# Glossary

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.

Categorical data have values that are categories. For example, data on blood groups is categorical data with values of type A, B, AB or O.

The circumference of a circle is the distance around the circle. That is, the perimeter of a circle.

A method of combining two numbers or algebraic expressions is commutative if the result of the combination does not depend on the order in which the objects are given. For example, addition of numbers has the commutative property, as a + b = b + a for all numbers a and b. Multiplication also has the commutative property but subtraction and division do not.

A process of reformulating an arithmetical problem to one that can be computed more easily mentally by making balanced changes to the numbers. For example, to find 78 + 27 add 2 to 78 to make 80 and compensate for this by subtracting 2 from 27 leaving 25. Compensation doesn’t changed the total but transforms the question to finding 80 + 25, which is easier to calculate.

Adding on to find the difference between two amounts. This method of using addition to complete a subtraction is commonly used in giving change. For example, the change from $50 for a purchase of$26 is $4 makes$30 and $20 makes$50.

A composite unit is a unit made up of multiple copies of another unit. For example, a composite unit of 10 is both one unit of ten and ten units of one.

In probability, a compound event is having more than one event occurring at the same time. For example, tossing a coin and selecting a card.

A numerical variable that can take any value that lies within an interval. In practice, the values taken are subject to the accuracy of the measurement instrument used to obtain these values. Examples include height, reaction time to a stimulus and systolic blood pressure.

To answer a question such as, “I have 9 grapes and I eat 3 grapes, how many remain?” the student says “Nine, …eight, seven, six,… six!”. This strategy is described as counting-down-from a number.

To solve questions where the number being taken away is not known, a student may count down from the larger number to the smaller number to determine how many have been removed. For example, “I have 9 and I remove some, 6 remain. How many did I remove?”. The student may say, “Nine, …eight, seven, six,…three!” This strategy requires keeping track of the backward counts and is described as counting-down-to a number.

Counting by ten starting from a number other than a multiple of ten. For example, 23, 33, 43, 53, …

Also described as counting on. To find the total of six and three a student can take six as the result of a count that has already occurred and say: “Six, … seven, eight, nine, … nine!”. The essential feature of this strategy is that the student counts on from “six”.

This strategy can be used to determine how many are missing with questions such as “6 plus some equals 9. How many?” The student counts up from “six” and keeps track of counts, but does not know in advance the number of counts. Rather, the student initially knows only the starting number and the number to which he or she is counting.