Intro to Ratios

What is a ratio? Shows the relative sizes between two or more values Behaves and can be manipulated like a fraction

Ratios can be written in different ways All ratios can be written: With a colon (e.g. “2:3”) In words (e.g. “2 to 3”) Part-to-whole ratios can also be written as: Fraction (remember: parts of a whole) Decimal Percent

Types of ratios Part-to-part ratio Part-to-whole ratio Two-term ratio Three-term ratio

Part-to-part Ratio Compares different parts of a group to each other E.g. 4:6 gives the ratio of white marbles to black marbles What is the ratio of black marbles to blue marbles in two different ways?

Part-to-whole Ratio Compares one part of a group to the whole group E.g. 4:12 gives ratio of white marbles to total marbles What is the ratio of blue marbles to total marbles in two different ways?

Ratios can be written in different ways All ratios can be written: With a colon (e.g. “2:3”) In words (e.g. “2 to 3”) Part-to-whole ratios can also be written as: Fraction (remember: parts of a whole) Decimal Percent

Two-term Ratio Compares two quantities measured in the same units Written as “a:b” or “a to b” Is a part-to-part ratio or part-to-whole ratio* E.g. 4:2 gives white to blue marbles E.g. 4:12 gives white to total marbles *Textbook says only part-to-part. Could be part-to-whole as well

Three-term Ratio Compares three quantities measured in the same units Written as a:b:c or a to b to c Is a part-to-part-to-part ratio E.g. 4:6:2 gives white to black to blue marbles E.g. 4:2:6 gives white to blue to black marbles 

Ratio in Lowest Terms A simplified ratio whose terms have no common factor E.g. 2:8 can be reduced to 1:4 by dividing each term by 2 (just like a fraction!) E.g. 4:6:2 can be reduced to 2:3:1 by dividing each term by 2

Are ratios and fractions the same? Similarities Differences Ratios can be converted into fractions  and manipulated the same way E.g. reduce, make equivalent fractions/ratios Fractions are only used to describe part to whole relationships Ratios can be used to describe almost any relationship (part to part or part to whole) No fraction equivalent for three-term ratios

Are ratios and fractions the same? Important: Because ratios are more flexible, it is very important to specify what your ratio represents. “4:6” is meaningless. Need to say what it refers to… “4:6 is the ratio of white marbles to black marbles”

Ratio practice activity Take a (smallish) handful of integer counters. Using the coloured counters you have, write 2 examples of each of the vocabulary words: Ratio Part-to-part ratio Part-to-whole ratio Two-term ratio Three-term ratio Four-term ratio*

Drawing Activity Ratio of height of pink part to height of lid is 4:1 (part to part) Ratio of width of pink part to width of pink part is 1:2 (part to part) Ratio of width of pink part to total height of water bottle is 1:2.5 (part to whole)

Drawing Activity Part 1: Find a partner Select an object in the classroom. Without tracing or using a ruler, estimate at least 3 different ratio relationships between different parts of the object. Use the ratios to draw the object to scale (with correct proportions). Part 2: (time-permitting) Find a different pair of partners. Without showing them the object, describe it using ratios and have them try to draw it based on your description.