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Planned Instruction for Math Grade 6
Code  Standard  Content  Benchmark  P  Time  Materials/Strategies/Activities  CET  PSSA 
2.4  A. Make conjectures based on logical reasoning and test conjectures by using counterexamples. 
A. Generalize from a pattern of observations, make predictions, and provide supporting examples. • If no one completed their homework, what conclusions could be drawn? • Even number + even number = even number 

B. Combine numeric relationships to arrive at a conclusion. 
B. Develop numeric relationships. • Develop patterns when changing fractions to decimals (use calculator to begin pattern, but continue by observation). • Use divisibility rules to aid in simplifying fractions. • Convert between decimal , percents and fractions to solve real world problems. 

C. Use if...then statements to construct simple, valid arguments. 
C. Examine if...then statements to determine if the statements are valid. 

D. Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers. 
D. Use algorithmic procedures for computing and estimating with whole numbers, fractions, and decimals. 

E. Distinguish between inductive and deductive reasoning. • Inductive (goes from specific to general). • Deductive (goes from general to specific.) 
E. Identify inductive and deductive reasoning. • Inductive (goes from specific to general) • Deductive (goes from general to specific) 

F. Use measurements and statistics to quantify issues (e.g., in family, consumer science situations). 
F. Use measurements to quantify issues. • Metric. 

2.5  A. Invent, select, use and justify the appropriate methods, materials and strategies to solve problems . 
A. Select, use and justify the methods , materials and strategies used to solve problems. • Problem solving methods included but are not limited to: guess and check, working backwards, solving a simpler problem, making a graph, making a model, making a list, using simulation, drawing a diagram , using logical reasoning, and using algebra. 
Yes  
B. Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas , charts , graphs and diagrams . 
B. Create a visual representation (e.g., illustration, scale drawing, diagram, table, manipulatives) of a problem, and use the visual representation to solve the problem and explain the solution using appropriate mathematical language (oral). 
Yes  
C. Justify strategies and defend approaches used and conclusions reached. 
C. Justify the solution using appropriate mathematical language (oral). 
Yes  
D. Determine pertinent information in problem situations and whether any further information is needed for solution. 
D. Determine whether a sufficient amount of information is given in order to solve the problem. 
Yes  
2.6  A. Compare and contrast different plots of data using values of mean , median, mode, quartiles 
A. Create picture graphs and accurate line graphs . • Use an accurate title and key. • Examine and organize data using mean, median, mode and range. 

B. Explain effects of sampling procedures and missing or incorrect information on reliability. 
B. Discuss the reliability of results gathered via convenience sampling. 

C. Fit a line to the scatter plot of two quantities and describe any correlation of the variables . 
C. Draw a scatter plot of two quantities. 

D. Design and carry out a random sampling procedure. 
D. Complete a teacher directed survey and organize the data in a frequency table. 

E. Analyze and display data in stemandleaf and boxandwhisker plots. • Analyze and choose the best statistical model to display the data (e.g., line, bar, circle graph). 
E. Display and analyze data using stem and leaf plots. Use an accurate title and key. 

F. Use scientific and graphing calculators and computer spreadsheets to organize and analyze data. 
F. Use a computer to produce double bar, circle and line graphs and analyze the data. • Use the calculator to determine the mean of a set of data. 

G. Determine the validity of the sampling method described in studies published in local or national newspapers. 
G. Evaluate whether the mean, median, mode or range of the data is the best representation of the given data. 

A. Determine the number of combinations and permutations for an event. 
A. Make and justify predictions that are based on experimental probability. 

B. Present the results of an experiment using visual representations (e.g., tables, charts, graphs). 
B. After determining all possible outcomes, identify the probability of an event. 

2.7  C. Analyze predictions (e.g., election polls). 
C. Identify reallife situations that use probability. • Express the probability of the event as a percent. 

D. Compare and contrast results from observations and mathematical models. 
D. Predict outcomes using sampling. 

E. Make valid inferences, predictions and arguments based on probability. 
E. Make predictions based on probability. 
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