The objective of the lesson is to allow students to solve an application problem using provided resources. Depending on the fluency of the individual student, this section may take more or less than the suggested time. Pairing students may help.
The purpose of the discussion is to help students reflect on and improve their problem solving skills. By having a group discussion students can see how others approached the same problem.
Students have created a written explanation outlining their problem solving process. Emphasis should be placed on the problem solving decisions made. Minor calculations errors or mistakes in using formulas should not greatly reduce the awarded points.
Make certain NOT to require all the help sections to be filled. These are present simply to help students when they do not know what to do.
If appropriate, have students grade each others explanation using the suggested rubric. This allows them to further analyze the problem solving processes of others.
Suggested Rubric - Adjust the point values and check box explanations as desired.
Algebra Standard for Grades 6-8:
Data Analysis and Probability Standard for Grades 6-8:
Measurement Standard for Grades 9-12:
6th Grade
2.1.a. Analyze patterns on graphs and tables and write a generalization to predict how the patterns will continue. 2.1.b. Create tables and graphs to represent given patterns and algebraic expressions 2.1.c. Write an algebraic expression from a graph or a table of values 2.1.d. Draw a graph from a table of values or to represent an equation 2.2.b. Solve two-step equations involving whole numbers and a single variable 5.1.a. Design investigations to answer questions by collecting and organizing data in a variety of ways 5.1.b. Collect, compare, and display data using an appropriate format (i.e., bar graphs, line graphs, line plots, circle graphs, scatter plots) 5.1.c. Compare two similar sets of data on the same graph and compare two graphs representing the same set of data 5.1.e. Develop and evaluate inferences and predictions based on data
2.1.a. Analyze patterns on graphs and tables and write a generalization to predict how the patterns will continue.
2.1.b. Create tables and graphs to represent given patterns and algebraic expressions
2.1.c. Write an algebraic expression from a graph or a table of values
2.1.d. Draw a graph from a table of values or to represent an equation
2.2.b. Solve two-step equations involving whole numbers and a single variable
5.1.a. Design investigations to answer questions by collecting and organizing data in a variety of ways
5.1.b. Collect, compare, and display data using an appropriate format (i.e., bar graphs, line graphs, line plots, circle graphs, scatter plots)
5.1.c. Compare two similar sets of data on the same graph and compare two graphs representing the same set of data
5.1.e. Develop and evaluate inferences and predictions based on data
Math 7
2.1.1. Describe a pattern using a mathematical rule or algebraic expression 2.1.3. Extend simple numerical and visual patterns 2.2.1. Write a variable expression to identify pattern relationships 2.2.2. Translate verbal expressions into symbolic representations 2.2.5. Evaluate algebraic expressions 2.2.6. Solve two-step single variable equations and inequalities 2.2.7. Use proportional reasoning to solve problems 2.3.1. Model and solve real-world problems using various representations, such as graphs, tables, manipulatives, and pictures 2.3.3. Use graphs and tables to identify and describe changes in related quantities 5.1.1. Identify appropriate questions for data collection and then collect, organize, and display responses to the questions 5.1.2. Collect, organize, and display data using frequency tables, line plots, bar graphs, circle graphs, line graphs, and stem-and-leaf plots 5.1.3. Display the same set of data utilizing two or more different types of representations 5.1.4. Compare two similar sets of data using the same type of graph 5.1.6. Predict basic trends illustrated in a graph
2.1.1. Describe a pattern using a mathematical rule or algebraic expression
2.1.3. Extend simple numerical and visual patterns
2.2.1. Write a variable expression to identify pattern relationships
2.2.2. Translate verbal expressions into symbolic representations
2.2.5. Evaluate algebraic expressions
2.2.6. Solve two-step single variable equations and inequalities
2.2.7. Use proportional reasoning to solve problems
2.3.1. Model and solve real-world problems using various representations, such as graphs, tables, manipulatives, and pictures
2.3.3. Use graphs and tables to identify and describe changes in related quantities
5.1.1. Identify appropriate questions for data collection and then collect, organize, and display responses to the questions
5.1.2. Collect, organize, and display data using frequency tables, line plots, bar graphs, circle graphs, line graphs, and stem-and-leaf plots
5.1.3. Display the same set of data utilizing two or more different types of representations
5.1.4. Compare two similar sets of data using the same type of graph
5.1.6. Predict basic trends illustrated in a graph
PreAlgebra
2.1.1. Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules 2.1.2. Describe simple patterns using a mathematical rule or algebraic expression 2.2.1. Evaluate algebraic expressions when given values for the variable(s) 2.2.2. Identify the horizontal and vertical intercepts of a linear relation from a graph or table 2.2.3. Determine the slope of a linear relation from a graph or ordered pairs 2.2.4. Solve one- and two-step single-variable equations and inequalities 2.3.1. Create a table, graph, or algebraic expression to represent the relationship between two variables 2.3.2. Graph ordered pairs of rational numbers on a rectangular coordinate system 2.3.3. Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system 2.3.4. Model real-world problems using various representations, such as graphs, tables, equations, manipulatives, and pictures 5.1.2. Organize and display data using graphical representations such as line plots, bar graphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, box plots (box-and-whisker plots), and pictographs 5.1.3. Make conjectures from a graphical representation 5.1.8. Make predictions and describe the limitations of the predictions when using data samples
2.1.1. Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules
2.1.2. Describe simple patterns using a mathematical rule or algebraic expression
2.2.1. Evaluate algebraic expressions when given values for the variable(s)
2.2.2. Identify the horizontal and vertical intercepts of a linear relation from a graph or table
2.2.3. Determine the slope of a linear relation from a graph or ordered pairs
2.2.4. Solve one- and two-step single-variable equations and inequalities
2.3.1. Create a table, graph, or algebraic expression to represent the relationship between two variables
2.3.2. Graph ordered pairs of rational numbers on a rectangular coordinate system
2.3.3. Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system
2.3.4. Model real-world problems using various representations, such as graphs, tables, equations, manipulatives, and pictures
5.1.2. Organize and display data using graphical representations such as line plots, bar graphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, box plots (box-and-whisker plots), and pictographs
5.1.3. Make conjectures from a graphical representation
5.1.8. Make predictions and describe the limitations of the predictions when using data samples
Elementary Algebra
1.1.3 Determine the reasonableness of an answer by relating it to the problem 2.1.2. Represent linear equations in slope-intercept form, y = mx + b, or standard form, ax + by = c 2.1.3. Distinguish between linear and non-linear functions or equations by examining a table, equation, or graph 2.1.4. Identify the slope of a linear function as an average rate of change in real-world situations 2.2.1. Solve real-world problems involving constant rates of change, e.g., rates of travel, hourly wages, or rates of interest 2.2.2. Solve multi-step equations and inequalities: Numerically; e.g., from a table or guess and check. Algebraically, including the use of manipulatives. Graphically. Using technology 2.3.2. Write the equation of a line when given: A set of ordered pairs. The slope and a point on the line. The graph of a line 4.1.1 Solve problems and express answers using appropriate units of measure
1.1.3 Determine the reasonableness of an answer by relating it to the problem
2.1.2. Represent linear equations in slope-intercept form, y = mx + b, or standard form, ax + by = c
2.1.3. Distinguish between linear and non-linear functions or equations by examining a table, equation, or graph
2.1.4. Identify the slope of a linear function as an average rate of change in real-world situations
2.2.1. Solve real-world problems involving constant rates of change, e.g., rates of travel, hourly wages, or rates of interest
2.2.2. Solve multi-step equations and inequalities: Numerically; e.g., from a table or guess and check. Algebraically, including the use of manipulatives. Graphically. Using technology
2.3.2. Write the equation of a line when given: A set of ordered pairs. The slope and a point on the line. The graph of a line
4.1.1 Solve problems and express answers using appropriate units of measure