Annotated Content Descriptions | Mathematics Year 2 CONTENT DESCRIPTIONS LANGUAGE/CULTURAL CONSIDERATIONS TEACHING STRATEGIES Measurement and geometry Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Abbreviations are used often in non-narrative texts, and may be considered to be known language (for example, in Mathematics: 3D = kg, cm). Teach the source words of the abbreviations to support the students’ understanding of the concept that the abbreviation is representing. Provide readily accessible charts of abbreviations. Measurement and geometry Compare masses of objects using balance scales (ACMMG038) Many Aboriginal and Torres Strait Islander languages don’t have of comparison (for example, ‘big mobs’, ‘big big mobs’). The language of comparison in English includes the use of the comparative and superlative adjective forms. ', in Mathematics, lighter, the lightest, adding ‘–er’ and using the article ‘the’ and adding the suffix ‘–est’ to one- or two-syllable adjectives. This is not intuitive knowledge for EAL/D students. Model the language structures of comparison, pointing out the suffix on the end of the word, and the use of the article ‘the’ when making the superlative. Provide wall charts of comparative and superlative of adjectives. Measurement and geometry Tell time to the quarter hour, the language of ‘past’ and ‘to’ (ACMMG039) The telling of time is constructed differently in different languages, and this often reflects concepts of time in different cultures. For example, in Greek ‘quarter to five’ is constructed as ‘six less a quarter’. Teach the language structures of telling the time, being aware of possible linguistic differences to better understand if problems with time-telling are linguistic or conceptual. Measurement and geometry Name and months and seasons (ACMMG040) Seasons are understood differently according to geographical locations, including the wet and dry seasons in the tropics, to the more complex seasonal descriptors used by some Aboriginal and Torres Strait Islander people. Relate work on seasons to the teaching and learning environment, using descriptors relevant to the geographical location. Use bilingual assistants, where available, or parents as useful sources of information about the local environment.
Number and algebra Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Some mathematical vocabulary carries different meanings in different contexts (for example, ‘eighth’ can be a fraction or an ordinal number). This can be confusing to EAL/D students in the Beginning and Emerging phases of English language learning. Teach vocabulary in mathematical tasks, including words and terminology being used in ways that EAL/D students may not have encountered before. Number and algebra Count and order small collections of Australian coins and notes according to their value (ACMNA034) All students have cultural experiences and knowledge that are valuable resources for the classroom. Make use of these resources and experiences in the classroom when exploring money. For example, many EAL/D students will have concrete experience, and samples, of other coins and money systems. Number and algebra Solve problems by writing number sentences for addition or subtraction (ACMNA036) Word problems in Mathematics often introduce sentence structures that are new learning and challenging for EAL/D students For example, the use of ellipsis, where the object is referred to once and then implied – ‘There are 12 pieces of pizza. When you take away 4 [pieces of pizza] how many [pieces of pizza] are left?’ Provide scaffolds into Mathematics word problems by using alternative wording. Teach the ellipsis in word problems, asking the students: ‘When it says to take away 4, what does it mean – take away 4 what?’ Statistics and probability Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Size of vocabulary is one of the best predictors of literacy success, and EAL/D students will not have had six or years of exposure to English vocabulary as we might expect of other students in the classroom, nor the same ‘prior knowledge’ to build upon, and so special attention must be paid to vocabulary development in the classroom. Explore the vocabulary of ‘certainty’ by placing terms on a continuum from least certain to most certain. Build synonym word banks for mathematical terminology. Teach the prefixes and suffixes and their meaning (for example, ‘un–likely’, ‘im–possible’) so that EAL/D students can build their vocabulary.
Statistics and probability Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068) In English, questions are formed in many ways and are quite challenging for EAL/D students. They can be formed by changing word order (for example, ‘Are you from Australia?’), or by using question words (for example, ‘Do you have a brother or sister?’ ‘How many brothers do you have?’), as well as the ‘wh’ question words – why, what, who, where. Monitor the language of EAL/D students when they pose questions, and explicitly teach English question forms. Statistics and probability Collect data and organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069) Diagrams in Mathematics are informational, and are different from the images that students usually create intuitively. For example, tables and graphs require accuracy in size relationships and precision in line work. Provide models of mathematical diagrams and tables in the same way as modelled written texts are provided to students. Discuss the features of the required visual texts. Statistics and probability Interpret and compare data displays (ACMSP070) It is important to subject-specific vocabulary explicitly and in context. In Mathematics, for example, words such as ‘tally’ and ‘data’ would not have been encountered by EAL/D students in any other context. Support all students to understand the vocabulary of tasks. Strategies include: providing word lists and visuals to accompany new learning building synonym lists constructing personal word books.
Statistics and probability Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096) Diagrams in mathematics are informational, and are different from the images that students usually create intuitively. For example, tables and graphs require accuracy in size relationships and precision in line work. Provide models of mathematical diagrams and tables in the same way as modelled written are provided to students. Discuss the features of the required visual texts.
Annotated Content Descriptions | Mathematics Year 9 CONTENT DESCRIPTIONS LANGUAGE/CULTURAL CONSIDERATIONS TEACHING STRATEGIES Measurement and geometry Calculate the surface area and volume of cylinders and solve related problems (ACMMG217) Abbreviations relevant to this skill are often considered to be known language, but EAL/D students may not have had exposure to these. Teach source words to support the students in understanding the abbreviation. Have charts of abbreviations available. Measurement and geometry Solve problems involving surface area and volume of right prisms (ACMMG218) Abbreviations relevant to this skill (for example, A = area, V = volume) are often considered to be known language, but EAL/D students may not have had exposure to these. source words to support the students in understanding the abbreviation. Have charts of abbreviations available. Measurement and geometry Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220) The vocabulary and sentence structures needed for this skill may impede an EAL/D learner from demonstrating their knowledge. Provide opportunities for students to show knowledge that is not language based; for example, physical manipulation of objects or the use of visuals. Model spoken language explanations of similarity and provide opportunities for EAL/D students to repeat those explanations for similar problems using the same sentence structure. Use vocabulary games such as snap and bingo to develop vocabulary. Measurement and geometry Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a angle in right-angled triangles (ACMMG223) Abbreviations relevant to this skill are often considered to be known language, but EAL/D students may not have had exposure to these. Teach source words to support the students in understanding the abbreviation. Have charts of abbreviations available. Number and algebra Solve problems involving direct proportion. Explore the relationship between the graphs and equations corresponding to simple rate problems (ACMNA208) Word problems are challenging for EAL/D students, as it can be difficult to determine the operation needed from the language used. This is particularly relevant for EAL/D students in the Beginning and Emerging phases of English language learning when students may not be making sense of all words. Teach students to identify the irrelevant contextual material in the question and to cross this out. Focus on how the operations are described differently in different questions.
Statistics and probability Investigate reports of surveys in digital and elsewhere for information on how data was obtained to estimate population means and medians (ACMSP227) Questioning ‘authority’ sources is not a skill taught in some cultures. EAL/D students may find this task confronting. Reassure students that it is necessary to question the validity of surveys and assist them in the language needed to express their findings. Teach investigation as a text form – structure, organisation, tenses and vocabulary. Statistics and probability Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228) Forming questions in English can be done in different ways, such as the use of question words (for example, ‘Why’, ‘What’, ‘How many’) or a change in word order (for example, ‘Can it ...’). Provide models of questions that students can use as a basis for their own work.
Annotated Content Descriptions | Mathematics Year 10 CONTENT DESCRIPTIONS LANGUAGE/CULTURAL CONSIDERATIONS TEACHING STRATEGIES Measurement and geometry Solve problems involving surface area and volume of a range of prisms, cylinders and composite solids (ACMMG242) Abbreviations relevant to this are often considered to be known language, but EAL/D students may not have had exposure to these. source words and support the students in understanding the abbreviation. Have charts of abbreviations available. Number and algebra Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229) Students from a limited schooling background may not have the required background knowledge to understand or attempt this skill. They may also lack some of the cultural understandings that may accompany word problems which attempt to contextualise the concept of compound interest. Teach the skills on which this more difficult Mathematics is based. Intensive support is needed in this instance. the contextual information surrounding problems as well as the maths skill, to allow EAL/D students to connect the maths with real-life situations. Number and algebra Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230) Using letters to represent numbers may cause confusion for a student with a limited literacy background and who is still learning that letters represent sounds. Explain the process of using letters to represent numbers in Mathematics, through scaffolding using visual or concrete stimulus, particularly for EAL/D students who are in the Beginning phase of English language learning. Number and algebra Simplify algebraic products and quotients using index laws (ACMNA231) Explain the use of index laws, through scaffolding using visual or concrete stimulus, particularly for EAL/D students who are in the Beginning and Emerging phases of English language learning. Number and algebra the four operations to simple algebraic fractions with numerical denominators (ACMNA232) Students from a limited schooling background may not have the required background knowledge to understand or attempt this skill. Teach the skills on which this more difficult mathematics is based. Intensive support is needed in this instance.
Number and algebra Use the definition of a logarithm to establish and the laws of logarithms (ACMNA265) EAL/D students in the Beginning and Emerging phases of English language learning are unlikely to have had cumulative exposure to the Western Australian Curriculum and Assessment Outline and so may not be familiar with the terminology or the mathematical concepts. Alternatively, they may come from school systems where they have learned the mathematical concepts to this level and perhaps beyond, but do not have the language to adequately demonstrate that understanding. Provide models of the required language, both oral and written, that the EAL/D learner can then use as a framework. Number and algebra Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266) EAL/D students in the Beginning and Emerging phases of English language learning are unlikely to have had cumulative exposure to the Western Australian Curriculum and Assessment Outline and so may not be familiar with the terminology or the mathematical concepts. Number and algebra Describe, interpret and sketch parabolas, hyperbolas and circles and exponential functions and transformations (ACMNA267) Students may have difficulty in expressing what they know (describe). Provide support in the vocabulary and language features required for this task. Provide visual models of the graphs required with accompanying labels. These should be on display for students to refer to. Number and algebra understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268) EAL/D students in the Beginning and Emerging phases of English language learning are unlikely to have had cumulative exposure to the Western Australian Curriculum and Assessment Outline and so may not be familiar with the terminology or the mathematical concepts. EAL/D students may understand polynomials but may still be developing the language to describe their understandings. Provide both oral and written models of descriptions that EAL/D students may then use as a scaffold into their own descriptions using different variables.