios.

The learner will: Define rates and ratios. Interpret graphs and tables to solve problems involving rates of change and ratios.

2nd

and 3

rd 9-

weeks

Determine ratios for various situations. Translate data from tables to graphs and graphs to tables. Apply variables to determine rates of change.

How can patterns be used to determine rates of change? How does a model or graph help to solve problems involving rates of change or ratios?

equivalent

ratios

proportions

Create a table and graph for the same data set using MS Excel. Provide real-world examples of rates of change and ratio problems that require the use of graphs and tables.

He Grew and Grew*


Architects in Action http://school.discoveryeducation.com/lessonplans/programs/architectsinaction/ Math Warehouse www.mathwarehouse.com/algebra




http://school.discoveryeducation.com/lessonplans/programs/architectsinaction/
















Resources



Middle Grades Curriculum Guide for Mathematics 6 ... * denotes a learning opportunity found at ....

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Transcript of Middle Grades Curriculum Guide for Mathematics 6 ... * denotes a learning opportunity found at ....