Grade 1 · Fractions · MAT-01-FRAC-002
Partition Shapes into Fourths
Partition shapes into four equal shares.
Learning objectives
What you should be able to do
- Partition shapes into four equal shares.
- Recognize one fourth as one of four equal shares.
- Explain the relationship between halves and fourths using the same whole.
Prerequisite check
Make sure the foundation is ready.
Checks equal-share understanding before extending to four shares.
Learn
Build the idea from meaning, not memorization.
Fourths come from four equal shares
When one whole is divided into exactly four shares of equal size, each share is one fourth. The equality rule is just as important as it was for halves.
A half can be split into two fourths
Start with a whole divided into two equal halves. If each half is divided into two equal pieces, there are four equal shares total. Each new piece is one fourth, and two fourths together cover one half.
Fourth does not mean simply 'the fourth piece'
A piece is one fourth only when the whole has been partitioned into four equal shares. The order in which the pieces are pointed to does not create fraction meaning.
Many shapes can show fourths
Squares, circles, rectangles, strips, and other shapes can all be partitioned into four equal shares. The partition can look different as long as all four shares are equal in size.
Interactive math lab
Change it. See what stays true.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- split halves again
- shade fourths
- compare half vs fourth
- detect unequal fourths
Worked examples
Twenty different ways to see the concept work.
Divide a square with one vertical and one horizontal midline.
4 equal squaresEach is one fourth.
Divide a rectangle into four equal vertical strips.
4 equal rectanglesEach strip is one fourth.
Divide a circle with two perpendicular diameters.
4 equal sectorsEach sector is one fourth.
A square is split into 4 pieces, but one piece is larger. Are they fourths?
NoAll four shares must be equal.
A rectangle is split into 4 equal horizontal strips.
Each is one fourthThe direction of the strips does not matter.
One half of a rectangle is divided into two equal parts, and the other half is too.
4 fourthsEach half contains two fourths.
How many fourths cover one half?
2Two of four equal shares make half the whole.
How many fourths make a whole?
4All four equal shares compose the whole.
Shade one fourth of a square divided into four equal cells.
Shade 1 of 4 cellsOne equal share out of four is one fourth.
Shade two fourths.
Shade 2 of 4 equal cellsTwo fourths cover half the whole.
Three of four equal sections are shaded. Is each section still one fourth?
YesFraction name depends on the partition, not how many are shaded.
A pizza is cut into 4 equal slices.
Each slice is one fourthFour equal shares.
A pizza is cut into 4 unequal slices.
No slice should automatically be called one fourthThe shares are not equal.
A strip is 12 equal units long and split into parts of 3 units.
4 equal groups of 3Each part is one fourth of 12 units.
A strip is 12 units and split 2,3,3,4.
Not fourthsThe four shares are unequal.
Compare one half and one fourth of the same whole.
One half is largerThe same whole is split into fewer equal pieces for halves.
Put two one-fourth pieces together.
They make one halfTwo fourths equal half the same whole.
Put four one-fourth pieces together.
They make one wholeAll four shares reconstruct the whole.
Can four triangles be fourths of a square?
Yes, if they are equal in areaShape type does not prevent equal sharing.
Explain why four equal shares are smaller than two equal shares of the same whole.
The same whole is divided among more equal partsMore equal shares means each share is smaller.
Practice
Guided practice with hints
01Partition a rectangle into four equal shares.
Hint: You can make four equal strips or split halves again.
Answer: Any valid four-equal-share partition.
02How many fourths make a whole?
Hint: Count all equal shares in a fourths partition.
Answer: 4
03How many fourths make one half?
Hint: Compare 2 of 4 shares with half the shape.
Answer: 2
04Are four unequal pieces fourths?
Hint: Check the word equal.
Answer: No
05Which is larger in the same whole: one half or one fourth?
Hint: Compare two equal shares with four equal shares.
Answer: One half
06What must stay true in every correct fourths partition?
Hint: Think about share sizes.
Answer: All four shares must be equal.
Practice
Independent practice
01Partition a square into fourths.
Answer: Any 4 equal shares.
02How many fourths make a whole?
Answer: 4
03How many fourths make one half?
Answer: 2
04Can unequal shares be fourths?
Answer: No
05Shade one fourth of a four-part equal model.
Answer: 1 equal share shaded.
06Shade two fourths.
Answer: 2 of 4 equal shares shaded.
07Which is smaller in the same whole: one half or one fourth?
Answer: One fourth
08If all four fourths are joined, what results?
Answer: One whole
Common mistakes
Learn to catch the error, not just the answer.
Verify the four shares are equal in size.
The denominator-like language counts equal shares; more shares make each individual share smaller.
Any whole can show fourths if it is divided into four equal shares.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Divide a paper snack mat into four equal regions for four equal portions.
- Fold a sheet in half, then fold it in half again to create four equal shares.
Challenge problems
Find two different ways to partition a rectangle into fourths.
For example, four strips or a 2-by-2 grid.
Why are two fourths the same amount as one half of the same whole?
Both cover two of four equal shares, which is half the total area.
Can four equal pieces of different orientations still be fourths?
Yes, if each has equal area.
Explain why one fourth becomes smaller if the whole stays fixed and is split into more pieces than halves.
The same total is distributed among more equal shares.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Fourth Builder
Create or identify models with exactly four equal shares.
Practice
Mastery check
01Define one fourth.
Answer: One of four equal shares of a whole.
02How many fourths make one whole?
Answer: 4
03How many fourths make one half?
Answer: 2
04Are four unequal parts fourths?
Answer: No
05Which is larger in the same whole, one half or one fourth?
Answer: One half
06Can a circle be partitioned into fourths?
Answer: Yes
07Why does splitting each half in two create fourths?
Answer: It creates four equal shares total.
08Describe one correct fourths partition for a rectangle.
Answer: Any partition into four equal regions.
Terminology
Words to know
- fourth
- One of four equal shares of a whole.
- quarter
- Another name for one fourth.
- equal shares
- Parts that are the same size.
- partition
- Divide a whole into parts.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 1 Geometry (1.G.A.3)
Fourth/quarter equal-share progression.