3B · Chapter 9 · Lesson 1
Fractions of a Whole
Partition one whole into equal parts and identify unit and nonunit fractions.
Today's mathematical question
A same-sized whole is split into 4 equal parts and 2 parts are shaded. What fraction is shaded?
Learning target
Partition one whole into equal parts and identify unit and nonunit fractions.
Before starting: Grade 3A: equal sharing and equal-sized parts. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
Four equal trays share 20 counters. How many per tray?
Reveal explanation
Answer: 5
There are four equal groups; place one counter into each tray repeatedly until all 20 are used. Each tray receives five counters, since 4 × 5 = 20.
- P2
If a whole is split into six equal parts, how many parts form the whole?
Reveal explanation
Answer: 6
The denominator tells all equal pieces.
- P3
Can two unequal pieces be called halves of the same whole?
Reveal explanation
Answer: No
A half must be one of two equal-sized parts.
Learn and understand
A fraction describes part of a specified whole that has been split into equal parts. The denominator tells how many equal pieces make one whole; the numerator counts the chosen pieces. A larger picture does not necessarily represent a larger fraction unless both pictures represent the same-sized whole. If a pizza is cut into four equal slices, one slice is one fourth. Four unequal slices do not each represent one fourth. Always identify the whole before naming a fraction.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Divide one rectangle into equal cells. Shade the number indicated by the numerator and count all equal parts for the denominator.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- whole
- the complete reference quantity
- numerator
- number of parts chosen
- denominator
- number of equal parts in one whole
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A same-sized whole is split into 4 equal parts and 2 parts are shaded. What fraction is shaded?
- Identify the whole, the units, and what the question asks.
- The denominator counts all 4 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 1/2.
- Check that the answer uses the right units and makes sense.
Answer: 1/2
Check your understanding 1
A same-sized whole is split into 3 equal parts and 1 part is shaded. What fraction is shaded?
Reveal answer and explanation
1/3 — The denominator counts all 3 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/3.
Worked example 2
Explore, calculate, verify
A same-sized whole is split into 12 equal parts and 6 parts are shaded. What fraction is shaded?
- Identify the whole, the units, and what the question asks.
- The denominator counts all 12 equal parts; the numerator counts the 6 shaded parts. In simplest form this is 1/2.
- Check that the answer uses the right units and makes sense.
Answer: 1/2
Check your understanding 2
A same-sized whole is split into 5 equal parts and 2 parts are shaded. What fraction is shaded?
Reveal answer and explanation
2/5 — The denominator counts all 5 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 2/5.
Worked example 3
Explore, calculate, verify
A same-sized whole is split into 8 equal parts and 1 part is shaded. What fraction is shaded?
- Identify the whole, the units, and what the question asks.
- The denominator counts all 8 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/8.
- Check that the answer uses the right units and makes sense.
Answer: 1/8
Check your understanding 3
A same-sized whole is split into 12 equal parts and 10 parts are shaded. What fraction is shaded?
Reveal answer and explanation
5/6 — The denominator counts all 12 equal parts; the numerator counts the 10 shaded parts. In simplest form this is 5/6.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
A same-sized whole is split into 5 equal parts and 3 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 3/5
The denominator counts all 5 equal parts; the numerator counts the 3 shaded parts. In simplest form this is 3/5.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G2
A same-sized whole is split into 8 equal parts and 3 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 3/8
The denominator counts all 8 equal parts; the numerator counts the 3 shaded parts. In simplest form this is 3/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G3
A same-sized whole is split into 10 equal parts and 4 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 2/5
The denominator counts all 10 equal parts; the numerator counts the 4 shaded parts. In simplest form this is 2/5.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G4
A same-sized whole is split into 12 equal parts and 2 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 1/6
The denominator counts all 12 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 1/6.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G5
A same-sized whole is split into 10 equal parts and 9 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 9/10
The denominator counts all 10 equal parts; the numerator counts the 9 shaded parts. In simplest form this is 9/10.
Each full bar represents the same-sized whole; shaded parts show the fraction.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A same-sized whole is split into 3 equal parts and 2 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 2/3
The denominator counts all 3 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 2/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I2
A same-sized whole is split into 4 equal parts and 3 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 3/4
The denominator counts all 4 equal parts; the numerator counts the 3 shaded parts. In simplest form this is 3/4.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I3
A same-sized whole is split into 12 equal parts and 11 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 11/12
The denominator counts all 12 equal parts; the numerator counts the 11 shaded parts. In simplest form this is 11/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I4
A same-sized whole is split into 4 equal parts and 1 part is shaded. What fraction is shaded?
Reveal explanation
Answer: 1/4
The denominator counts all 4 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/4.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I5
A same-sized whole is split into 8 equal parts and 4 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 1/2
The denominator counts all 8 equal parts; the numerator counts the 4 shaded parts. In simplest form this is 1/2.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I6
A same-sized whole is split into 12 equal parts and 7 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 7/12
The denominator counts all 12 equal parts; the numerator counts the 7 shaded parts. In simplest form this is 7/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I7
A same-sized whole is split into 8 equal parts and 7 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 7/8
The denominator counts all 8 equal parts; the numerator counts the 7 shaded parts. In simplest form this is 7/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I8
A same-sized whole is split into 5 equal parts and 1 part is shaded. What fraction is shaded?
Reveal explanation
Answer: 1/5
The denominator counts all 5 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/5.
Each full bar represents the same-sized whole; shaded parts show the fraction.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A ribbon is split into 7 equal pieces; 5 are colored. Another ribbon is twice as long but also has 5 colored of 7 equal pieces. Are the colored lengths equal?
Reveal explanation
Answer: No
Equal fractions of differently sized wholes need not represent equal physical lengths.
- C2
A rectangle is split into 7 equal parts and 5 are shaded. Explain what the top and bottom numbers of 5/7 tell us.
Reveal explanation
Answer: 5 selected out of 7 equal parts
The denominator gives the number of equal pieces in one whole; the numerator counts selected pieces.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A same-sized whole is split into 6 equal parts and 4 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 2/3
The denominator counts all 6 equal parts; the numerator counts the 4 shaded parts. In simplest form this is 2/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E2
A same-sized whole is split into 8 equal parts and 6 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 3/4
The denominator counts all 8 equal parts; the numerator counts the 6 shaded parts. In simplest form this is 3/4.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E3
A same-sized whole is split into 6 equal parts and 1 part is shaded. What fraction is shaded?
Reveal explanation
Answer: 1/6
The denominator counts all 6 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/6.
Each full bar represents the same-sized whole; shaded parts show the fraction.