Fractions: What’s the Big Idea(s)? By Ian Herr CD (with a “little help” from Dr. Marian Small, PhD.)

Fractions: the Big Idea(s) Understanding of fractions is based on a few simple ideas: Fractions can represent part of a set or group Fractions can represent parts of a region or area Fractions can represent measure of volume, capacity, mass, etc. Fractions can represent division (÷), or dividing into smaller parts Fractions can represent a ratio of parts to the whole Fractions can have more than one name A fraction has a numerator and a denominator. Each has a particular meaning The equal parts that the whole is divided into are equal in amount, but don't have to be identical Fractions parts do not need to be adjacent (side-by-side) If the numerator and denominator of a fraction are equal, it represents one whole something Fractions with numerators greater than their denominators represent an amount greater than 1 whole You have to know what the whole is to know what the fraction is

Fractions can represent part of a set or group Fractions tell you how many parts of a larger group are counted 𝟑 𝟏𝟏 𝒂𝒓𝒆 𝒔𝒐𝒄𝒄𝒆𝒓 𝒃𝒂𝒍𝒍𝒔 𝟒 𝟓 𝒊𝒔 𝒔𝒉𝒂𝒅𝒆𝒅 𝒃𝒍𝒖𝒆

Fractions can represent parts of a region or area Fractions can tell you how much of a region or area is shaded, used, counted, etc. Outer area = 10m x 6m = 60 m2 Yellow area = 4m x 4m = 16 m2 Yellow area fraction =   Reduces to of the region is yellow 6 m 10 m 4 m 𝟏𝟔 𝟔𝟎 𝟒 𝟏𝟓 𝟒 𝟏𝟓

Fractions can represent measure of volume, capacity, mass, etc. 𝟑 𝟏𝟐 𝒘𝒂𝒔 𝒆𝒂𝒕𝒆𝒏 𝟏 𝟑 𝟒 𝒄𝒖𝒑 𝒐𝒇 𝒎𝒊𝒍𝒌 𝟑 𝟓 𝒐𝒇 𝒂 𝒌𝒊𝒍𝒐𝒈𝒓𝒂𝒎

Fractions can represent division, or dividing into smaller parts Imagine 7 cookies being divided equally between 3 friends. 7 ÷ 3 = 𝟕 𝟑 , or 𝟐 𝟏 𝟑 Each friend gets = 𝟕 𝟑 , or 𝟐 𝟏 𝟑 cookies

Fractions can represent ratios of parts to the whole Ratios are comparisons of different amounts of similar things The set of hexagons is 𝟐 𝟓 red The ratio of red hexagons to all hexagons is 2:5

Fractions can have more than one name Different fractions can show the same amount, but have more than one way to express it 𝟏 𝟒 of the grid is red when you count by rows of squares 𝟐 𝟖 of the grid is red when you count by groups of 3 squares 𝟑 𝟏𝟐 of the grid is red when you count by pairs of squares 𝟏 𝟒 , 𝟐 𝟖 , and 𝟑 𝟏𝟐 are the same amount

A fraction has a numerator and a denominator A fraction has a numerator and a denominator. Each has a particular meaning The denominator tells you how many parts the whole has been divided into The numerator tells you how many of the parts you should count 𝟒 𝟓 of the circle is green

Parts that the whole is divided into are equal in amount, but don’t have to look identical The yellow and green sectors are equal, but not identical You can now see how both the yellow and green sectors are made up of two smaller, identical rights triangles 𝟑 𝟓 of the shapes are red

Fraction parts don’t need to be adjacent (side-by-side) The rectangle is 𝟐 𝟖 yellow, even though the yellow parts are not touching each other The rectangle is 𝟐 𝟖 blue, even though the blue parts are not adjacent to each other

If the numerator and denominator are the same number, then the fraction equals one whole 𝟖 𝟖 green ► the whole circle is green 𝟏𝟎 𝟏𝟎 blue ► the whole pentagon is blue

Fractions with numerators greater than the denominators are worth more than one (1) The pentagons are divided into fifths, so altogether there are 𝟏𝟐 𝟓 shaded in red That’s the same as 𝟐 𝟐 𝟓 shaded red

You have to know what the whole is before you can know what the fraction is ◄ You can’t know what fraction this represents, until you know how many parts make up the whole ◄ Now you can see the whole was divided into seven parts, and two are shaded blue. So it’s showing the fraction 𝟐 𝟕

A day without fractions is only half the fun THANKS FOR WATCHING