An array is an ordered collection of objects or numbers. Rectangular arrays are commonly used in primary mathematics; for example, two arrays of dots, 2 by 12 and 4 by 6, produce two different representations of the number 24.
Determine or find; for example a number or answer by using mathematical processes; obtain a numerical answer showing the relevant stages in the working; ascertain or determine from given facts, figures or information.
The amount that a container will hold; for example, the amount of water (mL) required to fill a fish tank is its capacity. Volume is the space (cm3) occupied.
A skill requiring being able to conceptualise and mentally manipulate numbers or quantities to find an approximate answer. The capacity to make reasonable adjustments to numbers is essential in estimating.
Two expressions are said to be equivalent if they are equal in value.
Equivalent fractions are alternative ways of writing the same fraction; for example: `1/2= 2/4= 5/10`
The results expected from calculating the probability.
Any of the individual flat surfaces of a solid object.
Numbers are factors, or divisors, of another number if they multiply to give that number; for example, 3 and 4 are factors of 12 as 3 × 4 = 12.
The ‘for each’ idea of multiplication is sometimes used as a way of describing the product of different combinations. For example, if for each sandwich there are two choices of bread and for each choice of bread there are three choices of filling, there will be six different sandwich options (2 x 3).
fractions as part-whole relationships
Dividing quantities using fractions as part-whole relationships requires maintaining the multiplicative relationship between each part and the whole; for example, sharing in the ratio 2 parts to 1 part means `2/3`and `1/3` of the whole.
A grid reference identifies a region on a map. Coordinates and gridlines are used to refer to specific features or locations; for example, “In the map below, the school is located at the grid reference C4”.
A number sentence is typically a statement of equality or inequality using numbers and common symbols; for example: 8 + 5 = 13 and 16 - ☐ = 10 are both number sentences.
order of operations
The order of performing mathematical operations:
- evaluate brackets or grouping symbols first
- evaluate any powers and roots
- working left to right, evaluate any multiplication and division
- working left to right, evaluate any addition or subtraction
May also be known as BODMAS, BIDMAS, BEDMAS, etc.
Partitioning means dividing a quantity into parts. In the early years, it commonly refers to the ability to think about numbers as made up of two or more parts, such as, 10 is 8 and 2 or 126 is 100 and 20 and 6. In later years it refers to dividing both continuous and discrete quantities into equal parts.
A picture graph is a statistical graph for organising and displaying categorical data.
place value system
The place value system of our numbers is based on 10. The value of a digit in a numeral is determined by multiplying its face value by the power of ten assigned to its position (283 = 2 x 100 + 8 x 10 + 3 x 1). The quantity represented by a numeral is then the sum of the values represented by its individual digits (283 = 200 + 80 + 3). The base-ten place value system used to write numerals has both multiplicative and additive properties.
The likelihood or chance of something; the relative frequency of the occurrence of an event as measured by the ratio of the number of cases or alternatives favourable to the event to the total number of cases or alternatives.
A product is the result of multiplying together two or more numbers; for example, 36 is the product of 9 and 4.
Selects a named numeral from a randomly displayed group of displayed numerals.
Expresses a number in equivalent ways by interpreting the relationship between the place value powers of ten; for example, 243 can be renamed 2 hundreds and 43 ones or 24 tens and 3 ones.
Adding the same number again and again. A strategy sometimes used for multiplication.
The decimal expansion of a real number is rounded when it is approximated by a terminating decimal that has a given number of decimal digits to the right of the decimal point.
Rounding to n decimal places is achieved by removing all decimal digits beyond (to the right of) the nth digit to the right of the decimal place and adjusting the remaining digits where necessary.
If the first digit removed (the(n+1)th digit) is less than 5 the preceding digit is not changed; for example, 4.02749 becomes 4.027 when rounded to 3 decimal places.
If the first digit removed is greater than or equal to 5, then the preceding digit is increased by 1; for example, 6.1234586 becomes 6.12346 when rounded to 5 decimal places.
Routine fractions are those fractions commonly used in estimating and for making comparisons to other numbers; for example, `1/2,1/3,1/4,3/4`
sharing model of division
In the sharing model of division, the divisor indicates a whole number of equal groups and the quotient, the result of division, is the size of each part. In 12 ÷ 3 = 4, twelve is shared into 3 equal groups and there are 4 in each group.
Skip counting is counting in multiples; for example, three, six, nine, twelve, …