# Mathematics 6

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6th Grade is a time when all of the basic math skills will be solidified, strengthened and deepened. In tandem with this basic skills development will be an emphasis on creative problem-solving strategies and generalizing patterns to push the growth of each child's abstract thinking and logical reasoning ability. The beginning of algebraic thinking will be woven throughout the curriculum. Saxon Math is the textbook that we use in 6th-8th grade as the backbone of our math curriculum. It is designed with a spiraling approach so that topics are introduced over a period of time and continue to be reinforced consistently throughout the year and over the 3 years. In addition to Saxon math, we supplement with a variety of materials and a variety of approaches since no single method is effective for every child. To balance the direct instructional style of Saxon math, Connected Math's student-directed curriculum will be integrated into the overall 6th grade math program. In addition, the students will be introduced to some computer programming during our gender-based grouping in the spring.

## Units

Unit Essential Questions Content Skills and Processes Assessment Resources Multicultural Dimension Integrated Learning
Prime Time
• In what way are prime numbers the foundation of all arithmetic?
• What are prime numbers and how are they different from composite numbers?
• How can prime numbers be used to help with calculating Least Common Multiple and Greatest Common Factors
• The Fundamental Theorem of Arithmetic
• Prime numbers vs. Composite Numbers
• Square numbers
• Perfect numbers
• Abundant numbers vs. Deficient Numbers
• How Venn diagrams communicate information
• Proper Factors vs. Factors
• Prime Factorization
• Positive Exponents
• Even vs. Odd Numbers
• Definition of product, multiple, factor, divisor
• Calculate Greatest Common Factor (GCF)
• Calculate Least Common Multiple (LCM)
• Use Venn Diagrams to determine GCF and LCM
• Use the rectangle method and rainbow method to factor numbers
• Use trees and upside-down cakes to find prime factorization
• Solve story problems requiring GCF and LCM; recognize what type of situation demands the calculation of one of these
• Use exponents in prime factorization
• Favorite Number Forever (FNF) Project
• Written Test
• Locker Problem, Mystery Numbers, Product Mazes, puzzles, games and story problems

Prime Time - Connected Math/MSU

Famous people and historical events from around the world.

• Historical events (Humanities) that happened in the same year as each student's FNF
• Contributions of famous people (Humanities) who were born on the same day as each student's FNF
• Atomic Elements (Science) with the same number as each student's FNF
• Shakespearean sonnets (English) with the same number as each student's FNF
• Visual display (Art) created for each students's FNF
• Famous athletes (PE) whose jersey number is the same number as each student's FNF
• Be able to pronounce and write your FNF in a foreign language.
Measurement and the Metric System
• How and why did systems of measurement first evolve?
• How and why was the metric system invented?
• Why is it important to learn the metric system?
• How is the metric system different from and similar to our system?
• What are the units of measurement in the metric system?

• History of measurement
• Evolution of the English Customary System
• Units of measure in the Customary System
• Design, invention and history of the Metric System
• The difference between Length, Volume, Mass and Weight
• Units of measure in the Metric System and how they were defined
• Metric prefixes and symbols
• Advantages of the metric system

• Powers of ten; exponent review
• Decimal place value
• Estimating quantities in metric units
• Converting between units within each system
• Use of appropriate measuring tools
• <Introduction to negative exponents and scientific notation>
• Metric Pre-Test
• Estimetrics Game
• Watermelon Relay Team Test
• Written Test
• EQUALS Watermelon Activity
• Estimetrics - CSUS
• Internet
• Powers of Ten DVD
• Evolution of measurement in different cultures; universality of measurement
• Historical development of the English Customary System
• Historical development of the Metric System in France
• International usage of the Metric System
• Use of the metric system in science
• Use of lab equipment for measuring
• Historical development of measurement (6th grade humanities)
• Calibration of the human body (6th grade science)
Geometry and Transformations
• How has geometry inspired artists?
• How is geometry used in product design and graphic arts?
• How are geometric shapes defined and classified by their properties?
• Definitions for line, segment, ray, angle (acute, obtuse, right), non/collinear points, midpoint, complementary/supplementary angles, intersecting/parallel lines, regular/irregular, congruent, circle, triangles, quadrilaterals, and other polygons
• Use the correct notations for geometric terms
• Types & properties of triangles and quadrilaterals
• Angular measurements in circles, triangles, and quadrilaterals
• Formulas for finding area of quadrilaterals, triangles, and circles and how were they derived
• Types of translations: translation (slide), rotation (turn), reflection (flip)

*Find missing angle measurements using complementary/supplementary properties, and 180 in a triangle and a line
*Calculate the degrees in a polygon and find each angle measurement for regular shapes
*Measure and draw angles accurately with a protractor
*Explain the differences between different types of triangles and quadrilaterals; know the properties of each
*Use the correct formulas for finding area of 2D shapes: quadrilaterals, triangles, circles
*Use a Mira to reflect and check for lines of symmetry
*Perform three types of transformations on a figure (slide, flip, turn)
*Combine transformations to create a tessellation

• Written Test
• Geometry Story: Write a short story that uses geometric shapes and properties symbolically (e.g. A love letter from a square to a circle)
• Tessellation Project
• Design packaging for a new product - find surface area from the 2D shapes that make the sides of the package.
• Protractors, rulers, geometric shape kits (plastic/cut-out), tangram sets
• Tangram sets
• Origami constructions
• <Straw Polyhedra>
• Flatland by Edwin Abbott
• Slides, Flips, and Turns
• Examples of Escher tessellations
• Tessellation Exploration software (Tom Snyder Productions)
• The work and life of MC Escher
• Extensions: Read Flatland - This book symbolically uses geometric shapes to connect with the social issues of caste systems and  fairness.
• Geometry and Art: Tesselations
• The work of MC Escher
• Product design and packaging (Arts and Engineering)
• Graphic Arts
• Geometry Story (Language Arts)
• Extensions: Read Flatland. (Language Arts and Humanities)
Intro to Computer Programming
• How is computer programming important in today's society?
• How do gender differences impact participation in this field?
• What is the basic structure and concepts of computer programming?
• How are creative thinking, logical reasoning and problem-solving used in computer programming?
• Statistics on the participation of women in computer science.
• Uses of computer programming in today's society
• Types of programming commands/blocks: Controls, Sensing, Operators, Loops, waits, reporters, variables, sounds, motion, appearance, broadcasts, lists, strings, boolean values
• Elements of the software interface
• Options in the paint editor

• create sprites
• create costumes
• create stages
• create scripts using various types of programming blocks
• add sounds, photos, images from the internet
• animate people/objects in a scene
• use the paint editor
• Holiday e-card Project
• Rubric for assessing SCRATCH programs
• Gender Based Attitude Survey
• PowerPoint on the State of Computer Programming in the US
• SCRATCH - MIT

Gender-based unit

Art, design, problem-solving, technology, linear and logical thinking

Statistics and Data Analysis
• How is information conveyed through statistics?
• How does the format of the statistic affect the message communicated?
• How can you critically evaluate statistical information?
• Definition of: mean, median, mode, range, and outlier; explain how to find each
• How an outlier may impact the mean
• When a median or mode might be more accurate or informative than the mean (Bill Gates example)
• How to talk back to a statistic. What questions should you ask?
• The difference between a random and biased sample
• How a graph can be misleading, and how it could be made honest
• The impact of sample size on statistics
• Design considerations when developing a survey or gathering data

*Review decimal arithmetic, especially division and estimation
*Calculate mean, median, mode, and range for a set of data in numerical list and graph forms
*Identify population & sample size
*Calculate the percent of a total and create a pie chart representation
*Review rounding decimal numbers, using a protractor to measure degrees, and fraction-decimal-% conversions
*Extract information from a bar, line, or pie graph, and use it to make decisions
*Create misleading bar, line, and picto- graphs
*Distinguish between unbiased and biased surveys

Written Test:
Statistics Survey: Choose a question to investigate, conduct a survey, create honest & misleading graphs; present the results
Graph Evaluation: Find three misleading graphs (newspaper, Internet); describe how it is misleading, how to make it more misleading, & how to make it more truthful

The Sneaker Problem and McDonalds (ranking information and making decisions)
Worksheets on mean, median, mode, outliers, line/bar/pie graphs
How to Lie with Statistics by Darrell Huff
Is Democracy Fair? by Leslie Johnson Nielsen and Michael de Villiers (different voting systems and ways of counting ballots)
USA Today web site Snapshots
Misleading graph images (online and printed)
GraphMaster software for creating line, bar, and pie graphs

Social Studies and Science examples of misleading and appropriate statistics

Fractions, Ratios, and Probability
• How do fractions relate to percents and ratios
• How do ratios relate to probability?
• How does probability relate to the "fairness" of a game or situation?
• Compare two fractions with different denominators
• Define: fraction, lowest terms, improper fraction, numerator, denominator, equivalent fractions
• Theoretical and experimental probability
• Relationship between P(A) and the P(not A)
• Logical operators affect counting
• Percent
• Factors that may influence a game or experiment
• Perform probability experiments, collect and analyze results to determine experimental probability
• Calculate theoretical probability for a given situation, including the use of logical (and, or, not) operators
• Create systematic lists as a method for counting possibilities
• Perform fraction arithmetic operations on fractions and mixed numbers, also be able to reduce fractions, convert to/from mixed numbers, and compare fractions
• Convert between fractions, decimals, and percents
• Determine a definition for fairness
• Decide whether a game or situation is fair (consider probability, value, influences)
• Calculate the probability of dartboards using area

*Test: Fraction arithmetic, reducing, comparing fractions, definitions
*Test: Probability and Percents. Convert between fraction/decimal/percent, calculate probabilities, list factors that may affect the experimental probability of a game
*Create a game in which the theoretical and experimental probabilities are the same (i.e., eliminate the external influences)

Fraction arithmetic worksheets
Probability books: handouts, games, worksheets
What is Fair? activity
Crossing the River with Dogs - Problem Solving