Mathematics for College Statistics (#1210305) 

Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Example: The expression  can be rewritten as  which is approximately equivalent to . This latter expression reveals the approximate equivalent monthly interest rate of 1.2% if the annual rate is 15%.

Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Example: Given the Compound Interest formula , solve for P. 

Mathematics for Data and Financial Literacy Honors Example: Given the Compound Interest formula , solve for t.

Clarification 2: Instruction includes the use of standard form, slope-intercept form and point-slope form.

Clarification 3: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation.

Clarification 4: Within the Algebra 1 course, notations for domain, range and constraints are limited to inequality and set-builder.

Clarification 5: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation. 

Clarification 3: Instruction includes understanding that when the logarithm of the dependent variable is taken and graphed, the exponential function will be transformed into a linear function. 

Clarification 4: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

The graph of the function  can be transformed into the straight line y=5t+2 by taking the natural logarithm of the function’s outputs.

Clarification 2: Numerical univariate includes histograms, stem-and-leaf plots, box plots and line plots; numerical bivariate includes scatter plots and line graphs; categorical univariate includes bar charts, circle graphs, line plots, frequency tables and relative frequency tables; and categorical bivariate includes segmented bar charts, joint frequency tables and joint relative frequency tables.
Clarification 3: Instruction includes the use of appropriate units and labels and, where appropriate, using technology to create data displays.

Clarification 2: Shape features include symmetry or skewness and clustering.

Clarification 3: Within the Probability and Statistics course, instruction includes the use of spreadsheets and technology.

Clarification 2: Problems include making a prediction or extrapolation, inside and outside the range of the data, based on the equation of the line of fit.

Clarification 2: Instruction includes determining whether the transformed scatterplot has an appropriate line of best fit, and interpreting the y-intercept and slope of the line of best fit. 

Clarification 3: Problems include making a prediction or extrapolation, inside and outside the range of the data, based on the equation of the line of fit.

Clarification 2: Instruction includes the use of a tree diagram when calculating relative frequencies to construct tables.

Clarification 2: Instruction includes calculating joint relative frequencies or conditional relative frequencies using tree diagrams. Clarification 3: Graphical representations include frequency tables, relative frequency tables, circle graphs and segmented bar graphs.

Clarification 2: Sampling methods include simple random, stratified, cluster, systematic, judgement, quota and convenience.

Clarification 2: Within the Algebra 1 course, functions are limited to one-variable such as f(x)=3x.

Clarification 2: Within this benchmark, the expectation is to identify the type of function from a written description or table.

• Cultivate a community of growth mindset learners. 
• Foster perseverance in students by choosing tasks that are challenging. 
• Develop students’ ability to analyze and problem solve. 
• Recognize students’ effort when solving challenging problems.

• Help students make connections between concepts and representations.
• Provide opportunities for students to use manipulatives when investigating concepts.
• Guide students from concrete to pictorial to abstract representations as understanding progresses.
• Show students that various representations can have different purposes and can be useful in different situations. 

• Provide students with the flexibility to solve problems by selecting a procedure that allows them to solve efficiently and accurately.
• Offer multiple opportunities for students to practice efficient and generalizable methods.
• Provide opportunities for students to reflect on the method they used and determine if a more efficient method could have been used. 

• Establish a culture in which students ask questions of the teacher and their peers, and error is an opportunity for learning.
• Create opportunities for students to discuss their thinking with peers.
• Select, sequence and present student work to advance and deepen understanding of correct and increasingly efficient methods.
• Develop students’ ability to justify methods and compare their responses to the responses of their peers. 

• Help students recognize the patterns in the world around them and connect these patterns to mathematical concepts.
• Support students to develop generalizations based on the similarities found among problems.
• Provide opportunities for students to create plans and procedures to solve problems.
• Develop students’ ability to construct relationships between their current understanding and more sophisticated ways of thinking.

• Have students estimate or predict solutions prior to solving.
• Prompt students to continually ask, “Does this solution make sense? How do you know?”
• Reinforce that students check their work as they progress within and after a task.
• Strengthen students’ ability to verify solutions through justifications. 

• Provide opportunities for students to create models, both concrete and abstract, and perform investigations.
• Challenge students to question the accuracy of their models and methods.
• Support students as they validate conclusions by comparing them to the given situation.
• Indicate how various concepts can be applied to other disciplines.

2-3 Students include relevant textual evidence in their written and oral communication. Students should name the text when they refer to it. In 3rd grade, students should use a combination of direct and indirect citations.

4-5 Students continue with previous skills and reference comments made by speakers and peers. Students cite texts that they’ve directly quoted, paraphrased, or used for information. When writing, students will use the form of citation dictated by the instructor or the style guide referenced by the instructor. 

6-8 Students continue with previous skills and use a style guide to create a proper citation.

9-12 Students continue with previous skills and should be aware of existing style guides and the ways in which they differ.

In grades 1-2, students build upon these skills by justifying what they are thinking. For example: “I think ________ because _______.” The collaborative conversations are becoming academic conversations.

In grades 3-12, students engage in academic conversations discussing claims and justifying their reasoning, refining and applying skills. Students build on ideas, propel the conversation, and support claims and counterclaims with evidence.