Math Power Standard 1 Unit Assessment #1 and #3 PS 1 - Estimate products and quotients of fractions and decimals (6.1.C) Big Idea: Estimating helps us decide if our answers make sense. Essential Questions: Why do you estimate products and quotients when working with fractions and decimals? approximate, benchmark, estimate, evaluate, integer, justify, number line, product, quotient, round Products and quotients can be estimated. Related Standards Identify or explain whether estimation or exact calculation is appropriate in situations involving multiplication and division of non-negative fractions and decimals Estimate in situations involving multiplication and division of nonnegative fractions and decimals Use estimation to determine whether a computation result is reasonable Describe or explain a strategy used for estimation involving multiplication and/or division of non-negative fractions and decimals Compare and order non-negative fractions, decimals, and integers using the number line, lists, and the symbols =, <, > (6.1.A). Represent multiplication and division of non-negative fractions and decimals using area models and the number line, and connect each representation to the related equation (6.1.B). Resources Bits and Pieces II: 3.1, 3.2, 3.3; Bits and Pieces III: 2.1, 2.2, 2.3, 3.1, Chapter 3 Pg. 97-98 Chapter 4 Pg. 114 116; 124-125
Math Power Standard 2 PS 2 Fluently and accurately multiply and divide non-negative fractions and explain the inverse relationship between multiplication and division with fractions (6.1.D). Big Idea: With fractions, mixed numbers and whole numbers, there is an inverse relationship between multiplying and dividing. Essential Questions: How does multiplying and dividing fractions, and mixed numbers compare to multiplying and dividing whole numbers? Key Vocabulary (on WASL) numerator, denominator, division, multiple, product Terms that May be Used with Definitions or Examples: Related Grade Level Expectations Quotient How mixed numbers and improper fractions relate Why we convert to improper fractions to multiply Answer doesn t follow whole number rules (multiplying can get smaller and dividing can get bigger) Dividing is finding how many groups of the divisor fit in the dividend. Multiplying means of. (2 x 2 = 2 of 2) Fraction bar = division (numerator divided by the denominator) explain or illustrate the meaning of multiplying or dividing non-negative fractions select and/or use an appropriate operation to show understanding of multiplication or division of non-negative fractions explain, with words or pictures, why multiplication of fractions can be done by multiplying denominators translate a given picture or illustration into an equivalent symbolic representation of multiplication or division of nonnegative fractions How to convert mixed numbers to improper fractions and viceversa. Compare and order non-negative fractions using the number line, lists, and the symbols =, <, >. Represent multiplication and division of nonnegative fractions using area models and the number line, and connect each representation to the related equation. Resources Bits and Pieces II: 3.4, 3.5 4.3, 4.4 Chapter 3 Pg. 93 98 (Multiplication); Pg. 98 106 (Division)
Grade Six Math Power Standard 3 PS 3 - Fluently and accurately multiply and divide non-negative decimals (6.1.F) Big Idea: Multiplying decimals can be compared to dividing decimals. Essential Questions: How are multiplying and dividing decimals related? first time at sixth grade) hundredths, integer, inverse, tenths, thousandths, whole number There is an inverse relationship between multiplying and dividing decimals Understand the inverse relationship between multiplication and division Work with different types of rational numbers including whole numbers and decimal numbers Related Grade Level Expectations Compare and order non-negative decimals using the number line, lists, and the symbols =, <, >. Represent multiplication and division of nonnegative decimals using area models and the number line, and connect each representation to the related equation. Resources Bits and Pieces III: 2.4, 3.3, 3.4 Chapter 6
Grade Six Math Power Standard 4 PS 4 - Write a mathematical expression or equation with variables to represent information in a table or given situation (6.2.A) Big Idea: Tables, expressions, equations, and inequalities represent mathematical relationships. Essential Questions: How do you use tables, graphs, expressions, equations, and inequalities to determine a rule? What does the rule mean? Related Standards =,,, <, >,,, axis, distributive property, equation, expression, identify, identity property, predict, relationship, rule, variable Rules can be used to describe patterns of two arithmetic operations. Tables, graphs, expressions, equations, or inequalities can represent situations involving two arithmetic operations. Rules can be used to evaluate expressions. Identify or write a simple expression, using variables, to represent a given situation. Identify or write a simple equation or simple inequality, with variables, to represent a given situation, using =,,, <, >,, or. Explain the meaning of variables in a formula, expression, equation, or inequality. Identify a situation that corresponds to a given expression, equation, or inequality. Identify or describe a number pattern given in tables, rules, or words. Extend a pattern by identifying or supplying missing elements in the beginning, middle, and/or end and/or describe the pattern or write a rule with alternating operations between terms. Create a pattern that uses the same rule as a given pattern. Create a pattern and explain what makes it a pattern. Write a simple expression for a given situation and evaluate the expression given the values for the variables. Evaluate an expression or formula given the values for the variables. Draw a first-quadrant graph in the coordinate plane to represent information in a table or given situation (6.2.B). Evaluate mathematical expressions when the value for each variable is given (6.2.C) Solve work problems using mathematical expressions and equations and verify solutions (6.2.F) Resources PPS Algebra Unit: Investigation 1, 2, 3 Chapter 8 Chapter 9 Chapter 10
Math Power Standard 5 PS 5 - Solve one-step equations using order of operations and verifying solutions (6.2.E) Big Idea: Logical patterns exist and are a regular occurrence in mathematics Essential Questions: How can looking for patterns help us solve every day problems? =,,, <, >,, or, equation, expression, function, identify, inequality, interval, order of operations, relationship, solution, variable Order of operations (PEMDAS) Informal use of inverse operations Related Grade Level Expectations Identify or write a simple expression, using variables, to represent a given situation Identify or write a simple equation or simple inequality, with variables, to represent a given situation using =,,, <, >,, or Explain the meaning of variables in a formula, expression, equation, or inequality Identify a situation that corresponds to a given expression, equation, or inequality Solve work problems using mathematical expressions and equations and verify solutions (6.2.F) Resources PPS Algebra Unit: Investigations 1, 2, 3 Chapter 9
Math Power Standard 6 PS 6 - Represent percents visually and numerically, and convert between the fractional, decimal, and percent representations of a number (6.3.C) Big Idea: Many numbers exist between whole numbers. A relationship exists between fractions, decimals and percents. Essential Questions: What relationship exists between fractions, decimals, and percents and how do you relate them? How do we use numbers between whole numbers? Why do we use numbers between whole numbers? =,,, <, >,, or, decimal, denominator, fraction, greatest common factor, improper fraction, least common multiple, lowest terms, mixed number, number line, numerator, percent The relationship between fractions, decimals, and percents. Positive non-negative rational numbers (2 ½, 2.5, 250% etc.) Explain when a fraction, decimal or percent of one whole is not the same as the same fraction, decimal or percent of another whole. Convert between fractions, improper fractions, mixed numbers, percents, and/or decimals. Compare and/or order non-negative proper and improper fractions, mixed numbers, percents, and decimals on a number line with illustrations or symbolically. Explain why one fraction, decimal, or percent is greater than, equal to, or less then another fraction, decimal, or percent. Related Standards Resources Bits and Pieces III: 4.1, 4.2 Identify and write ratios as comparisons of part-to-part and part-to-whole relationships. Chapter 3 Chapter 4
Grade Six Math Power Standard 7 PS 7 - Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions (6.3.D) Big Idea: Decimals can be written as fractions and percents. Percent means out of 100. Ratios can be written as fractions. A ratio is a relationship between two units. Essential Questions: How should ratios be written? How do you represent part-to-part and part-to-whole and whole-to-whole relationships? first time at sixth grade) Resources conclude, conclusion, per, percent, rate, ratio, scale, support, unit rate, verify Ratios can be represented in part-to-part, part-to-whole, and whole-to-whole relationships A rate is a type of ratio Identify or write ratios in part/part and part/whole relationships using objects, pictures, and symbols Create a ratio equivalent to a given ratio to determine an unknown value for a dimension or a number of events or objects. Identify, demonstrate, or explain percent as 100 equal sized parts of a set. Represent equivalent percentages using different objects, pictures, and/or symbols. Identify or illustrate the use of percent. Identify or represent equivalent ratios and/or percents. Identify or determine a ratio or percent in a given situation. Explain or show the meaning of a ratio or percent. Give examples of ratio and/or percents in a situation. Identify or determine fraction, decimal, or percent equivalents for common percents such as 90%, 75%, 66% 50%, 33%, 25%, and 10%. Bits and Pieces III: 4.3, 5.1, 5.2; Comparing and Scaling: 1.1, 1.2, 1.3, 2.1, 2.2, 2.3 (Blue Book) Chapter 6
Math Power Standard 10 PS 8 - Determine the probability of a simple event using data collected in an experiment and represent the probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100 (6.3.F,G) Big Idea: Probability is the likelihood of an event happening. Essential Questions: How would you determine the probability of an event happening? complement, event, experiment, justify, outcome, probability (experimental and theoretical), random, sample space (all possible outcomes) Probability can be expressed as a ratio. There are various ways to determine outcomes of events or situations. Explain why some outcomes are equally likely or more or less likely to happen than others and how much more or less. Identify, predict, or determine the probability of an event in a simple experiment or situation as a ratio, decimal, or percent. Demonstrate an understanding that probability is a ratio between and including 0 and 1 or a percent between and including 0% and 100%. Identify or determine the sample space of simple experiments or activities. Translate between representations of probability. Create a spinner, game, or situation that would produce a given, fair or unfair, outcome. Explain why a game is fair or unfair. Resources How Likely Is It?: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4 Chapter 12
Grade Six Math Power Standard 9 PS 9 - Determine the perimeter and area of a composite figure that can be divided into triangles, rectangles, and parts of circles (6.4.B) Big Idea: Dividing composite figures into individual shapes can help us determine the area and perimeter of the figures. Essential Questions: How can formulas be used to determine area and perimeter of composite figures? Related Grade Level Expectations acre, area, attribute, centimeter, circumference, circle, compare, diameter, edge, foot/feet, inch, kilometer, length, meter, mile, millimeter, perimeter, pi (π), radius/radii, slant height, square unit, unit, yard area and perimeter formulas composite figures area and circumference of circles determine whether measurement has been done correctly in a given situation find the perimeter and/or area of a rectangle or right triangle determine linear dimensions of a rectangle or right triangle based on a given perimeter or area find the area of a circle using πr² find the circumference or a circle using 2πr or πd identify or describe circles using geometric properties Identify the ratio of the circumference to the diameter of a circle as the constant π, and recognize 22/7 and 3.14 as common approximations of π (6.3.E). Determine the circumference and area of circles (6.4.A). Describe and classify polyhedral by their attributes: parallel faces, types of faces, number of faces, edges, and vertices (6.4.G). Resources Covering and Surrounding: Investigations 1, 2, 3, 4, 5 Chapter 7
Math Power Standard 10 PS 10 - Determine the surface area and volume of rectangular prisms using appropriate formulas and explain why the formulas work (6.4.E) Big Idea: Volume is the space within a three-dimensional rectangular shape expressed in cubic units. Surface area is the combined area of the outside surfaces of a three-dimensional rectangular shape expressed in square units. Essential Questions: What does volume mean and how do you use it? What is the difference between volume and surface area? first time at sixth grade angle, area, centimeter, compare, construct, cube, cubic unit, degree, edge, face, foot/feet, inch, kilometer, meter, mile, millimeter, net, perimeter, polyhedron, prism, pyramid, rectangle, regular polyhedron, right angle, square unit, surface area, tetrahedron, three-dimensional, two-dimensional, volume, yard Rules to determine volume and surface area of rectangular prisms. Importance of the relationship between volume and surface area. Identify or describe angles in a picture, diagram, or object. Identify or describe angles by their relationship to a right angle. Compare the meaning of surface area and volume of a rectangular prism Use area or volume to compare rectangles, right triangles, or rectangular prisms. Identify the volume for a given rectangular prism from a picture or model. Identify examples of surface area and/or volume. Use surface area and volume to describe a rectangular prism. Label measurements of a rectangular prism to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms and that area is measured in square units and volume in cubic units. Related Standards Resources Determine the surface area of a prism. Describe and sort polyhedra by their attributes: parallel faces, type of faces, number of faces, edges, and vertices. Filling and Wrapping: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3 (Blue Book) Chapter 7 Chapter 8