Mathematics
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MYP 2

Année 8 — Tous les objectifs

Building topic foundations

8.1 Fractions review

Term 1

Fractions Review

  1. 1. Understand the concept of a fraction as a representation of division and a part of a whole.
  2. 2. Convert between mixed numerals and improper fractions.
  3. 3. Simplify fractions and find equivalent fractions.
  4. 4. Write two or more fractions with a common denominator.
  5. 5. Add and subtract fractions with the same and with different denominators.
  6. 6. Multiply fractions, including by a whole number and by a mixed numeral.
  7. 7. Divide fractions, including by a whole number.
  8. 8. Convert between fractions, decimals and percentages.

8.2 Ratio and Rates

Term 1

Ratio and Rates

  1. 1. Define and apply the concept of a ratio in real contexts.
  2. 2. Identify and use equivalent ratios.
  3. 3. Simplify ratios, including ratios involving different units.
  4. 4. Share an amount in a given ratio.
  5. 5. Understand and calculate unit rates.
  6. 6. Find a given percentage of a quantity.
  7. 7. Find the whole given a percentage part (reverse percentage).
  8. 8. Calculate percentage increases and decreases.

8.3 Proportions

Term 1

Proportions

  1. 1. Define a proportional relationship.
  2. 2. Test whether two quantities are in a proportional relationship using a ratio table.
  3. 3. Determine the constant of proportionality.
  4. 4. Write an equation of the form y = kx for a proportional relationship.
  5. 5. Graph proportional relationships and interpret the gradient as the constant of proportionality.
  6. 6. Apply direct proportion to solve word problems (recipes, distance-time, costs).

8.4 Scale and Similarity

Term 1

Scale and Similarity

  1. 1. Create and interpret scale drawings.
  2. 2. Understand and use the concept of scale factor (linear).
  3. 3. Use map scales to calculate real distances.
  4. 4. Convert between scale lengths and real lengths in mixed units.
  5. 5. Recognise similar figures and find missing sides using the scale factor.
  6. 6. Understand that area scales by the square of the linear scale factor.

8.5 Directed Number and Algebra Basics

Term 1–2

Directed Number

  1. 1. Add and subtract directed numbers.
  2. 2. Multiply and divide directed numbers.
  3. 3. Apply the order of operations, including calculations with exponents and directed numbers.
  4. 4. Use the distributive property with a single bracket involving directed numbers.

Algebra Basics

  1. 5. Use algebraic vocabulary correctly (term, expression, coefficient, variable, constant).
  2. 6. Use algebraic notation and conventions correctly (e.g. write 3x not x3, write n² not n × n).
  3. 7. Collect like terms in algebraic expressions.
  4. 8. Understand and use algebraic products (e.g. 3 × a × a = 3a²).

8.6 Patterns

Term 2

Patterns

  1. 1. Continue and describe numeric and visual patterns.
  2. 2. Describe linear patterns using algebraic expressions (e.g. 3n + 4).
  3. 3. Find a formula for the nth term of a linear sequence.
  4. 4. Verify whether a given value is a term of a sequence.
  5. 5. Find the position n of a term in a sequence by solving an equation.
  6. 6. Use linear-pattern formulas in real-world contexts (e.g. matchstick or table-seating patterns).

8.7 Algebra Expressions

Term 2

Algebra Expressions

  1. 1. Identify and work with equivalent expressions.
  2. 2. Substitute values into algebraic expressions, including with directed numbers.
  3. 3. Simplify algebraic products.
  4. 4. Apply the distributive rule involving a single bracket.
  5. 5. Factorise expressions involving a single bracket.
  6. 6. Simplify algebraic fractions where numerator and denominator share a common factor.

8.8 Equations

Term 2

Equations

  1. 1. Use function machines to understand inverse algebraic operations.
  2. 2. Solve one-step and two-step equations involving a single variable.
  3. 3. Solve equations with brackets (using the distributive rule first).
  4. 4. Solve multi-step equations including those with x on both sides.
  5. 5. Solve equations involving fractional coefficients or fractions of x.
  6. 6. Form an equation from a word problem and solve it.

8.9 Statistics Foundations

Term 2–3

Statistics Foundations

  1. 1. Calculate the mean of an ungrouped data set.
  2. 2. Calculate the median of an ungrouped data set.
  3. 3. Identify the mode of a data set.
  4. 4. Calculate the range of a data set.
  5. 5. Identify an outlier and comment on its effect on the mean and median.
  6. 6. Construct and interpret tally charts.
  7. 7. Construct and interpret frequency tables (ungrouped).
  8. 8. Find a missing data value given the mean of a set.

8.10 Sampling

Term 2–3

Sampling

  1. 1. Distinguish between population, sample, census and survey.
  2. 2. Understand how sample size affects the reliability of inferences.
  3. 3. Apply random and stratified sampling techniques.
  4. 4. Design a survey with valid, non-biased questions.
  5. 5. Identify sources of bias in a sampling design and suggest improvements.
  6. 6. Collect data and clean a dataset (handling outliers, missing values, units).

8.11 Presenting Data

Term 3

Presenting Data

  1. 1. Construct a bar chart for categorical or discrete data.
  2. 2. Construct a pie chart and convert frequencies to angles.
  3. 3. Construct a histogram for continuous data, choosing appropriate class widths.
  4. 4. Construct a line chart for time-series data.
  5. 5. Choose an appropriate display for a given data type and audience.
  6. 6. Use technology (spreadsheets) to produce data displays.

8.12 Analysing Data

Term 3

Analysing Data

  1. 1. Describe a distribution using spread, symmetry, tails and outliers.
  2. 2. Describe skew (positive, negative or none) from a display.
  3. 3. Calculate the mean absolute deviation (MAD) of a small data set.
  4. 4. Make comparative inferences across two data sets using measures of centre and spread.
  5. 5. Evaluate the validity of an inference (sample size, representativeness, bias).
  6. 6. Use measures of centre and variability to support or challenge claims about data.
  7. 7. Compare two data sets using boxplots and the five-number summary.

8.13 Circles and Angles

Term 3

Circles and Angles

  1. 1. Differentiate between concave and convex shapes.
  2. 2. Identify and classify different types of angles (acute, right, obtuse, straight, reflex).
  3. 3. Understand the definition of a circle and the concept of π as the ratio of circumference to diameter.
  4. 4. Calculate the circumference of circles using C = 2πr or C = πd.
  5. 5. Calculate the area of circles using A = πr².
  6. 6. Find the radius or diameter of a circle given its circumference or area.
  7. 7. Solve composite problems involving circles, semicircles and rectangles.

8.14 Triangles

Term 3

Triangles

  1. 1. Label triangles using three capital letters for the vertices.
  2. 2. Name angles using a capital letter with a hat (e.g. ABĈ).
  3. 3. Name sides using a single lowercase letter or two capital letters for the endpoints.
  4. 4. Understand and apply the triangle inequality (any two sides must sum to more than the third).
  5. 5. Identify uniqueness conditions for constructing a triangle (SSS, SAS, ASA, RHS).
  6. 6. Classify triangles by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse).

8.15 Parallel Lines and Polygons

Term 3

Parallel Lines and Polygons

  1. 1. Identify alternate, corresponding and co-interior angles formed by a transversal crossing parallel lines.
  2. 2. Calculate unknown angles in parallel-line diagrams.
  3. 3. Apply the triangle angle sum theorem to determine unknown angles.
  4. 4. Calculate the sum of the interior angles of a polygon using (n − 2) × 180°.
  5. 5. Calculate the size of one interior angle of a regular polygon.
  6. 6. Use the fact that exterior angles of a polygon sum to 360°.
  7. 7. Solve algebraic angle problems where angles in parallel-line or polygon diagrams are given as expressions in x.

8.16 Constructions

Term 3

Constructions

  1. 1. Use a protractor accurately to measure and draw angles.
  2. 2. Use compasses and a straight-edge to construct line segments and copy lengths.
  3. 3. Construct an equilateral triangle on a given segment.
  4. 4. Construct a perpendicular bisector of a segment.
  5. 5. Construct the seed of life (six interlocking circles).
  6. 6. Construct a regular hexagon from a circle.
  7. 7. Describe each construction step with mathematical reasoning.