Word Problems — Part 1
4A · Chapter 8 · Lesson 7 · MATH-4A-C08-L07
Learning goal. Draw single-stage fraction-of-set bars for contextual quantities.
Before you begin
Recall: 4A Ch6/7: equal partitions, mixed numbers and fraction operations; Multiplying a Whole Number by a Fraction — Part 2. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Find 2/3 of a set of 9 objects.
Show answer & reasoning
Divide into 3 equal groups of 3, then choose 2 groups for 6 objects.
Find 1/3 of a set of 12 objects.
Show answer & reasoning
Divide into 3 equal groups of 4, then choose 1 groups for 4 objects.
Find 1/5 of a set of 30 objects.
Show answer & reasoning
Divide into 5 equal groups of 6, then choose 1 groups for 6 objects.
Key vocabulary
- unit fraction
- fraction with numerator one
- fraction of a set
- part of a discrete collection
- reference whole
- quantity to which a fraction applies
- remaining amount
- quantity after some part is removed
Understand the concept
In a one-stage fraction story, first label the original whole. If a library lends 3/8 of its 40 books, the lent amount is 15 and the remaining amount is 25. A bar divided into eight equal units shows which part is selected and which is left.
Model it: labeled fraction-of-set comparison bar. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
A teacher has 32 cards. She gives 3/4 of them away. How many cards remain?
3/4 of 32 is 24; subtract from the original 32.
Check your understanding 1
A teacher has 32 cards. She gives 5/8 of them away. How many cards remain?
Show answer & reasoning
5/8 of 32 is 20; subtract from the original 32.
Worked example 2
A teacher has 45 cards. She gives 2/5 of them away. How many cards remain?
2/5 of 45 is 18; subtract from the original 45.
Check your understanding 2
A teacher has 30 cards. She gives 1/5 of them away. How many cards remain?
Show answer & reasoning
1/5 of 30 is 6; subtract from the original 30.
Worked example 3
A teacher has 32 cards. She gives 1/8 of them away. How many cards remain?
1/8 of 32 is 4; subtract from the original 32.
Check your understanding 3
A teacher has 30 cards. She gives 5/6 of them away. How many cards remain?
Show answer & reasoning
5/6 of 30 is 25; subtract from the original 30.
Guided practice
A teacher has 27 cards. She gives 1/3 of them away. How many cards remain?
Show answer & reasoning
1/3 of 27 is 9; subtract from the original 27.
A teacher has 28 cards. She gives 3/4 of them away. How many cards remain?
Show answer & reasoning
3/4 of 28 is 21; subtract from the original 28.
A teacher has 18 cards. She gives 3/6 of them away. How many cards remain?
Show answer & reasoning
3/6 of 18 is 9; subtract from the original 18.
A teacher has 20 cards. She gives 3/4 of them away. How many cards remain?
Show answer & reasoning
3/4 of 20 is 15; subtract from the original 20.
A teacher has 72 cards. She gives 6/8 of them away. How many cards remain?
Show answer & reasoning
6/8 of 72 is 54; subtract from the original 72.
Independent practice
A teacher has 8 cards. She gives 1/2 of them away. How many cards remain?
Show answer & reasoning
1/2 of 8 is 4; subtract from the original 8.
A teacher has 12 cards. She gives 2/4 of them away. How many cards remain?
Show answer & reasoning
2/4 of 12 is 6; subtract from the original 12.
A teacher has 10 cards. She gives 1/2 of them away. How many cards remain?
Show answer & reasoning
1/2 of 10 is 5; subtract from the original 10.
A teacher has 64 cards. She gives 2/8 of them away. How many cards remain?
Show answer & reasoning
2/8 of 64 is 16; subtract from the original 64.
A teacher has 24 cards. She gives 1/8 of them away. How many cards remain?
Show answer & reasoning
1/8 of 24 is 3; subtract from the original 24.
A teacher has 60 cards. She gives 4/10 of them away. How many cards remain?
Show answer & reasoning
4/10 of 60 is 24; subtract from the original 60.
A teacher has 24 cards. She gives 4/6 of them away. How many cards remain?
Show answer & reasoning
4/6 of 24 is 16; subtract from the original 24.
A teacher has 40 cards. She gives 2/10 of them away. How many cards remain?
Show answer & reasoning
2/10 of 40 is 8; subtract from the original 40.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A classroom has 40 cards and gives three-eighths away. How many cards remain?
Show answer & reasoning
Three-eighths of forty is fifteen, and forty minus fifteen is twenty-five.
A teacher has 48 cards. She gives 1/6 of them away. How many cards remain?
Show answer & reasoning
1/6 of 48 is 8; subtract from the original 48.
Exit check
A teacher has 10 cards. She gives 2/5 of them away. How many cards remain?
Show answer & reasoning
2/5 of 10 is 4; subtract from the original 10.
A teacher has 12 cards. She gives 1/2 of them away. How many cards remain?
Show answer & reasoning
1/2 of 12 is 6; subtract from the original 12.
A teacher has 15 cards. She gives 2/3 of them away. How many cards remain?
Show answer & reasoning
2/3 of 15 is 10; subtract from the original 15.