Year 10 Number and Algebra by Texas Instruments

Students factorise and expand algebraic expressions including monic quadratic expressions; simplify algebraic products and quotients using index laws and apply the four operations to simple algebraic fractions with numerical denominators. They solve linear simultaneous equations, using algebraic and graphical techniques, explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials.

Year 10: Number and Algebra Classroom Activities		Download
Linear and non-linear relationships
Standard ACMNA238 Solve problems involving parallel and perpendicular lines Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Amazing Locus Students are presented with a challenging problem and provided with the tools to help break it down to see the relatively simple, yet amazing, solution. The problem requires students to calculate gradients, gradients of perpendicular lines, the equation of a line given point and gradient and finally solve a set of equations simultaneously.	ACMNA238 ACMNA237	Download5
Standard ACMNA215 Sketch linear graphs using the coordinates of two points and solve linear equations Activity: String Graphs Part1 This is part one of a four part series. In this activity students use the gradient and intercept form of a straight line to form a curved envelope similar to that found on the Chords bridge. In the second half of this activity students learn to use a parameter so that the family of graphs can be generated using a single equation.	ACMNA215	Download13
Standard ACMNA215 Sketch linear graphs using the coordinates of two points and solve linear equations Activity: String Graphs Part2 This is part two of a four part series. In this activity students are given two points that lie on a straight line, they determine the equation for each line that eventually forms a curved envelope that forms a parabola. In the second half of this activity students learn to use a parameter so that the family of graphs can be generated using a single equation.	ACMNA215	Download10
Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: String Graphs Part3 This is part three of a four part series. In this activity students find the points of intersection between consecutive straight lines. (Simultaneous Equations). Students use a range of techniques: by-hand, graphically and using CAS. Students then formulate equations to summaries the consecutive points of intersection.	ACMNA237	Download5
Standard ACMNA239 Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate Activity: Ball Bounce Students collect data for a bouncing ball using a CBR connected to their calculator. Consecutive ball bounces are modelled using combinations of translational, intercept and standard form of a quadratic equation. Each student has their own data so each student’s working and answers will be unique making it the ideal assessment task!	ACMNA239	Download46
Midpoints This activity is part of the coordinate geometry series. In this activity students use the midpoint tool to explore and establish the formula for the midpoint of two points. Students then go on to explore the path of the midpoint for a fixed point and a point on a line.		Download7
Standard ACMNA238 Solve problems involving parallel and perpendicular lines Activity: Parallel and Perpendicular Watch Activity Tutorial In this activity students watch the above video to gain an understanding or parallel and perpendicular lines in the context of coordinate geometry. After watching the video students answer a series of questions followed by a small investigation into quadrilaterals with vertices on the midpoints of a larger quadrilateral.	ACMNA238	Download7
Standard ACMNA214 Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software Standard ACMNA238 Solve problems involving parallel and perpendicular lines Standard ACMNA296 Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Circumcentre Watch Activity Tutorial Coordinate Geometry - Students calculate gradients, perpendicular gradients, equations to lines (given point and gradient), solve simultaneous equations and calculate the distance between two points, and much more! This activity is part of a series on coordinate geometry and includes companion video tutorials and lots of extension opportunities.	ACMNA214 ACMNA238 ACMNA296 ACMNA237	Download1
Standard ACMNA234 Substitute values into formulas to determine an unknown Standard ACMMG243 Formulate proofs involving congruent triangles and angle properties Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Centroid This activity is aligned with the Circumcentre and Orthocentre activities forming a natural progression for the Euler line activity. Students calculate gradients, equations to lines, solve equations simultaneously and use the calculator's tools to check their answers.	ACMNA234 ACMMG243 ACMNA237	Download3
Standard ACMNA238 Solve problems involving parallel and perpendicular lines Standard ACMNA296 Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Orthocentre Watch Activity Tutorial Coordinate Geometry - Students calculate midpoints, gradients, perpendicular lines and use simultaneous equations to help determine the location of the orthocentre. A really cool property of the orthocentre is revealed in the extension component of the activity.	ACMNA238 ACMNA296 ACMNA237	Download6
Standard ACMNA238 Solve problems involving parallel and perpendicular lines Activity: Euler Line This activity combines the result of the Circumcentre, Orthocentre and Centroid activities to locate the Euler line. The problem is explored entirely on the Cartesian plane and provides ample opportunity for students to demonstrate an understanding of perpendicular lines and midpoints, determination of equations and solutions to simultaneous equations with a purpose. Standards Textbook	ACMNA238	Download6
Standard ACMNA239 Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate Activity: Number Sums This activity starts with a problem to solve: Determine the number of cans in a stack, 30 rows high. Students use a range of visual and numerical representations of similar, related problems to build an understanding of associated algebraic formulas that can be used to solve this problem. The focus of the activity is on developing algebraic formulas with a fundamental understanding of their structure and therefore a deeper understanding of their meaning.	ACMNA239	Download42
Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Simultaneous Equatons Elimination Students are provided with 10 pairs of equations to solve by elimination with the assistance of sliders and a pre-made template to make the process easier to understand. Reducing the number of steps makes the concept easier to understand so that focus can be cast upon the coefficients in the equations. An extension option includes solving equations with three variables including the 3D representation of the successive results as the intersection of planes, lines and points.	ACMNA237	Download29
Standard ACMNA238 Solve problems involving parallel and perpendicular lines Activity: ACMNA238 – Parallel and Perpendicular Lines - Year 10 Electronic, auto correcting assessment for the Australian Mathematics Curriculum standard ACMNA238 using the TI-Navigator system including a companion PDF of the same for schools that do not have TI-Navigator.	ACMNA238	Download136
Standard ACMNA241 Solve simple quadratic equations using a range of strategies Activity: ACMNA241 – Solving Quadratic Equations - Test Electronic, auto correcting assessment for the Australian Mathematics Curriculum standard ACMNA241 using the TI-Navigator system including a companion PDF of the same.	ACMNA241	Download87
String Art This task provides a creative way to reinforce linear function algebra with Years 9–10 students land to learn about transformations of sets of such functions. The focus is on the students discovering what effect each parameter in the function (e.g. gradient & y-intercept) might have on the shape and location of the set of graphs.		Download36
Standard ACMNA239 Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate Activity: Graphic Designs This task provides a creative way for helping students learn about transformations of simple linear and quadratic functions. The focus is on the students discovering what effect each parameter in the function (e.g. a, b) might have on the shape and location of its graph.	ACMNA239	Download31
Money and financial mathematics
Standard ACMNA229 Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies Activity: Growing Interest In this activity, students will compare the different growth patterns for a sum of money invested under a simple interest plan and a compound interest plan.	ACMNA229	Download148
Patterns and Algebra
Standard ACMNA213 Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate Standard ACMNA233 Expand binomial products and factorise monic quadratic expressions using a variety of strategies Standard ACMNA239 Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate Standard ACMSP246 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 Activity: Probable Factors What is the probability that a randomly generated quadratic will factorise? This investigation looks at a significantly reduced set of quadratics using dice to generate the coefficients. The coefficient of x is the sum of two dice and the constant is the product of two dice. Simulation is used for predicting the probability followed by theoretical computations.	ACMNA213 ACMNA233 ACMNA239 ACMSP246	Download806
Standard ACMNA234 Substitute values into formulas to determine an unknown Activity: Cat and Mouse The aim of this investigation is to determine positive integer solutions for a game of Cat and Mouse, which is represented as a linear equation. Spreadsheets and graphs will be used to help identify possible solutions.	ACMNA234	Download67
Standard ACMNA214 Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software Standard ACMNA238 Solve problems involving parallel and perpendicular lines Standard ACMNA296 Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations Standard ACMNA237 Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology Activity: Circumcentre Watch Activity Tutorial Coordinate Geometry - Students calculate gradients, perpendicular gradients, equations to lines (given point and gradient), solve simultaneous equations and calculate the distance between two points, and much more! This activity is part of a series on coordinate geometry and includes companion video tutorials and lots of extension opportunities.	ACMNA214 ACMNA238 ACMNA296 ACMNA237	Download1
Standard ACMNA267 Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations Activity: Introduction to Parabolas Students start with a simple paper folding task that leads to a dynamic geometry approach to the construction of a parabolas. Students gain a better appreciation of a parabola and its properties when they know how it is constructed.	ACMNA267	Download49
Standard ACMNA231 Simplify algebraic products and quotients using index laws Activity: ACMNA231 – Index Laws Test Electronic, auto correcting assessment for the Australian Mathematics Curriculum standard ACMNA231 using the TI-Navigator system including a companion PDF of the same.	ACMNA231	Download50
Standard ACMNA241 Solve simple quadratic equations using a range of strategies Activity: ACMNA241 – Solving Quadratic Equations - Test Electronic, auto correcting assessment for the Australian Mathematics Curriculum standard ACMNA241 using the TI-Navigator system including a companion PDF of the same.	ACMNA241	Download87

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Standard ACMNA238

Standard ACMNA237

Activity: Amazing Locus

Standard ACMNA215

Activity: String Graphs Part1

Standard ACMNA215

Activity: String Graphs Part2

Standard ACMNA237

Activity: String Graphs Part3

Standard ACMNA239

Activity: Ball Bounce

Midpoints

Standard ACMNA238

Activity: Parallel and Perpendicular

Standard ACMNA214

Standard ACMNA238

Standard ACMNA296

Standard ACMNA237

Activity: Circumcentre

Standard ACMNA234

Standard ACMMG243

Standard ACMNA237

Activity: Centroid

Standard ACMNA238

Standard ACMNA296

Standard ACMNA237

Activity: Orthocentre

Standard ACMNA238

Activity: Euler Line

Standard ACMNA239

Activity: Number Sums

Standard ACMNA237

Activity: Simultaneous Equatons Elimination

Standard ACMNA238

Activity: ACMNA238 – Parallel and Perpendicular Lines - Year 10

Standard ACMNA241

Activity: ACMNA241 – Solving Quadratic Equations - Test

String Art

Standard ACMNA239

Activity: Graphic Designs

Standard ACMNA229

Activity: Growing Interest

Standard ACMNA213

Standard ACMNA233

Standard ACMNA239

Standard ACMSP246

Activity: Probable Factors

Standard ACMNA234

Activity: Cat and Mouse

Standard ACMNA214

Standard ACMNA238

Standard ACMNA296

Standard ACMNA237

Activity: Circumcentre

Standard ACMNA267

Activity: Introduction to Parabolas

Standard ACMNA231

Activity: ACMNA231 – Index Laws Test

Standard ACMNA241

Activity: ACMNA241 – Solving Quadratic Equations - Test

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