Introduction to Fractions
Your child discovers that a whole can be cut into equal parts, and that each family of parts has its own name: halves, thirds, fourths, on up to tenths. The fraction circles make this concrete — every piece is a real, holdable part of the same red circle.
Materials
- Fraction circles: ten red circles in green square frames — one whole, then circles cut into 2 through 10 equal pieces (sold as "fraction metal insets"; the virtual material below works too)
- Household substitute: ten paper plates or traced paper circles, one left whole and the others cut into 2–10 equal wedges — keep each family in its own labeled envelope
- A work mat, tray, or solid-color placemat
- An apple, tortilla, or sandwich and a table knife for the opening moment
- Pencil and paper for writing the first fraction symbols
No materials at home? Use the virtual Fraction Circles.
Before this lesson
Aims
Direct
- Understand that a fraction is one or more equal parts of a whole
- Learn the family names: half, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth
- Connect a quantity of pieces to its written symbol, e.g. one fifth to 1/5
Indirect
- Prepare for fraction equivalence and the four operations with fractions
- Plant the idea that the bottom number names the family and the top number counts the pieces
- Prepare for decimal fractions — tenths return later on the decimal board
Presentation
- 1 Start at the table with something real. Cut an apple (or tortilla) into two pieces as equal as you can manage, and hold the halves together to remake the whole.I cut it into two equal pieces. Each piece is one half. Two halves make the whole.
- 2 Move to the mat with the fraction circles. Point to the uncut circle first and trace it with a finger.This circle is one whole.
- 3 Lift one piece out of the halves circle and set it on the mat. Let your child hold it and fit it back before lifting it out again.This circle is cut into two equal pieces. This piece is one half.
- 4 Do the same with the thirds and fourths circles: lift one piece, name it, and let your child fit it back into its frame.Three equal pieces — this is one third. Four equal pieces — this is one fourth.
- 5 Give a three-period lesson with the three pieces on the mat: name them, ask your child to hand you each one, then point and ask what each is called.Show me one third. … Now, what is this one called?
- 6 Set one half beside one tenth and let your child compare them in their hands. Count the tenths in their frame together, touching each piece.The more pieces we cut, the smaller each piece is.
- 7 When the names are comfortable — today or another day — write 1/2 on paper. Point to the bottom number, then the top number, then match the symbol to the real piece.The bottom number tells how the whole was cut: into two pieces. The top number counts how many pieces we have: one. One half.
- 8 Show your child how to return every piece to its frame and check that each circle is complete before putting the work away.Every family fills its own circle exactly.
Points of interest
- Lifting the smooth red pieces out of their frames and fitting them back perfectly
- How slim a tenth is next to the big, heavy-looking half
- The family names sound like counting words: third, fourth, fifth, sixth…
- A cut-up circle can always be rebuilt into a whole again
Control of error
- Each piece fits only its own frame exactly — a wrong piece leaves a gap or overlaps the others
- Counting the pieces in any frame confirms its family name (the fifths circle has exactly five pieces)
- The rebuilt apple (or paper circle) visibly succeeds or fails at being whole
Vocabulary
- whole
- half, halves
- third, fourth (also called a quarter), fifth, sixth, seventh, eighth, ninth, tenth
- fraction
- equal parts
Variations
- A feeling game: with eyes closed, your child finds the half — or the tenth — from three paper-plate wedges by touch alone
- A fraction hunt at mealtime: name the fractions you see when pizza, oranges, or sandwiches are divided
- Name a piece and have your child fetch it from across the room, keeping the name in mind as they walk
Extensions
- Trace the whole circle on paper, then trace a single piece inside it and color it red
- Lay out one piece from every family in a row, biggest to smallest, and read the names down the line
- Label paper-plate wedges with their symbols (1/2, 1/3, 1/4…) and shuffle them for a matching game
Follow-up work (pencil & paper)
- Print a fractions page at the naming level: your child looks at each pictured piece, says its name aloud, and writes the fraction symbol underneath in pencil.Printable: Fractions
- Fold paper circles into halves and fourths, cut along the folds, color one piece of each, and write its symbol on the piece — a scissors-and-crayon version of today’s lesson.
- Draw three "pizzas" on paper. Divide one into halves, one into thirds, one into fourths, shade one slice of each, and label the shaded slice with its fraction.
What comes next
When your child names the pieces easily and reads simple symbols like 1/4, move on to Fraction Equivalence, where they discover that two fourths make exactly one half. Much later, the tenths from this box return in the Introduction to the Decimal Board.
Next in this strand: Fraction Equivalence