Week 5 · Letters for unknowns and the parts of an expression · 3 lessons
1
Using a letter for an unknown amount
Discover Mathematics P6: Term 1, Unit 3, Lessons 1–2
GoalUse a letter for an unknown or changing amount and write simple expressions for situations.
New words
variable · a letter that stands for an amount that is unknown or can changeexpression · a maths phrase with numbers, letters and operations but no = signevaluate · find the value of an expression when the letter has a number
Explanation
In algebra a letter, called a variable, stands for an amount that we do not know yet or that can change. If one pack has 6 pencils, then n packs have 6 × n pencils. We write 6n and leave out the times sign between a number and a letter. If Salma has s LE and Karim has 12 LE more, Karim has s + 12 LE. Such a phrase is an expression. It has no equals sign. When the letter gets a number, the expression gets a value: if n = 3 then 6n = 18. The same letter in one expression always stands for the same number.
Worked examples
n
1
2
3
4
Pencils, 6n
6
12
18
24
n packs of 6 pencils. One pack has 6, two packs have 12, and n packs have 6n pencils. When n = 4, 6n = 24.
b
1
2
5
10
Cost, 3b (LE)
3
6
15
30
A loaf of bread costs 3 LE. Buying b loaves costs 3b LE. For b = 5 the cost is 3 × 5 = 15 LE.
Person
Expression
y = 10
Youssef
y
10
Sister
y + 4
14
Father
3y
30
Youssef is y years old. His sister is 4 years older: y + 4. His father is 3 times as old: 3y. If y = 10, the sister is 14 and the father is 30.
Class activity
Letter stories. Choose a letter, for example m for the number of marbles in a bag. Make up three expressions about the bag, such as m + 5 (five more marbles) or 2m (two bags). Pick a number for m and work out each value. A grown-up guesses the story behind each expression.
Practice
1
A box holds 8 oranges. Write an expression for the oranges in b boxes.
8b.
2
Hana has h LE. Rana has 15 LE more than Hana. Write Rana’s money.
h + 15.
3
A ribbon is 20 cm long and c cm is cut off. Write the length that is left.
20 − c.
4
n pencils are shared equally among 4 children. Write each child’s share.
