IXL skill plan | Years 4-5 Standard plan for IB Middle Years Programme

Skill plan for IB Middle Years Programme - Years 4-5 Standard

IXL provides skill alignments with recommended IXL skills for each branch of mathematical study. Find the IXL skills that are right for you below!

Branch of mathematical study

Numerical and abstract reasoning
Thinking with models
Spatial reasoning
Reasoning with data

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Numerical and abstract reasoning
Number
Absolute values		Absolute value expressions 1. Evaluate absolute value expressions Absolute value equations 2. Solve absolute value equations 3. Graph solutions to absolute value equations Absolute value inequalities 4. Solve absolute value inequalities 5. Graph solutions to absolute value inequalities
Absolute values
Absolute value expressions 1. Evaluate absolute value expressions Absolute value equations 2. Solve absolute value equations 3. Graph solutions to absolute value equations Absolute value inequalities 4. Solve absolute value inequalities 5. Graph solutions to absolute value inequalities

Representing and solving inequalities, including compound and double inequalities		Represent inequalities 1. Graph inequalities 2. Write inequalities from graphs 3. Identify solutions to inequalities One-step linear inequalities 4. Solve one-step linear inequalities: addition and subtraction 5. Solve one-step linear inequalities: multiplication and division 6. Solve one-step linear inequalities 7. One-step inequalities: word problems 8. Graph solutions to one-step linear inequalities Two-step linear inequalities 9. Solve two-step linear inequalities 10. Graph solutions to two-step linear inequalities Advanced linear inequalities 11. Solve advanced linear inequalities 12. Graph solutions to advanced linear inequalities Compound inequalities 13. Graph compound inequalities 14. Write compound inequalities from graphs 15. Solve compound inequalities
Representing and solving inequalities, including compound and double inequalities
Represent inequalities 1. Graph inequalities 2. Write inequalities from graphs 3. Identify solutions to inequalities One-step linear inequalities 4. Solve one-step linear inequalities: addition and subtraction 5. Solve one-step linear inequalities: multiplication and division 6. Solve one-step linear inequalities 7. One-step inequalities: word problems 8. Graph solutions to one-step linear inequalities Two-step linear inequalities 9. Solve two-step linear inequalities 10. Graph solutions to two-step linear inequalities Advanced linear inequalities 11. Solve advanced linear inequalities 12. Graph solutions to advanced linear inequalities Compound inequalities 13. Graph compound inequalities 14. Write compound inequalities from graphs 15. Solve compound inequalities

Irrational numbers		Classify numbers 1. Identify rational and irrational numbers 2. Classify numbers
Irrational numbers
Classify numbers 1. Identify rational and irrational numbers 2. Classify numbers

Surds, roots, and radicals, including simplifying		Square roots and cube roots 1. Square roots 2. Cube roots Simplify radical expressions 3. Simplify radical expressions 4. Simplify radical expressions involving fractions 5. Simplify radical expressions using the distributive property 6. Simplify radical expressions: mixed review Operations with radical expressions 7. Multiply radical expressions 8. Add and subtract radical expressions
Surds, roots, and radicals, including simplifying
Square roots and cube roots 1. Square roots 2. Cube roots Simplify radical expressions 3. Simplify radical expressions 4. Simplify radical expressions involving fractions 5. Simplify radical expressions using the distributive property 6. Simplify radical expressions: mixed review Operations with radical expressions 7. Multiply radical expressions 8. Add and subtract radical expressions

Standard form (scientific notation)		Convert and compare 1. Convert between ordinary numbers and standard form 2. Compare numbers written in standard form Operations 3. Add and subtract numbers written in standard form 4. Multiply numbers written in standard form 5. Divide numbers written in standard form
Standard form (scientific notation)
Convert and compare 1. Convert between ordinary numbers and standard form 2. Compare numbers written in standard form Operations 3. Add and subtract numbers written in standard form 4. Multiply numbers written in standard form 5. Divide numbers written in standard form

Laws of exponents, including integer and negative exponents		Negative exponents 1. Negative indices Law of exponents 2. Multiplication with positive indices 3. Multiplication with integer indices 4. Division with integer indices 5. Multiplication and division with integer indices 6. Power rule with positive indices 7. Power rule with integer indices Evaluate exponential expressions 8. Evaluate expressions using properties of indices: integer indices Equivalent exponential expressions 9. Identify equivalent expressions involving integer indices Simplify exponential expressions 10. Multiply monomials 11. Divide monomials 12. Multiply and divide monomials 13. Powers of monomials
Laws of exponents, including integer and negative exponents
Negative exponents 1. Negative indices Law of exponents 2. Multiplication with positive indices 3. Multiplication with integer indices 4. Division with integer indices 5. Multiplication and division with integer indices 6. Power rule with positive indices 7. Power rule with integer indices Evaluate exponential expressions 8. Evaluate expressions using properties of indices: integer indices Equivalent exponential expressions 9. Identify equivalent expressions involving integer indices Simplify exponential expressions 10. Multiply monomials 11. Divide monomials 12. Multiply and divide monomials 13. Powers of monomials

Number systems notation		1. Identify rational and irrational numbers 2. Classify numbers
Number systems notation
1. Identify rational and irrational numbers 2. Classify numbers

Direct and inverse proportion		Direct proportion 1. Identify proportional relationships 2. Find the constant of variation 3. Write direct variation equations 4. Write and solve direct variation equations Identify direct and inverse proportion 5. Identify direct variation and inverse variation Inverse proportion 6. Write inverse variation equations 7. Write and solve inverse variation equations
Direct and inverse proportion
Direct proportion 1. Identify proportional relationships 2. Find the constant of variation 3. Write direct variation equations 4. Write and solve direct variation equations Identify direct and inverse proportion 5. Identify direct variation and inverse variation Inverse proportion 6. Write inverse variation equations 7. Write and solve inverse variation equations

Number sequences (prediction, description)		1. Identify arithmetic and geometric sequences 2. Arithmetic sequences 3. Geometric sequences
Number sequences (prediction, description)
1. Identify arithmetic and geometric sequences 2. Arithmetic sequences 3. Geometric sequences
Algebra
Factorizing quadratic expressions		1. Factorise quadratics with leading coefficient 1 2. Factorise quadratics with other leading coefficients 3. Factorise quadratics: special cases 4. Factorise by grouping
Factorizing quadratic expressions
1. Factorise quadratics with leading coefficient 1 2. Factorise quadratics with other leading coefficients 3. Factorise quadratics: special cases 4. Factorise by grouping

Solving quadratic equations		Square roots 1. Solve a quadratic equation using square roots Zero product property 2. Solve a quadratic equation using the zero product property Factor 3. Solve a quadratic equation with other leading coefficients by factorising Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant Word problems 8. Solve quadratic equations: word problems
Solving quadratic equations
Square roots 1. Solve a quadratic equation using square roots Zero product property 2. Solve a quadratic equation using the zero product property Factor 3. Solve a quadratic equation with other leading coefficients by factorising Complete the square 4. Complete the square 5. Solve a quadratic equation by completing the square Quadratic formula 6. Solve a quadratic equation using the quadratic formula 7. Using the discriminant Word problems 8. Solve quadratic equations: word problems

Changing the subject of an equation		1. Rearrange multi-variable equations 2. Linear equations: solve for y
Changing the subject of an equation
1. Rearrange multi-variable equations 2. Linear equations: solve for y

Thinking with models
Thinking with models
Mappings		1. Relations: convert between tables, graphs, mappings and lists of points
Mappings
1. Relations: convert between tables, graphs, mappings and lists of points

Function notation		Domain and range 1. Domain and range of relations Identify functions 2. Identify functions 3. Identify functions: vertical line test Interpret functions 4. Interpret functions using everyday language Evaluate functions 5. Find values using function graphs 6. Evaluate a function 7. Evaluate a function: plug in an expression 8. Complete a function table from an equation
Function notation
Domain and range 1. Domain and range of relations Identify functions 2. Identify functions 3. Identify functions: vertical line test Interpret functions 4. Interpret functions using everyday language Evaluate functions 5. Find values using function graphs 6. Evaluate a function 7. Evaluate a function: plug in an expression 8. Complete a function table from an equation

Linear functions		Identify linear functions 1. Identify linear functions Evaluate linear functions 2. Complete a table and graph a linear function 3. Interpret points on the graph of a linear function Word problems 4. Write an equation in y=mx+c form from a word problem Compare linear functions 5. Compare linear functions: graphs, tables and equations
Linear functions
Identify linear functions 1. Identify linear functions Evaluate linear functions 2. Complete a table and graph a linear function 3. Interpret points on the graph of a linear function Word problems 4. Write an equation in y=mx+c form from a word problem Compare linear functions 5. Compare linear functions: graphs, tables and equations

y = mx + c (see also spatial reasoning)		Slope-intercept form 1. Graph an equation in y=mx+c form 2. Write an equation in y=mx+c form from a graph 3. Write an equation in y=mx+c form 4. Write an equation in y=mx+c form from a table Horizontal and vertical lines 5. Equations of horizontal and vertical lines 6. Graph a horizontal or vertical line Find and interpret slope and intercepts 7. Find the gradient and y-intercept of a linear equation • Coming soon: Interpret the slope and y-intercept of a linear function Transformations 8. Transformations of linear functions
y = mx + c (see also spatial reasoning)
Slope-intercept form 1. Graph an equation in y=mx+c form 2. Write an equation in y=mx+c form from a graph 3. Write an equation in y=mx+c form 4. Write an equation in y=mx+c form from a table Horizontal and vertical lines 5. Equations of horizontal and vertical lines 6. Graph a horizontal or vertical line Find and interpret slope and intercepts 7. Find the gradient and y-intercept of a linear equation • Coming soon: Interpret the slope and y-intercept of a linear function Transformations 8. Transformations of linear functions

Parallel and perpendicular lines (see also spatial reasoning)		Construct lines 1. Construct parallel lines 2. Construct a perpendicular line Parallel lines 3. Write an equation for a parallel line
Parallel and perpendicular lines (see also spatial reasoning)
Construct lines 1. Construct parallel lines 2. Construct a perpendicular line Parallel lines 3. Write an equation for a parallel line

Systems of equations/simultaneous equations		Understand solutions 1. Is (x, y) a solution to the simultaneous equations? Number of solutions 2. Find the number of solutions to simultaneous equations by graphing 3. Find the number of solutions to simultaneous equations Solve by graphing 4. Solve simultaneous equations by graphing 5. Solve simultaneous equations by graphing: word problems Solve by substitution 6. Solve simultaneous equations using substitution 7. Solve simultaneous equations using substitution: word problems Solve by elimination 8. Solve simultaneous equations using elimination 9. Solve simultaneous equations using elimination: word problems Solve using any method 10. Solve simultaneous equations using any method 11. Solve simultaneous equations using any method: word problems
Systems of equations/simultaneous equations
Understand solutions 1. Is (x, y) a solution to the simultaneous equations? Number of solutions 2. Find the number of solutions to simultaneous equations by graphing 3. Find the number of solutions to simultaneous equations Solve by graphing 4. Solve simultaneous equations by graphing 5. Solve simultaneous equations by graphing: word problems Solve by substitution 6. Solve simultaneous equations using substitution 7. Solve simultaneous equations using substitution: word problems Solve by elimination 8. Solve simultaneous equations using elimination 9. Solve simultaneous equations using elimination: word problems Solve using any method 10. Solve simultaneous equations using any method 11. Solve simultaneous equations using any method: word problems

Quadratic functions		Characteristics of quadratic functions 1. Characteristics of quadratic functions: graphs 2. Characteristics of quadratic functions: equations Function tables 3. Complete a function table: quadratic functions Graph quadratic functions 4. Match quadratic functions and graphs 5. Graph a quadratic function Write quadratic functions 6. Write a quadratic function from its zeros 7. Write a quadratic function in vertex form
Quadratic functions
Characteristics of quadratic functions 1. Characteristics of quadratic functions: graphs 2. Characteristics of quadratic functions: equations Function tables 3. Complete a function table: quadratic functions Graph quadratic functions 4. Match quadratic functions and graphs 5. Graph a quadratic function Write quadratic functions 6. Write a quadratic function from its zeros 7. Write a quadratic function in vertex form

Algorithms		Linear equations 1. Solve linear equations: mixed review System of equations 2. Solve simultaneous equations using any method 3. Solve simultaneous equations using any method: word problems Quadratic equations 4. Factorise polynomials
Algorithms
Linear equations 1. Solve linear equations: mixed review System of equations 2. Solve simultaneous equations using any method 3. Solve simultaneous equations using any method: word problems Quadratic equations 4. Factorise polynomials

Spatial reasoning
Geometry
Metric conversions		1. Convert rates and measurements: imperial units 2. Convert rates and measurements: metric units
Metric conversions
1. Convert rates and measurements: imperial units 2. Convert rates and measurements: metric units

Volume of regular polyhedra		1. Volume of prisms and cylinders 2. Volume of pyramids and cones
Volume of regular polyhedra
1. Volume of prisms and cylinders 2. Volume of pyramids and cones

Similarity and congruence		Understand congruence 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts Congruence theorems 3. SSS and SAS Theorems 4. ASA and AAS Theorems 5. SSS, SAS, ASA and AAS Theorems 6. SSS Theorem in the coordinate plane 7. Hypotenuse-Leg Theorem Determine congruence 8. Identify congruent figures 9. Determine if two figures are congruent: justify your answer 10. Congruency in isosceles and equilateral triangles Understand similarity 11. Ratios in similar figures 12. Similarity statements 13. Identify similar figures Measurements in similar figures 14. Side lengths and angle measures in similar figures 15. Similar triangles and indirect measurement 16. Perimeters of similar figures Similarity theorems 17. Angle-angle criterion for similar triangles 18. Similarity rules for triangles 19. Similar triangles and transformations
Similarity and congruence
Understand congruence 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts Congruence theorems 3. SSS and SAS Theorems 4. ASA and AAS Theorems 5. SSS, SAS, ASA and AAS Theorems 6. SSS Theorem in the coordinate plane 7. Hypotenuse-Leg Theorem Determine congruence 8. Identify congruent figures 9. Determine if two figures are congruent: justify your answer 10. Congruency in isosceles and equilateral triangles Understand similarity 11. Ratios in similar figures 12. Similarity statements 13. Identify similar figures Measurements in similar figures 14. Side lengths and angle measures in similar figures 15. Similar triangles and indirect measurement 16. Perimeters of similar figures Similarity theorems 17. Angle-angle criterion for similar triangles 18. Similarity rules for triangles 19. Similar triangles and transformations

Coordinate geometry, including distance, midpoint and gradient formulae		Midpoint 1. Midpoint formula: find the midpoint 2. Midpoint formula: find the endpoint Distance 3. Distance between two points Coordinate plane 4. Area and perimeter in the coordinate plane I 5. Area and perimeter in the coordinate plane II Gradient 6. Find the gradient of a graph 7. Find the gradient from two points 8. Find a missing coordinate using gradient
Coordinate geometry, including distance, midpoint and gradient formulae
Midpoint 1. Midpoint formula: find the midpoint 2. Midpoint formula: find the endpoint Distance 3. Distance between two points Coordinate plane 4. Area and perimeter in the coordinate plane I 5. Area and perimeter in the coordinate plane II Gradient 6. Find the gradient of a graph 7. Find the gradient from two points 8. Find a missing coordinate using gradient

Movement on a plane—isometric transformations, enlargements, and tessellations		Classify congruence 1. Identify translations, reflections and rotations Translations 2. Translations: graph the image 3. Translations: find the coordinates 4. Translations: write the rule Reflections 5. Reflections: graph the image 6. Reflections: find the coordinates Rotations 7. Rotate polygons about a point 8. Rotations: graph the image 9. Rotations: find the coordinates Mixed transformations 10. Reflections and rotations: write the rule 11. Transformations that carry a polygon onto itself 12. Translations, reflections and rotations: mixed review Sequences of transformations 13. Describe transformations 14. Sequences of translations, reflections and rotations: graph the image 15. Sequences of congruence transformations: choose the sequence Dilations 16. Dilations: graph the image 17. Dilations: find the coordinates 18. Dilations: scale factor and classification
Movement on a plane—isometric transformations, enlargements, and tessellations
Classify congruence 1. Identify translations, reflections and rotations Translations 2. Translations: graph the image 3. Translations: find the coordinates 4. Translations: write the rule Reflections 5. Reflections: graph the image 6. Reflections: find the coordinates Rotations 7. Rotate polygons about a point 8. Rotations: graph the image 9. Rotations: find the coordinates Mixed transformations 10. Reflections and rotations: write the rule 11. Transformations that carry a polygon onto itself 12. Translations, reflections and rotations: mixed review Sequences of transformations 13. Describe transformations 14. Sequences of translations, reflections and rotations: graph the image 15. Sequences of congruence transformations: choose the sequence Dilations 16. Dilations: graph the image 17. Dilations: find the coordinates 18. Dilations: scale factor and classification

y = mx + c, gradients and intercepts (see also functions and models)		1. Graph an equation in y=mx+c form 2. Graph an equation in ax + by = c form 3. Graph a horizontal or vertical line
y = mx + c, gradients and intercepts (see also functions and models)
1. Graph an equation in y=mx+c form 2. Graph an equation in ax + by = c form 3. Graph a horizontal or vertical line

Gradient of parallel lines		1. Write an equation for a parallel line
Gradient of parallel lines
1. Write an equation for a parallel line

Circle geometry		Circle vocabulary 1. Parts of a circle Central and inscribed angles 2. Central angles Arc length and sector area 3. Understand arc length and sector area of a circle 4. Arc measure and arc length 5. Area of sectors 6. Circle measurements: mixed review Chords, secants, and tangents 7. Arcs and chords 8. Tangent lines 9. Perimeter of polygons with an inscribed circle 10. Inscribed angles 11. Angles in inscribed right triangles 12. Angles formed by chords, secants, and tangents 13. Segments formed by chords, secants, and tangents
Circle geometry
Circle vocabulary 1. Parts of a circle Central and inscribed angles 2. Central angles Arc length and sector area 3. Understand arc length and sector area of a circle 4. Arc measure and arc length 5. Area of sectors 6. Circle measurements: mixed review Chords, secants, and tangents 7. Arcs and chords 8. Tangent lines 9. Perimeter of polygons with an inscribed circle 10. Inscribed angles 11. Angles in inscribed right triangles 12. Angles formed by chords, secants, and tangents 13. Segments formed by chords, secants, and tangents

Rotation around a given point		1. Rotate polygons about a point 2. Rotations: graph the image 3. Rotations: find the coordinates
Rotation around a given point
1. Rotate polygons about a point 2. Rotations: graph the image 3. Rotations: find the coordinates
Trigonometry
Triangle properties		1. Exterior Angle Theorem 2. Triangle inequality • Coming soon: Triangle Inequality Theorem
Triangle properties
1. Exterior Angle Theorem 2. Triangle inequality • Coming soon: Triangle Inequality Theorem

Bearings		1. Compass directions and vectors
Bearings
1. Compass directions and vectors

Pythagoras' theorem		1. Pythagoras' Theorem 2. Pythagoras' theorem: word problems 3. Converse of Pythagoras' theorem 4. Pythagoras' Inequality Theorems
Pythagoras' theorem
1. Pythagoras' Theorem 2. Pythagoras' theorem: word problems 3. Converse of Pythagoras' theorem 4. Pythagoras' Inequality Theorems

Trigonometric ratios in right-angled triangles		Trigonometric ratios 1. Trigonometric ratios: sin, cos and tan 2. Trigonometric ratios in similar right triangles Special right triangles 3. Special right triangles 4. Find trigonometric functions of special angles: sin, cos and tan Inverse trigonometric functions 5. Inverses of trigonometric functions Solve triangles 6. Trigonometric ratios: find a side length 7. Trigonometric ratios: find an angle measure 8. Solve a right triangle
Trigonometric ratios in right-angled triangles
Trigonometric ratios 1. Trigonometric ratios: sin, cos and tan 2. Trigonometric ratios in similar right triangles Special right triangles 3. Special right triangles 4. Find trigonometric functions of special angles: sin, cos and tan Inverse trigonometric functions 5. Inverses of trigonometric functions Solve triangles 6. Trigonometric ratios: find a side length 7. Trigonometric ratios: find an angle measure 8. Solve a right triangle

Reasoning with data
Reasoning with data
Sampling techniques
Sampling techniques


Data manipulation and misinterpretation		1. Identify biased samples
Data manipulation and misinterpretation
1. Identify biased samples

Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)		Line plots 1. Create line plots 2. Interpret line plots Circle graphs 3. Interpret pie charts Stem-and-leaf plots 4. Interpret stem-and-leaf plots Box plots 5. Box plots Histograms 6. Interpret bar graphs for grouped data 7. Create bar graphs for grouped data Scatter plots 8. Identify trends with scatter plots 9. Outliers in scatter plots
Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)
Line plots 1. Create line plots 2. Interpret line plots Circle graphs 3. Interpret pie charts Stem-and-leaf plots 4. Interpret stem-and-leaf plots Box plots 5. Box plots Histograms 6. Interpret bar graphs for grouped data 7. Create bar graphs for grouped data Scatter plots 8. Identify trends with scatter plots 9. Outliers in scatter plots

Lines of best fit		1. Identify lines of best fit 2. Write an equation for a line of best fit
Lines of best fit
1. Identify lines of best fit 2. Write an equation for a line of best fit

Data processing: quartiles and percentiles		1. Calculate quartiles and interquartile range
Data processing: quartiles and percentiles
1. Calculate quartiles and interquartile range

Measures of dispersion: interquartile range		1. Calculate quartiles and interquartile range 2. Identify an outlier 3. Identify an outlier and describe the effect of removing it
Measures of dispersion: interquartile range
1. Calculate quartiles and interquartile range 2. Identify an outlier 3. Identify an outlier and describe the effect of removing it

Correlation, qualitative handling		1. Match correlation coefficients to scatter plots 2. Correlation and causation
Correlation, qualitative handling
1. Match correlation coefficients to scatter plots 2. Correlation and causation

Relative frequency
Relative frequency


Response rates
Response rates


Sets, including notation and operations up to three sets
Sets, including notation and operations up to three sets


Probability with Venn diagrams, tree diagrams, and sample spaces		1. Probability of mutually exclusive events and overlapping events 2. Find probabilities using two-way frequency tables
Probability with Venn diagrams, tree diagrams, and sample spaces
1. Probability of mutually exclusive events and overlapping events 2. Find probabilities using two-way frequency tables

Mutually exclusive events		1. Probability of mutually exclusive events and overlapping events
Mutually exclusive events
1. Probability of mutually exclusive events and overlapping events

Combined events		1. Compound events: find the number of outcomes 2. Find conditional probabilities using two-way frequency tables
Combined events
1. Compound events: find the number of outcomes 2. Find conditional probabilities using two-way frequency tables

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