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New Brunswick - Mathematics: Patterns and Relations
New Brunswick Curriculum | Adopted: 2002
A: : Students will demonstrate number sense and apply number theory concepts.
A.1: : demonstrate an understanding of and apply zero and negative exponents
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.2: : develop, demonstrate an understanding of, and apply properties of exponents
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.8: : demonstrate an understanding of the exponential growth nature of compound interest
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
B: : Students will demonstrate operation sense and apply operation principles and procedures in both numeric and algebraic situations.
B.3: : apply the quadratic formula
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
B.5: : demonstrate an understanding of and apply compound interest
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
C: : Students will explore, recognize, represent and apply patterns and relationships, both informally and formally.
C.1: : model real-world phenomena using quadratic equations
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
C.4: : demonstrate an understanding of patterns that are arithmetic, power and geometric
![Screenshot of Finding Patterns](/Assets/img/blank.gif)
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
C.5: : determine and describe patterns and use them to solve problems
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
C.6: : explore, describe, and apply the Fibonacci sequence
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
![Screenshot of Finding Patterns](/Assets/img/blank.gif)
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
C.12: : describe and apply the characteristics of quadratic relationships
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
C.13: : describe and apply the characteristics of exponential relationships
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
C.21: : create and analyze scatter plots and determine the equations for curves of best fit, using appropriate technology
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
C.23: : solve problems involving quadratic equations
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
C.25: : solve problems involving exponential equations
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
C.26: : solve problems involving compound interest
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
C.29: : analyze tables and graphs to distinguish between linear, quadratic and exponential relationships
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
![Screenshot of Compound Interest](/Assets/img/blank.gif)
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Points, Lines, and Equations](/Assets/img/blank.gif)
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Quadratics in Vertex Form](/Assets/img/blank.gif)
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
D: : Students will demonstrate an understanding of and apply concepts and skills associated with measurement.
D.4: : solve problems using the sine, cosine, and tangent ratios
![Screenshot of Cosine Function](/Assets/img/blank.gif)
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Sine, Cosine, and Tangent Ratios](/Assets/img/blank.gif)
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
![Screenshot of Sum and Difference Identities for Sine and Cosine](/Assets/img/blank.gif)
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
![Screenshot of Translating and Scaling Sine and Cosine Functions](/Assets/img/blank.gif)
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
F: : Students will solve problems involving the collection, display and analysis of data.
F.2: : use curve-fitting to determine the equations of quadratic relationships
![Screenshot of Zap It! Game](/Assets/img/blank.gif)
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
F.4: : interpolate and extrapolate to predict and solve problems
![Screenshot of Estimating Population Size](/Assets/img/blank.gif)
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
Correlation last revised: 9/16/2020
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