
Ratio  a comparison using division, often comparing different parts of a group. Examples: 3 cars: 1 truck, 5 oz of yellow paint to 3 oz of blue paint.
Fraction  a type of ratio where a part of a group is compared to the total or the whole. Examples: 3 cars : 4 total vehicles, 1/4 of the vehicles are trucks.
Rate  a type of ratio that is always parttopart since a total cannot be found. Examples: 100 cows to 3 farms, 9 steps : 3 sec, 60 miles/ 2 hours
Unit rate  a type of rate where one quantity is 1. Examples: 3 steps per second, 30 miles/hr, 20 students/class.
RATE TABLES
UNIT RATE  per 1
Scale  the consistent value you count by on a number line or axis (what space between each mark is worth)
Coordinate graph  a graph that examines the relationship between two variables. The independent variables goes on the xaxis while the dependent variables goes on the yaxis. Each axis needs a consistent scale, but the scale does not need to be the same on the two axes. Points are placed at the intersection of values for the two variables. Points are connected for continuous data (where there is data between points).
VARIABLE – a quantity (number) that can change.
Examples
Nonexamples
# of people
A person’s hair color
# of dogs
5 dogs
The length of a pencil
A pencil
Height (in)
How cute you are
The length of different tables at school
The length of a table in math class
C = cost ($)
$2.50
Independent Variable (IV) – the variable that is in “control”. The one you need first in a situation.
Dependent Variable (DV) – the variable that depends on the other.
EXAMPLES:
The Phoenix Team is charging $5 per person to get into the dance. The more students who come (IV), the more money (DV) they make. [$5$]per person is a unit rate].
The time it takes you to run the mile in PE (DV) depends on the speed at which you run (IV).
The length of your hair (DV) depends on the time between hair cuts (IV).
Here are some strategies shared when asked to find the time it would take to walk 90m, based on average time to walk 25 m.
Coordinate Graphing
Proportion
A way to scale a ratio or rate up or down in a proportional situation (equal rates, ratios, or fractions)
Example:
Strategies for solving for scaled part when given a parttopart ratio
Strategies for finding scaled parts when given a scaled total and a parttopart ratio
Strategies for finding scaled parts when given a scaled total and a parttopart ratio (rounding needed)
Strategies for finding a percent from a parttopart ratio
UNIT RATE IN TABLES, GRAPHS AND EQUATIONS
STUDENTS HAVE A DEFINITION AND EXAMPLES FOR UNIT RATE WHEN PROPORTIONAL IN THE VOCABULARY SECTION OF THEIR BINDERS.
MODELS FOR TELLING IF A TABLE SHOWS A PROPORTIONAL RELATIONSHIP
CONSTANT OF PROPORTIONALITY  the unit rate in a proportional relationship.
If a graph is linear, but does not go through (0,0), then there is a unit rate, but not a constant of proportionality since there is no proportional relationship.