# Unit Essential Question: When do we need standard symbols, operations, and rules in mathematics? (CAIU)

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1 Page 1 Whole Numbers Unit Essential : When do we need standard symbols, operations, and rules in mathematics? (CAIU) M6.A Whole Number Operations Dividing with one digit (showing three forms of answers) M6.D Sequencing (pattern must show at least 3 repetitionsmay use up to 2 operations with whole numbers.) M6.D Pattern Rules (displayed on a table, chart, or graph; pattern must show at least 3 repetitions). How do you solve problems involving operations (+,-,x, ) with whole numbers? How do you create, extend or find a missing element in a pattern displayed in a table, chart, or graph? How do you determine a rule based on a pattern or illustrate a pattern based on a given rule? Division Dividend Divisor Quotient Remainder Pattern Rule Pattern Rule -Division Review Sheet -Division Coded Message -1.2 Practice -Can you tell the hidden message? -1.2 Practice -Can you tell the hidden message?

2 Page 2 Whole Numbers Unit Essential : When do we need standard symbols, operations, and rules in mathematics? (CAIU) M6.A Compare and/or order whole numbers M6.A Estimation M6.A Exponents How do you compare and/or order whole number? How do you use estimation to solve problems involving whole numbers? How do you represent a number in exponential form (eg., 10 x 10 x 10 = 10³)? Compare Order Estimate Rounding Base Exponent -1.3 Study Guide/ Practice -Estimation Station -1.6 Study Guide/Practice

3 Page 3 Whole Number Unit Essential : When do we need standard symbols, operations, and rules in mathematics? (CAIU) Order of Operations M6.C Plot, locate or identify points in Quadrant I and/or on the x and y axes with intervals of 1,2,5 or 10 unitsup to 200 by 200 grid. Points may be in-between lines. question Why do you need the order of operations? How do you plot points on a coordinate grid? Parenthesis Order of operations Exponents Quadrants x axis Y axis ordered pair -Order of Operations Puzzle -Monster Math Posters Study Guide/Practice

4 Page 1 Statistics/Data Analysis Unit Essential : What kinds of things in life can equations help us do? (CAIU) M6.D Match an equation or expression involving one variable, to a verbal math situation (one operation only). M6.D Identify the inverse operation needed to solve one step equations. M6.D Solve a one step equation (i.e., using the inverse operation whole numbers only). How do you match an equation or expression to a math situation? What is an inverse operation? How do you solve a one step equation? Equation, expression, variable Operation, inverse Inverse operation, equation , 12.2, 12.3 Guide/ Practice -12.1, 12.2, 12.3 Guide/ Practice

5 Page 2 Statistics/Data Analysis Unit Essential : What kinds of things in life can equations help us do? (CAIU) M6.A Complete equations by using the following properties: associative, commutative, distributive, and identity. What is the difference between the associative, commutative, distributive, and identity properties? analyze -

6 Page 1 Decimals Unit Essential : How do we write and use the basic operations with decimals? Decimal Place Value Writing Decimals M6.A Compare and/or order decimals and whole numbers through thousandths. What are the decimal place values? How do you say and write decimals correctly? How do you compare and order decimals? Tenths Hundredths Thousandths Point = and Tenths Hundredths Thousandths Compare Order Greater than Less Than -Decimal Roundup -Rounding Game -Stumpers 3.1 Study Guide/Practice -3.3 Study Guide/Practice -Weighty Problems

7 Page 2 Decimals Unit Essential : How do we write and use the basic operations with decimals? M6.A Solve problems involving operations (+,-,x, ) with decimals (through thousandths). Adding and Subtracting M6.A Solve problems involving operations (+,-,x, ) with decimals (through thousandths). Multiplying M6.A Solve problems involving operations (+,-,x, ) with decimals (through thousandths). Dividing by whole numbers How do you set up and addition problem with decimal numbers? How do you determine the number of decimal place values in the answer of a multiplication problem? How do you place the decimal in the answer when dividing a decimal by a whole number? Borrow Carry Product Multiplier Quotient Divisor Dividend -Absolutely Magical -3.6 Study Guide/Practice - x decimal cross number puzzle -4.5 Study Guide/Practice

8 Page 3 Decimals Unit Essential : How do we write and use the basic operations with decimals? M6.A Solve problems involving operations (+,-,x, ) with decimals (through thousandths). Dividing by Decimals M6.A Differentiate between a terminating decimal and a repeating decimal. M6.A Use estimation to solve problems involving decimals (up to 2 digit divisors and 4 operations). What must you do before dividing a decimal by a decimal? What is the difference between terminating and repeating decimals? How do you use estimation to solve problems involving decimals? Quotient Divisor Dividend -4.6 Study Guide/Practice

9 Page 1 Fractions Unit Essential : What are fractions and how do we use them in everyday life? M6.A Use divisibility rules for 2, 3, 5, and/or 10 to draw conclusions and/or solve problems. Prime vs. Composite Prime Factorization What are the tricks to help you determine if a number is divisible by another? What is the difference between prime and composite numbers? How do we find the prime factorization of a number? Divisibility Prime Composite Factors Prime Factor Tree Composite -Foldable -Graphic Organizer -5.1 Study Guide/Practice -Graphic Organizer -5.2 Study Guide/Practice -5.2 Study Guide/Practice

10 Page 2 Fractions Unit Essential : What are fractions and how do we use them in everyday life? M6.A Greatest common Factor (through 50) M6.A Least Common Multiple (through 50) Fraction Introduction How do you find the greatest common factor (GCF)? What do you use least common multiple for? What are the different kinds of fractions? What are the pieces and parts of a fraction? Factor Greatest Common Multiple Least Common Numerator Denominator Mixed Number Equivalent Improper Fraction -5.3 Study Guide/Practice -5.7 Study Guide/Practice -Fractions Crossword

11 Page 3 Fractions Unit Essential : What are fractions and how do we use them in everyday life? M6.A Use the GCF to simplify fractions. M6.A Mixed to Improper/Improper to Mixed M6.A Compare and/or order mixed numbers and fractions. Why do we simplify fractions? What are the steps to changing a mixed number into an improper fraction/improper fractions to mixed number? When you compare and order fractions, what must be the same? Greatest Common Factor Numerator Denominator Numerator Denominator Whole Number Common Denominator Numerator -Fraction Flowers -Graphic Organizer -5.5 Study Guide/Practice -Fraction Squares -5.8 Study Guide/Practice

12 Page 4 Fractions Unit Essential : What are fractions and how do we use them in everyday life? M6.A Multiplying Fractions and Mixed Numbers M6.A Dividing Fractions and Mixed Numbers M6.A Adding and Subtracting Fractions (Like & Unlike Denominators, Mixed Numbers, Subtracting with Borrowing) What are the steps to multiplying fractions? What must be done before we multiply mixed numbers? How is dividing fractions and multiplying fractions similar? When adding and subtracting fractions, what must be the same? Numerator Denominator Reciprocal Numerator Denominator Least Common Multiple Common Factor Materials/Resource -7.2 Study Guide/Practice -7.5 Study Guide/Practice -7.6 Study Guide/Practice -6.3 Study Guide/Practice -Sum It Summit Game -6.4 Study Guide/Practice

13 Page 5 Fractions Unit Essential : What are fractions and how do we use them in everyday life? M6.A Convert between fractions and decimals Cross Cancelling How do you convert fractions to decimals and back? How do you use cross cancelling to solve multiplication fractions problems? Quotient Divisor Dividend Numerator Denominator -5.9 Study Guide/Practice

14 Page 1 Geometry Unit Essential : Why is it important to understand the properties of geometric figures? M6.C Identify, draw and/or label points, planes, lines, line segments, rays, angles, and vertices. M6.C Lines M6.B Define, label and/or identiy right, straight, acute, and obtuse angles. How do you identify, draw and/or label points, planes, lines, line segments, rays, angles, and vertices? How do you identify, describe, and/or label parallel, perpendicular, or intersecting lines? What are the characteristics of the different types of angles? Plane, Lines, Points, Ray, Angles, Vertices Parallel, Perpendicular, Intersecting Right, Straight, Acute, Obtuse, -Understanding the concept of geometric lines -Understanding the concept of geometric lines -9.1 Study Guide/Practice

15 Page 2 Geometry Unit Essential : Why is it important to understand the properties of geometric figures? M6.B Measure angles using a protractor up to 180 protractor must be drawn-one side of angle to be measured should line up with the straight edge of protractor. M6.C Identify and/or describe properties of all types of triangles (scalene, equilateral, isosceles, right, acute, obtuse.) M6.C Identify and/or use the total number of degrees in a triangle, quadrilateral, and/or circle. How do you measure an angle using a protractor? What are the properties of different triangles? How do you identify and use the degrees of a triangle? How do you identify and use the degrees of a quadrilateral? How many degrees in a circle Acute, Obtuse, Straight, Right, Protractor Scalene, Equilateral, Isosceles, Right, Acute, Obtuse Degrees, Triangle, Circle, Quadrilateral -9.1Study Guide/Practice -Identifying Triangles -Finding the degrees of angles in triangles

16 Page 3 Geometry Unit Essential : Why is it important to understand the properties of geometric figures? M6.C Identify, classify, and/or compare polygons (up to ten sides.) M6.B Find the perimeter of any polygon (may include regular polygons where only the measure of one side is given-same units throughout). Area of Polygons (Squares, rectangles, triangles, and parallelogram). What are the different types and properties of polygons? How do you find the perimeter of a polygon? How do you find the area of polygons? Triangle, Quadrilateral, Pentagon, Hexagon, Septagon, Octagon, nonagon, Decagon Perimeter, Units Length, width, height, base, square units -Overhead Notes -Graphic Organizer -How do we find perimeter? -Perimeter -Rectangles and squares -4.4 Study Guide/Practice Study Guide/Practice

17 Page 4 Geometry Unit Essential : Why is it important to understand the properties of geometric figures? M6.A Multiplying Fractions and Mixed Numbers M6.A Dividing Fractions and Mixed Numbers M6.A Adding and Subtracting Fractions (Like & Unlike Denominators, Mixed Numbers, Subtracting with Borrowing) What are the steps to multiplying fractions? What must be done before we multiply mixed numbers? How is dividing fractions and multiplying fractions similar? When adding and subtracting fractions, what must be the same? Numerator Denominator Reciprocal Numerator Denominator Least Common Multiple Common Factor Materials/Resource -7.2 Study Guide/Practice -7.5 Study Guide/Practice -7.6 Study Guide/Practice -6.3 Study Guide/Practice -Sum It Summit Game -6.4 Study Guide/Practice

18 Page 5 Geometry Unit Essential : Why is it important to understand the properties of geometric figures? M6.C Identify and/or determine the measure of the diameter and/or radius of a circle (when one or the other is given). What are the parts and properties of a circle? Diameter, Radius, Circumference Study Guide/Practice -Graphic Organizer

19 Page 1 Measurement Unit Essential : How do we use measurement to make sense out of real life? (CAIU) M6.B Use or read a ruler to measure to the nearest 1/16 inch or millimeter. M6.E.B Choose the more precise measurement of a given object (e.g., smaller measurements are more precise). M6.B Determine and/or compare elapses time to the minute (time may cross AM to PM or more than one day). How do you use a ruler to measure to the nearest 1/16 of an inch or millimeter? How do you know which unit would be more useful for a given object? How do you determine how much time has passes between a given time period? Inch, millimeter, ruler, measure Inch, millimeter, ruler, measure, unit Hours, Minutes, Seconds, elapses -5.6 Study Guide/Practice Study Guide/Practice

20 Page 1 Percents Unit Essential : How are fractions, decimals and percents notations alike and how are they different? M6.A Represent common percents as fractions and/or decimals (e.g., 25% =1/4 =.25)-common percents are 1%, 10%, 25%, 75%, 100%. M6.A Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc.) How do you show percents as a fraction or decimal? How do you show a percent with a picture or graph? Percent Numerator Denominator Percent Numerator Denominator -8.4 Study Guide/Practice -8.5 Study Guide/Practice -8.4 Study Guide/Practice -8.5 Study Guide/Practice

21 Page 1 Probability Unit Essential : What is the best way of examining patterns and trends in order to predict future events? (CAIU) M6.E Define and/or find the probability of a simple event (express as a fraction in lowest terms). M6.E Determine/show all possible combinations involving no more than 20 total arrangements (e.g., tree diagram, table, grid.) How do you find the probability of a simple event? How do you show all possible combinations of a given event? Probability, simple event Operation, inverse -Determine Probability -Drawing a tree diagram or making a list

22 Page 1 Statistics/Data Analysis Unit Essential : How can we represent and interpret data to show trends? (CAIU) M6.E Determine/calculate the mean, median, mode and/or range of displayed data (data can be displayed in a table or line plot-whose whole numbers. M6.E Display date in frequency tables, circle graphs, double bar and line graphs, or line plots using a title, appropriate scale, labels, and key. M6.E Choose the appropriate representation for a specific set of data (choices should be the same type of graph). How do you calculate mean, median, mode, and range? How do you create tables and graphs? How do you determine which graph would work best for the information given? Data, Mean, Median, Mode, Range Graphs, Bar, Circle, scale, label, key, title -2.7 Study Guide/Practice -2.2 & 2.2Study Guide/ Practice

23 Page 2 Statistics/Data Analysis Unit Essential : How can we represent and interpret data to show trends? (CAIU) M6.A.E Analyze data and/or answer questions pertaining to data represented in frequency tables, circle graphs, double bar and line graphs. How do you analyze data to answer questions? analyze -This will be done throughout the unit.

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