Grade 2 · Fractions · MAT-02-FRAC-002
Name Unit Fractions from Visual Models
Identify one half, one third, and one fourth in visual models.
Learning objectives
What you should be able to do
- Identify one half, one third, and one fourth in visual models.
- Connect unit-fraction names to number of equal parts in the whole.
- Explain why a unit fraction represents one equal share.
Prerequisite check
Make sure the foundation is ready.
Checks equal partition concept.
Learn
Build the idea from meaning, not memorization.
A unit fraction names one equal share
At this grade, one half, one third, and one fourth are verbal unit fractions: each represents exactly one equal share from a whole partitioned into2,3,or4 equal parts.
The denominator-like word tells total equal shares
The word third signals three equal shares in the whole; fourth signals four. The 'one' tells us we are considering one of those shares.
Visual models must show equal parts
One shaded region out of three unequal pieces is not one third. The model must first be a valid equal partition.
Orientation and shading position do not matter
Any one of equal thirds represents one third, whether left,middle,right,top,or rotated.
Interactive math lab
Change it. See what stays true.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- select share
- name share
- validate equality
- rotate model
Worked examples
Twenty different ways to see the concept work.
1 of2 equal shaded.
one halfOne share of2.
1 of3 equal.
one thirdOne of3.
1 of4 equal.
one fourthOne of4.
Different half region selected.
still one halfAny equal share.
Middle third shaded.
one thirdPosition irrelevant.
Bottom fourth shaded.
one fourthPosition irrelevant.
1 of3 unequal pieces shaded.
not valid one thirdPartition invalid.
1 of4 unequal.
not valid fourthEquality required.
No shading but point to one of3 equal regions.
one thirdSelection can replace shading.
Whole split2, choose either.
one halfTwo equal shares.
How many unit thirds in whole?
3Three shares.
How many unit fourths?
4Four shares.
How many halves?
2Two shares.
Compare one half vs one fourth same whole.
half largerShare-size relation.
Rotate model.
unit name unchangedPartition unchanged.
Large whole third vs small whole third.
both one third, physical sizes may differName is relationship.
One equal share of4 called?
one fourth/quarterName.
One equal share of3 called?
one thirdName.
One equal share of2 called?
one halfName.
Why 'unit' fraction?
It refers to one equal shareOne part as unit.
Practice
Guided practice with hints
011 of3 equal shaded.
Hint: Count total equal parts.
Answer: one third
021 of4.
Hint: one fourth
Answer:
031 of2.
Hint: one half
Answer:
04Unequal3 parts.
Hint: Valid?
Answer: No
05Does position matter?
Hint: Equal shares interchangeable.
Answer: No
06How many one-fourths form whole?
Hint: 4.
Answer: 4
Practice
Independent practice
011 of2
Answer: one half
021 of3
Answer: one third
031 of4
Answer: one fourth
04Unequal fourth model valid?
Answer: No
053 unit thirds whole?
Answer: Yes
064 unit fourths whole?
Answer: Yes
07Rotate changes name?
Answer: No
08Unit fraction means
Answer: one equal share of whole
Common mistakes
Learn to catch the error, not just the answer.
Validate equal shares first.
Any equal share has same unit-fraction name.
Fraction name alone does not fix absolute size.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Label equal food portions.
- Identify single equal shares in diagrams/maps.
Challenge problems
If whole has4 equal regions, can each be called one fourth?
Yes
Why one third not always same physical size?
Wholes may differ.
Can one region be both one half and one fourth of same whole?
Not if whole partition/reference is fixed in usual equal-share model.
Why unit fraction useful?
It provides a repeatable equal-share building block.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Name That Share
Identify unit fractions from varied valid/invalid models.
Practice
Mastery check
011 of3 equal
Answer: one third
021 of4 equal
Answer: one fourth
031 of2 equal
Answer: one half
04Unequal3-part model one third?
Answer: No
05How many one-thirds whole
Answer: 3
06Position matter
Answer: No
07What unit means
Answer: one equal share
08Whole size effect
Answer: Physical share size can vary.
Terminology
Words to know
- unit fraction
- A fraction representing one equal share of a whole.
- one third
- One of3 equal shares.
- one fourth
- One of4 equal shares.
- model
- A representation used to show mathematical relationships.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.G.A.3
Describe equal shares using fraction language.