Math // Fractions

Halves & Quarters of Shapes

Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters

Ages
6 to 7
Type
Concept
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

If you give the learner a round pizza or a rectangular chocolate bar, can they divide it into four equal pieces and tell you each piece is called a quarter or a fourth?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Divide a circle into two equal halves
  • Divide a rectangle into four equal quarters
  • Describe the whole as 'two halves' or 'four quarters'

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • What Is a Half?Required

    Fractions // Ages 5 to 6

    Partitioning shapes into halves extends from Y1 understanding of halves

  • Finding halves and quarters (age 5+)Required

    Fractions // Ages 5 to 6

    Partitioning into fourths/quarters extends from Y1 understanding of quarters

You are here

Halves & Quarters of Shapes

Ages 6 to 7 // Concept

Leads to

2 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children partition continuous shapes (circles, rectangles) into two and four EQUAL parts, name them halves and quarters, and describe the whole as 'two halves' or 'four quarters'. The core ideas are equality of parts (equal in size, not necessarily the same shape), the part-whole relationship (equal parts recompose the whole), and that a shape can be partitioned validly in more than one way as long as the parts are equal.

Common misconceptions

  • Accepting unequal parts as halves/quarters because the number of pieces is right
  • Thinking a shape can only be partitioned one 'correct' way (rejecting valid alternative cuts)
  • Confusing the number of CUTS with the number of PARTS
  • Not seeing the whole as composed of its equal parts (cannot say two halves/four quarters make the whole)

Useful representations

  • Circles partitioned into 2 and 4 equal sectors
  • Rectangles partitioned into 2 and 4 equal parts (different orientations)
  • Overlay/rotation to check parts are equal
  • Parts reassembling into the whole shape

Teaching practices

  • Partition by folding and cutting so equality is physical; verify by overlaying parts
  • Show more than one correct way to halve/quarter the same shape (e.g. a rectangle split vertically or horizontally) so 'halves' is not tied to one cut
  • Always recompose: 'two halves make the whole', 'four quarters make the whole'
  • Count the resulting PARTS (regions), not the cuts
  • Name as you go and have children label their partitions

Activities to try

  1. 1

    Cut it, check it, rebuild it

    Why it works: Halves are two equal parts and quarters are four equal parts; the equal parts together rebuild the whole, and the same shape can be halved or quartered in more than one correct way provided the parts are equal in size.

    1. Take a paper circle and a paper rectangle and fold or draw a line to make two parts.
    2. Overlay or rotate the two parts on top of each other to check they match exactly (equal).
    3. On fresh copies of the same rectangle, make two halves a DIFFERENT way (e.g. vertically, then horizontally, then a single diagonal through opposite corners) and check equality again. For the diagonal, cut along it and turn one triangle half a turn to lay it on the other, because folding a non-square rectangle along its diagonal will not make the halves line up.
    4. Now partition a circle and a rectangle into four equal parts (e.g. the rectangle as four equal strips or a 2x2 grid) and check all four match.
    5. Slide or stick the parts back together to rebuild the whole, saying aloud 'two halves make the whole' and 'four quarters make the whole'.
  2. 2

    Halves, quarters, or neither?

    Why it works: Deciding whether a partition shows halves or quarters depends on whether the parts are equal in size, not on the number of pieces or on a familiar orientation.

    1. Sort a set of partitioned shapes into three groups: 'halves', 'quarters', and 'neither'.
    2. Include a shape split into two UNEQUAL parts (right number of pieces, wrong equality) to place in 'neither'.
    3. Include a non-standard but valid cut (e.g. a diagonally-halved rectangle or a circle halved by a slanted line through its centre) to place in 'halves'.
    4. For each decision, explain how you know, e.g. 'the parts are equal' or 'the parts are not the same size'.
  3. 3

    Diagnostic: unequal pieces with the right count

    Why it works: Having the right NUMBER of pieces is not enough; halves and quarters must be EQUAL parts, which together recompose the whole, and there can be more than one valid partition.

    1. Look at a circle divided by an off-centre line into two clearly unequal parts, and a rectangle divided into four parts where three are small and one is large.
    2. Answer: 'Is the circle cut into two halves? Is the rectangle cut into four quarters? How do you know?'
    3. Then answer: 'If you put the parts of the rectangle back together, what do they make? Is there more than one way to cut the circle into two halves?'

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.G.3

Math // Fractions

More in Fractions

All 67 topics