Subject: Math 6.1.1 Select and use appropriate strategies to estimate fraction and decimal products and quotients. Select (1) Use (3) Estimate (3) Strategies Products/quotients Fraction Decimal Both estimation and exact answers are useful at different times when solving problems with fraction and decimal products and quotients. When is estimation of fractions and decimal products and quotients useful? How does estimation help us understand real world problems? Or, how can they be used in real life?
Subject: Math 6.1.2 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of fractions. 6.1.3 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of decimals. Use (3) Analyze(4) Use (3) Analyze(4) 6.1.2 Multiplication/division of fractions Strategies Models Problem solving 6.1.3 Multiplication/division of decimals Strategies Models Problem solving Multiplication and division of fractions and decimals can be modeled using a variety of strategies. How can models help solve problems involving the multiplication and division of fractions and decimals? Why do we need to be able to multiply and divide fractions and decimals? When do we do this? What is the relationship between fractions and decimals?
Subject: Math 6.1.4 Develop fluency with efficient procedures for multiplying and dividing fractions and decimals and justify why the procedures work. 6.1.5 Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work. Understanding (2) Justify (5) 6.1.4 Multiply and divide fractions / decimals Efficient procedures Procedures 6.1.5 Apply (3) Justify (5) Multiplication/division whole number Inverse relationship Multiplication/division fractions Procedures Both estimation and exact answers are useful at different times when solving problems with fraction and decimal products and quotients. When is estimation of fractions and decimal products and quotients useful? How does estimation help us understand real world problems? Or, how can they be used in real life?
Subject: Math Apply (3) Simplify (4) 6.1.6 Apply the properties of operations to simplify calculations. Properties Operations Calculations Understanding of basic operations can be used to simplify calculations. How do we determine which operations to use when solving problems?
Subject: Math Use (3) Solve (3) 6.1.7 Use the relationship between common decimals and fractions to solve problems including problems involving measurement. Relationships Common Decimals Common fractions Problems Measurement Measurement can be used to model the relationship between common fractions and decimals Measurement can be used to compare a variety of elements (money, distance, weight, etc.). What do we measure in the world around us? Do all measurements use fractions and decimals? Why do we need to know and be able to use common measurement terms?
Subject: Math Develop (6) Analyze (4) Apply (3) Solve (3) 6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and percent to solve problems. Meaning of Ratio Rate Percent Problems Development of ratio, rate, and percent apply to everyday life problem solving. Ratio, rate, and percent relate to the relationship of fractions and decimals. Why are ratio, rate, and percent necessary to learn? What is the relationship between ratio and rate? How can the understanding of percent help solve problems?
Subject: Math Numbers & Operations and Probability 6.2.2 Determine decimal and percent equivalents for common fractions, including approximations. Determine (2) Decimal and percent equivalents for common fractions including approximations Knowledge of decimal and percent equivalents for common fractions is necessary for estimations. Whether we estimate or compute the exact answer depends on the needs of the situation. When do we estimate? When do we need the exact answer? What is the relationship between fractions, decimals, and percents?
Subject: Math Numbers & Operations and Probability 6.2.3 Understand the meaning of probability and represent probabilities as ratios, decimals, and percents. Understand (1) Represent (2) Meaning of probability Probabilities as Ratios Decimals Percents Fractions, decimals, and percents can represent the same amount differently. Number sense means understanding the relationship between numbers. What is number sense? How can we use it to solve mathematical problems? What is the relationship between fractions, decimals, and percents?
Subject: Numbers & Operations and Probability 6.2.4 Determine simple probabilities, both experimental and theoretical. Determine (3) Probabilities Experimental Theoretical Knowledge of probability is an essential skill. Why do we need to be exposed to the concept of probability? What are some situations that involve probability?
Subject: Math Numbers & Operations and Probability 6.2.5 Develop the concept of π(pi) as the ratio of the circumference of a circle to its diameter. Develop (3) π (pi) as the ratio of the circumference of a circle to its diameter. Knowledge of the relationship of the diameter to the circumference of a circle. When is estimation of fractions and decimal products and quotients useful? When and why is π used in determining the circumference of the circle?
Subject: Math - Algebra 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols. Use (3) Simplify (4) Order of operations Expressions Exponents Grouping symbols Knowledge of order of operations relating to exponents and grouping symbols. When is it appropriate to simplify an expression? Why do we need to solve equations in a specific order?
Subject: Math - Algebra 6.3.2 Develop the meanings and uses of variables. 6.3.6 Recognize that the solutions of an equation are the values of the variables that make the equation true. Develop (2) Recognize (1) 6.3.2 Meanings Uses of variables 6.3.6 Solutions of an equation Values of variables Numbers can be represented by many different symbols. When can we use variables in equations? Why do we use variables in equations? How do we solve equations?
Subject: Math - Algebra 6.3.3 Write, evaluate, and use expressions and formulas to solve problems. 6.3.4 Identify and represent equivalent expressions (e.g., different ways to see a pattern). Write (1) Evaluate (5) Use (3) Solve (3) 6.3.3 Expressions Formulas 6.3.4 Problems There are different ways to identify, write, evaluate, use and represent expressions and formulas and their equivalents. There are different formulas and expressions used to solve real life problems. Why is it important to use the proper formula or expression when problem solving? How do you know which expression or formula to use? What are formulas and expressions? What do they have in common and what are the differences? How can formulas and expressions help in solving real life problems? What are some examples of this?
Subject: Math - Algebra 6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs, words and when possible, symbols. Represent (2) Analyze (4) Determine (3) Use (3) Relationships Patterns Tables Graphs Words Symbols Graphs, patterns, symbols and words can be used to represent and analyze relationships between expressions and equations. When is it useful to use graphs to show relationships? Patterns? Symbols? Words? How can equations and expressions be represented? When is it important to show relationships between equations or expressions?
Subject: Math - Algebra 6.3.7 Solve one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. Solve (3) Use (3) One-step equations Number sense Properties of operations Equality on both sides of equation Numbers on each side of an = sign must be equal. Equations are solved in an organized, systematic way. Why do we solve equations in a specific order? Why do we learn mathematical formulas? What does it mean to be equal?