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- Mathematics: Math 4
North Carolina - Mathematics: Math 4
Standard Course of Study | Adopted: 2019
NC.M4.N: : Number and Quantity
NC.M4.N.1: : Apply properties and operations with complex numbers.
NC.M4.N.1.1: : Execute procedures to add and subtract complex numbers.
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
NC.M4.N.1.2: : Execute procedures to multiply complex numbers.
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
NC.M4.N.2: : Apply properties and operations with matrices and vectors.
NC.M4.N.2.1: : Execute procedures of addition, subtraction, multiplication, and scalar multiplication on matrices.
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
NC.M4.N.2.2: : Execute procedures of addition, subtraction, and scalar multiplication on vectors.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
NC.M4.AF: : Algebra and Functions
NC.M4.AF.2: : Apply properties of trigonometry to solve problems.
NC.M4.AF.2.1: : Translate trigonometric expressions using the reciprocal and Pythagorean identities.
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
NC.M4.AF.2.3: : Interpret key features (amplitude, period, phase shift, vertical shifts, midline, domain, range) of models using sine and cosine functions in terms of a context.
Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
NC.M4.AF.3: : Apply the properties and key features of logarithmic functions.
NC.M4.AF.3.3: : Interpret key features of a logarithmic function using multiple representations.
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
NC.M4.AF.4: : Understand the properties and key features of piecewise functions.
NC.M4.AF.4.2: : Construct piecewise functions to model a contextual situation.
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
NC.M4.AF.5: : Understand how to model functions with regression.
NC.M4.AF.5.1: : Construct regression models of linear, quadratic, exponential, logarithmic, & sinusoidal functions of bivariate data using technology to model data and solve problems.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
NC.M4.AF.5.2: : Compare residuals and residual plots of non-linear models to assess the goodness-of-fit of the model.
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
NC.M4.SP: : Statistics and Probability
NC.M4.SP.1: : Create statistical investigations to make sense of real world phenomenon.
NC.M4.SP.1.1: : Construct statistical questions to guide explorations of data in context.
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected. 5 Minute Preview
Sight vs. Sound Reactions
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview
Time Estimation
Try to estimate the passage of time by selecting a time interval, clicking the Start button, and clicking Stop when you think the interval has passed. The estimate and percent error are recorded. Compare different techniques for estimating time, as well as the average error for long time intervals versus shorter intervals. 5 Minute Preview
NC.M4.SP.1.2: : Design sample surveys and comparative experiments using sampling methods to collect and analyze data to answer a statistical question.
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
Sight vs. Sound Reactions
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview
Time Estimation
Try to estimate the passage of time by selecting a time interval, clicking the Start button, and clicking Stop when you think the interval has passed. The estimate and percent error are recorded. Compare different techniques for estimating time, as well as the average error for long time intervals versus shorter intervals. 5 Minute Preview
NC.M4.SP.2: : Apply informal and formal statistical inference to make sense of, and make decisions in, meaningful real world contexts.
NC.M4.SP.2.1: : Design a simulation to make a sampling distribution that can be used in making informal statistical inferences.
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
NC.M4.SP.3: : Apply probability distributions in making decisions in uncertainty.
NC.M4.SP.3.1: : Implement discrete probability distributions to model random phenomenon and make decisions (e.g., expected value of playing a game, etc.).
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
NC.M4.SP.3.2: : Implement the binomial distribution to model situations and make decisions.
Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
Correlation last revised: 4/1/2022
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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