Mathematics (Standard) · MYP 1 (Grade 6)

Four strands stay constant across years — Numerical & Abstract Reasoning, Spatial Reasoning, Thinking with Models, Reasoning with Data — with difficulty rising year-over-year.

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Curriculum tree

4 units · 17 sets. Click any set to see the learning objectives.

Unit 1 · Numerical and Abstract Reasoning

Integers, Factors & Multiples (1 set)

Set 1(3 objectives)
- Read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines
- Represent composite numbers as a product of their prime factors, including through the use of factor trees
- Understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10 and 11

Fractions, Decimals & Percentages (1 set)

Set 1 · Four Operations(3 objectives)
- Finding the whole given a part and the percentage
- Finding percentage increase and percentage decrease
- Use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used

Ratio, Proportion & Rates (3 sets)

Set 1 · Ratio notation and equivalence(5 objectives)
- Notation, representations and interpretation of a:b and a:b:c, where a, b and c are whole numbers, excluding ratios involving fractions and decimals
- Equivalent ratios
- Expressing a ratio in its simplest form
- Finding the ratio of two or three given quantities
- Finding the missing term in a pair of equivalent ratios
Set 2 · Ratio reasoning and tables(5 objectives)
- Dividing a quantity in a given ratio
- Relationship between fraction and ratio
- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities
- Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane; use tables to compare ratios
- Use ratio and rate reasoning to solve real-world and mathematical problems
Set 3 · Unit rates, percentages and conversions(4 objectives)
- Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship
- Solve unit rate problems including those involving unit pricing and constant speed
- Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent
- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities

Unit 2 · Expressions, Equations & Inequalities

Expressions & Equations (3 sets)

Set 1 · Notation and structure of expressions(4 objectives)
- Write, read, and evaluate expressions in which letters stand for numbers
- Write expressions that record operations with numbers and with letters standing for numbers
- Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity
- Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems
Set 2 · Operations and equivalence(4 objectives)
- Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)
- Apply the properties of operations to generate equivalent expressions
- Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them)
- Write and evaluate numerical expressions involving whole-number exponents
Set 3 · Variables and solving equations(2 objectives)
- Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set
- Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers

Inequalities (1 set)

Set 1(4 objectives)
- Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
- Use substitution to determine whether a given number in a specified set makes an equation or inequality true
- Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem
- Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams

Unit 3 · Spatial Reasoning

Lines & Angles (1 set)

Set 1(3 objectives)
- Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
- Know that the sum of the angles around a point is 360°, and use this to calculate missing angles
- Recognise the properties of angles on parallel lines and transversals, perpendicular lines, and intersecting lines

2D Shapes (2 sets)

Set 1 · Polygons, quadrilaterals and circles(5 objectives)
- Identify, describe and sketch regular polygons, including reference to sides, angles and symmetrical properties; understand that if two 2D shapes are congruent, corresponding sides and angles are equal
- Derive the property that the sum of the angles in a quadrilateral is 360°, and use this to calculate missing angles
- Identify and describe properties of quadrilaterals (including the parallelogram, rhombus and trapezium), and classify using parallel sides, equal sides, and equal angles
- Know the parts of a circle: centre, radius, diameter, circumference, chord, tangent
- Identify reflective symmetry and order of rotational symmetry of 2D shapes and patterns
Set 2 · Transformations(4 objectives)
- Use knowledge of translation of 2D shapes to identify the corresponding points between the original and the translated image, without the use of a grid
- Reflect 2D shapes on coordinate grids in a given mirror line (x- or y-axis), recognising that the image is congruent to the object after a reflection
- Rotate shapes 90° and 180° around a centre of rotation, recognising that the image is congruent to the object after a rotation
- Understand that the image is mathematically similar to the object after enlargement; use positive integer scale factors to perform and identify enlargements

Proofs & Constructions (1 set)

Set 1(2 objectives)
- Draw parallel and perpendicular lines, and quadrilaterals
- Construct simple geometrical figures from given data using compasses, ruler, set squares and protractor

Unit 4 · Data Analysis and Probability

Statistics (2 sets)

Set 1 · Representations and data analysis(4 objectives)
- Choose and explain which representation to use in a given situation: Venn and Carroll diagrams, tally charts, frequency tables and two-way tables, dual and compound bar charts, waffle diagrams and pie charts, frequency diagrams for continuous data, line graphs
- Record, organise and represent categorical, discrete and continuous data
- Analysis and interpretation of tables
- Interpret primary and secondary data, identifying patterns and trends, within and between data sets, to answer statistical questions
Set 2 · Statistical measures and conclusions(4 objectives)
- Use knowledge of mode, median, mean and range to describe and summarise large data sets; choose and explain which one is the most appropriate for the context
- Data processing, including mean, median (measure of central tendency) and mode, for discrete and grouped data
- Measures of dispersion, including range
- Present conclusions, considering data sampling as one source of variation, and validate predictions

Probability (2 sets)

Set 1 · Probability language and outcomes(3 objectives)
- Use the language associated with probability and proportion to describe, compare, order and interpret the likelihood of outcomes
- Understand and explain that probabilities range from 0 to 1, and can be represented as proper fractions, decimals and percentages
- Identify all the possible mutually exclusive outcomes of a single event, and recognise when they are equally likely to happen
Set 2 · Experimental and theoretical probability(3 objectives)
- Design and conduct chance experiments or simulations, using small and large numbers of trials
- Analyse the frequency of outcomes to calculate experimental probabilities
- Understand how to find the theoretical probabilities of equally likely outcomes

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