🔢 MathGrade 2Lesson 34
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Fractions — Thirds and Equal Parts of Sets

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Learning Objectives

  • 1Divide a shape into 3 equal parts
  • 2Name each part one third (⅓)
  • 3Identify two thirds (⅔) on a shape divided into 3 equal parts
  • 4Find one third of a set of objects by dividing the total into 3 equal groups
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Mini Lesson

You already know about halves and quarters. Now we are going to learn about thirds — what happens when you split something into 3 equal parts.

One third — ⅓

  • Split a whole into 3 equal parts.
  • Each part is called one third, written ⅓.
  • The bottom number (3) tells you how many equal parts there are.
  • The top number (1) tells you how many parts you are describing.

Two thirds — ⅔

  • If you shade 2 of the 3 equal parts, you have shaded two thirds, written ⅔.
  • ⅔ is greater than ⅓ because 2 parts is more than 1 part out of the same whole.
  • Three thirds (3/3) equals the whole — all parts shaded.

Equal parts of a set

  • Fractions also work with groups of objects, not just shapes.
  • To find one third of a set, divide the total into 3 equal groups and count one group.
  • Example: ⅓ of 9 stars = 9 ÷ 3 = 3 stars in each group.
  • Example: ⅓ of 12 apples = 12 ÷ 3 = 4 apples in each group.
Shape divided into thirds showing one third, two thirds, and three thirdsThree rectangles side by side. The first shows 1 of 3 parts shaded in blue labeled one third. The second shows 2 of 3 parts shaded in orange labeled two thirds. The third shows all 3 parts shaded in green labeled three thirds equals whole.Thirds of a Shapeshaded⅓one thirdshadedshaded⅔two thirds3/3= whole
Three panels: 1 of 3 parts shaded (⅓ blue), 2 of 3 parts shaded (⅔ orange), all 3 parts shaded (3/3 whole, green).
Equal parts of a set — one third of nine starsNine stars arranged in three groups of three. The first group is highlighted in blue as one third, 3 stars. Below the equation 9 divided by 3 equals 3. A note says to find one third of a set, divide by 3.Equal Parts of a Set9 stars ÷ 3 equal groups = 3 in each⅓ → 3 stars3 stars3 stars9 ÷ 3 = 3⅓ of 9 = 3To find ⅓ of a set: divide the total by 3.⅓ of 12 = 12 ÷ 3 = 4 • ⅓ of 6 = 6 ÷ 3 = 2
Nine stars split into 3 equal groups of 3. One group is highlighted as ⅓, and the equation 9 ÷ 3 = 3 shows how to find a third of a set.
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Ask yourself: "Are the parts equal? How many parts in total? How many am I describing?"

Vocabulary
Third
One of three equal parts of a whole, written 1/3e.g. A third of the cake is one of three equal slices.
Two thirds
Two of three equal parts, written 2/3e.g. I shaded two thirds of the rectangle.
Whole
All of something before it is splite.g. Three thirds make one whole.
Equal parts
Pieces that are all the same sizee.g. A fraction needs equal parts.
Set
A group of objects, like 9 starse.g. A third of a set of 9 stars is 3 stars.
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