How to learn High school: Mathematics

North Dakota academic standards: Mathematics, High school

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1. Ninth and Tenth Grades · Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

1. Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions

2. Ninth and Tenth Grades · Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

1. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

3. Eleventh and Twelfth Grades · Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

1. Scatter Graphs: Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate

4. Eleventh and Twelfth Grades · Analyze and graph functions expressed symbolically (by hand in simple cases and using technology for more complicated cases), identifying key features of the graph.

1. Estimating answers (age 13+): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts

5. Eleventh and Twelfth Grades · Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

1. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
2. Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions

6. Eleventh and Twelfth Grades · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

1. Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

7. Eleventh and Twelfth Grades · Interpret expressions that represent a quantity in context.

1. Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

8. Eleventh and Twelfth Grades · Add and subtract vectors. Represent vector subtraction graphically by connecting the tips in the appropriate order and using the components to perform vector subtraction.

1. Plotting Linear Graphs: Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line