Grade 10 | Mathematics

Action steps

1. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

2. Create linear equations to represent relationships between quantities.

3. Graph these equations on coordinate axes with labels and scales.

4. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Action steps

1. Prove that linear functions grow by equal differences over equal intervals.

2. Prove that exponential functions grow by equal factors over equal intervals.

3. Recognize situations in which one quantity change at a constant rate per unit interval relative to another.

4. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

5. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

6. Write a function that describes a relationship between two quantities.

7. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

8. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

9. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasingly linearly or exponentially.

10. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

11. Graph linear and exponential functions and show intercepts, maxima, and minima.

12. Graph exponential functions, showing intercepts and end behavior.

13. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

14. Rearrange linear formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

15. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

16. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

17. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

18. Estimate the rate of change from a graph.

19. Identify the effect of the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative).

20. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Action steps

1. Interpret linear models by distinguishing between correlation and causation.

2. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.

3. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

4. Informally assess the fit of a linear function by plotting and analyzing residuals.

5. Fit a linear function for a scatter plot that suggests a linear association.

6. Compute (using technology) and interpret the correlation coefficient of a linear fit.

7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Action steps

1. Prove that, given a system of equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

2. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

3. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

4. Find the solutions to the equations y = f(x) and y = g(x) approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.

5. Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

6. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Action steps

1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.

2. Show that polynomials can be added, subtracted, and multiplied.

3. Write a quadratic function that describes a relationship between two quantities.

4. Graph linear and quadratic functions and show intercepts, maxima, and minima.

5. For a quadratic function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Action steps

1. Interpret parts of a quadratic expression, such as terms, factors, and coefficients.

2. Interpret complicated quadratic expressions by viewing one or more of their parts as a single entity.

3. Use the structure of a quadratic expression to identify ways to rewrite it.

4. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

5. Use the process of factoring and completing the square in a quadratic function to show zeroes, extreme values, and symmetry of the graph, and interpret these in terms of a context.

6. Factor a quadratic expression to reveal the zeros of the function it defines.

7. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

8. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Action steps

1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different sets.

3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

4. Summarize categorical data for two categories in two-way frequency tables.

5. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies).

6. Recognize possible associations and trends in the data.