Glossary of Terms
- 2D shapes
- flat shapes that have length and width and exist in a plane, but lack depth or thickness. Includes but not limited to circle, square, rectangle, triangle, heart, kit.
- 3D objects
- geometric objects that have length, width, and depth (or height), occupy space and have volume. Includes but not limited to sphere, cone, cube, rectangular prism, triangular pyramid and square pyramid.
- Acute angle
- and angle that measures more than 0 degrees but less than 90 degrees.
- Acute triangle
- all 3 interior angles are less than 90 degrees.
- Attribute
- description of an element in a pattern, (e.g., colour, shape, size, number/letter/symbol, object, direction, position).
- Balanced (equation)
- Equations need to have the same value on both sides of the equal sign, similar to a balance scale where both sides weigh the same.
- Bar graph
- A way of showing numerical data by category using the height or length of a bar. Also known as a column chart. Bar graphs are used to compare things between different groups or to show data collected in different times or places.
- Benchmarks
- a familiar, measurable quantity used to help estimate or understand other quantities, (e.g., 5, 10, 100, 1000, 25, 50).
- Cardinality
- knowing that the last number said when counting represents the quantity of objects in a set.
- Cartesian Plane
- also known as a coordinate plane, is formed by two perpendicular number lines, the x-axis and y-axis, intersecting at a point called the origin. It’s used to locate points and represent relationships between two variables.
- Change tasks
- a task in which a student demonstrates changing a quantity using concrete, pictorial, and symbolic models (e.g., using blocks to show changing 8 to 12 by adding 4 more blocks).
- Commutative property
- the order of the numbers in an addition equation does not change the sum, (e.g., 3 + 5 = 5 + 3 = 8).
- Compensating
- bridging to or decomposing to a benchmark or friendly number [ex: 47 + 28 add 3 to 47 to make 50 (friendly number) subtract 3 from 28 to compensate = 25 50 + 25 = 75].
- Compose/Recompose
- building or rebuilding a set of objects or a number from smaller parts. For example, 5 can be made from 1 and 4 or 2 and 3.
- Concrete forms
- concrete materials or physical objects help students learn through actions such as placing, moving, grouping, or splitting objects. Examples include manipulatives (e.g., base-10 blocks, counters), natural or found materials, loose parts.
- Concrete graph
- A graph that organizes and displays data using concrete objects like blocks or stickers, with appropriate labels.
- Conservation
- knowing that the number of objects remains the same despite changing the size of objects or how they are laid out.
- Contextual problem
- a problem that is set within a real-world or practical situation, requiring students to apply mathematical concepts to solve it. Students identify and apply the best mathematical operation and strategy to fit the context, and based on their current knowledge and available tools.
- Core
- repeated element in a repeating pattern, (e.g., AAB is the core of AABAABAAB)
- Counting on and counting back
- starting from a number and counting on by the added number or back by the subtracted number.
- Decompose
- breaking down a number into smaller parts or simpler parts to support computation. For example, 12 = 10 + 2, or 147 can be broken into 100, 40, and 7 OR 14 tens and 7 ones, or 47 + 28 decompose by place value: 47 = 40 + 7; 28 = 20 + 8 add by place value: 40 + 20 = 60; 7 + 8 = 15 add total: 60 + 15 = 75.
- Doubles
- e.g., 3 + 3 = 6, 7 + 7 = 14.
- Equilateral Triangle
- a triangle that has all equal angles (60 degrees) and all sides of equal length.
- Equivalents
- quantities that are equal in value, function, amount, or meaning, but not necessarily number, i.e., 1 m = 100 cm, 4 quarters = 1 loonie.
- Estimate
- to approximate a number, calculation, quantity, or measurement based on an educated guess, rounding, or a visual comparison with a referent or benchmark
- Expanded form
- breaking down numbers as the sum of the digits and their place value, (e.g., 123 = 100 + 20 + 3).
- Experimental Probability
- the probability of an event occurring based on actual results from an experiment or observation.
- Fact families
- sets of related addition/subtraction or multiplication/division math facts such as 12 + 6 = 18 and 18 – 6 = 12, or 2 x 7 = 14 and 14 ÷ 7 = 2. Fact families illustrate how sets can be decomposed and recomposed.
- Factor
- a number that divides another number evenly, leaving no remainder
- Fractions
- numbers which can represent a part of a whole, part of a region, part of a set, or part of a length. The denominators of fractions represent equal-sized portions of a whole or unit. The numerators represent the number of portions within the fraction. For example, 2 3 represents 2 portions (the numerator) out of a whole that has been divided into 3 portions (the denominator).
- Friendly numbers
- bridging to or decomposing to a benchmark or friendly number (ex. 7 = 5 + 2, 5 is a “friendly number”). Often used in conjunction compensating, decomposing, or making 10/bridging over 10 strategies 1.
- Hundred Chart
- jumping along the hundred chart (similar to counting up and counting back) [ex: 47 + 28 Start at 47, add 20 (move 2 rows down) to 67, then add 8 (move 8 squares to the right) to 75].
- Improper fraction
- A fraction that has a value greater than 1, where the numerator is greater than the denominator.
- Irregular polygons
- 2D shapes in which all sides are not equal in length or all angles not equal in measure.
- Isosceles Triangle
- has two sides that are the same length and two angles that are also the same.
- Line graph
- A graph with the data points connected by a line. Used to show change in the data over time.
- Making 10/bridging over 10
- “bridging” to the nearest 10 (ex. 8 + 5. The 8 can be “bridged” to 10 by adding 2 out of 5. Then, add the remaining 3 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13).
- Many-to-one correspondence
- On a concrete graph or pictograph, one symbol represents a group of objects (e.g., one square may represent five cookies).
- Math facts
- fluent and automatized knowledge of addition/subtraction and multiplication/division equations.
- Mixed number
- A number that combines a whole number and a proper fraction, representing a value between consecutive whole numbers.
- Nets
- representations of 3D objects if cut open and laid flat.
- Non-standard units
- measurement units using everyday objects (e.g., a pencil, arm, shoe, Unifix cubes).
- Non-uniform units
- not consistent in size (e.g., children’s hands, pencils).
- Number pattern
- also known as number sequences, are a series of numbers that follow a specific rule or have a relationship between successive numbers. Number sequences can be arithmetic (adding or subtracting by a constant, aka increasing or decreasing patterns. (e.g., 75, 70, 65, 60, 55, …), or geometric (multiplying or dividing by a constant e.g., 1, 2, 4, 8, 16…).
- Obtuse angle
- an angle that measures between 90 and 180 degrees.
- Obtuse triangle
- a triangle with one angle greater than 90 degrees.
- One-to-one correspondence
- when counting the number of objects in a set, using one number per object for accuracy.
- One to one correspondence
- On a concrete graph or pictograph, one picture symbol corresponds to one unit of data (e.g., one dot represents one flower).
- Open number line
- jumping along the number line (similar to counting up and counting back) [ex: 47 + 28 start at 47, jump 20 to 67, jump 3 to 70, jump 5 to 75].
- Part-to-part ratio
- compares the quantities of two different parts within a whole. For example, if a box has 10 apples and 15 oranges, the part-to-part ratio could be the ratio of apples to oranges (10:15), or the ratio of oranges to apples (15:10). This type of ratio does not involve the total number of items
- Part-to-whole ratio
- compares the quantities of one part within a whole to the whole. For example, if a box has 10 apples and 15 oranges, the part-to-whole ratio could be the ratio of apples to fruit (10:25), or the ratio of oranges to fruit (15:25).
- Pattern rule
- Pattern rules describe the relationship between elements in the pattern. Pattern rules can be based on attributes or mathematical operations. Patterns can be repeating, or number (increasing or decreasing) patterns.
- Perimeter
- total distance around the outside of a 2D shape. The perimeter of a circle is also called the circumference.
- Pictograph
- A way of showing data using images, where each image stands for quantity (one to one correspondence or many to one correspondence). Pictographs are used to express large amounts of information in a simple manner as it is easy to read.
- Pictorial forms
- pictorial forms help students see a model which represents a number. Examples include pictures of counting collections, number lines, tally marks, 10-frames
- Place value
- the relationship between the digits within a number and their value, (e.g., the digit 4 in 49 has the value of 40).
- Polygons
- an enclosed 2D shape made up of straight lines.
- Preservation of shape
- the orientation/position of a shape will not change its attributes but will change its appearance.
- Prime factorization
- the process of breaking down a composite number into its prime number factors. The prime factorization of a number is the unique set of prime numbers that, when multiplied together, equal the original number.
- Proper fraction
- A fraction that has a value between 0 and 1, where the numerator is less than the denominator.
- Ratio table
- a table to help understand the relationship between the quantities (e.g., a t-chart could record the total number of meals eaten at a camp, per day—one column could be the number of days, another column could be the number of meals). Ratio tables are also known as t-tables, function machines, or in and out machines.
- Referents
- a known number of concrete or pictorial representations that can be used for comparison, to help estimate an unknown quantity. For example, a 10-frame (grid consisting of 2 lines of 5 squares) can be used as a referent for amounts less than or more than 5.
- Reflex angle
- an angle that measures between 180 and 360 degrees.
- Regular polygons
- 2D shapes in which all sides are equal in length and all angles equal in measure.
- Right angle
- an angle that measures 90 degrees
- Right triangle
- has one interior angle that is 90 degrees.
- Scalene Triangle
- has all different measurements for its sides and angles.
- Scatter Plot
- A graph with a variety of points plotted that are not connected. Used to graph discrete data points.
- Skeletons
- representation of a 3D shape without the faces.
- Skip counting
- method of counting in which students add a number to the previous number (also known as multiples). For example, skip counting by 5, starting at 0 is 0, 5, 10, 15, …
- Stable order counting
- accurately counting numbers in the correct sequence.
- Standard units
- measurement units within established systems such as the metric system.
- Straight angle
- an angle that measures 180 degrees.
- Subitize
- instantly recognizing how many there are in a set without counting, e.g. knowing the number of dots on dice without counting. Subitizing can usually be done for a group of up to 5 objects.
- Symbolic forms
- symbolic forms are abstract mathematical notations which represent numbers. Examples include numerals, tallies, musical notes, fractions.
- Symbols of equality and inequality
- The = sign means “the same as”, e.g., 4 + 6 = 3 + 7. Elements on both sides of the = sign are balanced regardless of size or shape. Symbols of inequality include less than
<; greater than>; and not equal≠. - Table of values
- an organizational table that represents the relationship between two sets of numbers, often used in mathematics and data analysis. It typically consists of two columns, with one column representing input values (often ‘x’) and the other representing the corresponding output values (often ‘y’) calculated from a given equation or rule.
- Theoretical Probability
- the likelihood of an event happening, determined through reasoning and analysis of possible outcomes, rather than by conducting experiments.
- Transformation
- a process that manipulates a geometric figure, changing its position or orientation on a plane or coordinate system. Transformations include but are not limited to rotations (turns), translations (slides) and reflections (flips).
- Uniform units
- consistent in size (e.g., interlocking cubes, standard paper clips).
- Unit fractions
- fractions with 1 in the numerator, such as 1 2 or 1 5 . They allow the comparison of the size of fractions (e.g., 1 2 granola bar > 1 5 granola bar).
