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  • Mathematics: 10th Grade

Australian Curriculum - Mathematics: 10th Grade

Australian Curriculum | Adopted: 2010

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

1: : Number and Algebra


1.1: : Money and financial mathematics

1.1.1: : Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies

Screenshot of Compound Interest

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


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1.2: : Patterns and algebra

1.2.1: : Factorise algebraic expressions by taking out a common algebraic factor

Screenshot of Factoring Special Products

Factoring Special Products

Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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1.2.2: : Simplify algebraic products and quotients using index laws

Screenshot of Dividing Exponential Expressions

Dividing Exponential Expressions

Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Multiplying Exponential Expressions

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Simplifying Algebraic Expressions II

Simplifying Algebraic Expressions II

Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview


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1.2.4: : Expand binomial products and factorise monic quadratic expressions using a variety of strategies

Screenshot of Factoring Special Products

Factoring Special Products

Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>

Modeling the Factorization of ax2+bx+c

Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview


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Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

Modeling the Factorization of x2+bx+c

Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview


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Screenshot of Quadratics in Factored Form

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


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1.3: : Linear and non-linear relationships

1.3.1: : Solve problems involving linear equations, including those derived from formulas

Screenshot of Absolute Value with Linear Functions

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


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Screenshot of Linear Functions

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


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Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Modeling and Solving Two-Step Equations

Modeling and Solving Two-Step Equations

Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview


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Screenshot of Solving Equations by Graphing Each Side

Solving Equations by Graphing Each Side

Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Solving Two-Step Equations

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Standard Form of a Line

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview


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1.3.2: : Solve linear inequalities and graph their solutions on a number line

Screenshot of Compound Inequalities

Compound Inequalities

Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview


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Screenshot of Exploring Linear Inequalities in One Variable

Exploring Linear Inequalities in One Variable

Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview


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Screenshot of Solving Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview


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1.3.3: : Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Screenshot of Cat and Mouse (Modeling with Linear Systems)

Cat and Mouse (Modeling with Linear Systems)

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview


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Screenshot of Solving Equations by Graphing Each Side

Solving Equations by Graphing Each Side

Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview


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Screenshot of Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Matrices and Special Solutions)

Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview


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Screenshot of Solving Linear Systems (Standard Form)

Solving Linear Systems (Standard Form)

Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview


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1.3.5: : Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate

Screenshot of Circles

Circles

Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview


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1.3.7: : Solve simple quadratic equations using a range of strategies

Screenshot of Roots of a Quadratic

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


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2: : Measurement and Geometry


2.1: : Using units of measurement

2.1.1: : Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids

Screenshot of Prisms and Cylinders

Prisms and Cylinders

Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview


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Screenshot of Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Prisms and Cylinders

Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview


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Screenshot of Surface and Lateral Areas of Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview


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2.2: : Geometric reasoning

2.2.1: : Formulate proofs involving congruent triangles and angle properties

Screenshot of Congruence in Right Triangles

Congruence in Right Triangles

Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview


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Screenshot of Proving Triangles Congruent

Proving Triangles Congruent

Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview


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2.2.2: : Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

Screenshot of Classifying Quadrilaterals

Classifying Quadrilaterals

Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview


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2.3: : Pythagoras and trigonometry

2.3.1: : Solve right-angled triangle problems including those involving direction and angles of elevation and depression

Screenshot of Sine, Cosine, and Tangent Ratios

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


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3: : Statistics and Probability


3.1: : Chance

3.1.1: : Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence

Screenshot of Probability Simulations

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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Screenshot of Theoretical and Experimental Probability

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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3.1.2: : Use the language of ?if...then, ?given?, ?of?, ?knowing that? to investigate conditional statements and identify common mistakes in interpreting such language

Screenshot of Biconditional Statements

Biconditional Statements

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview


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3.2: : Data representation and interpretation

3.2.1: : Determine quartiles and interquartile range

Screenshot of Box-and-Whisker Plots

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


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3.2.2: : Construct and interpret box plots and use them to compare data sets

Screenshot of Box-and-Whisker Plots

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


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Screenshot of Stem-and-Leaf Plots

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview


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3.2.6: : Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data

Screenshot of Box-and-Whisker Plots

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


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Screenshot of Correlation

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


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Screenshot of Polling: City

Polling: City

Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview


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Screenshot of Polling: Neighborhood

Polling: Neighborhood

Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview


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Screenshot of Real-Time Histogram

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


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Screenshot of Stem-and-Leaf Plots

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview


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Correlation last revised: 9/16/2020

* © Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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