Discover Mathematics P6: Term 1, Unit 3, Lessons 3–5
GoalWrite an algebraic expression with one or two operations from a sentence in words.
New words
sum · the answer to an additiondifference · the answer to a subtractiontwice · 2 times
Explanation
Words in a sentence tell us the operation. Plus, sum, more than and increased by mean add. Minus, difference, less than and decreased by mean subtract. Times, product and twice mean multiply. Divided by, quotient and shared equally mean divide. Be careful with “less than”: “5 less than x” means x − 5, because we start from x and take 5 away. It is not 5 − x. With two operations, do them in the order the sentence says: “twice a number plus 3” is 2n + 3, and “7 less than the product of 3 and n” is 3n − 7.
Words
Symbols
sum, plus, more than
+
difference, minus, less than
−
product, times, twice
×
quotient, divided by
÷
Worked examples
x
9
12
20
5 less than x
4
7
15
“5 less than x” is x − 5. Check with x = 12: 5 less than 12 is 7, and 12 − 5 = 7.
n
1
5
10
2n + 3
5
13
23
“Twice a number plus 3” is 2n + 3. If n = 5, twice 5 is 10, and 10 + 3 = 13.
x
8
20
40
x ÷ 4 + 6
8
11
16
“x divided by 4, then add 6” is x ÷ 4 + 6. If x = 20, then 20 ÷ 4 = 5 and 5 + 6 = 11.
Class activity
Sentence swap. Write five word sentences on paper, such as “9 more than a number”, “a number divided by 3, plus 1”. Swap papers with a grown-up and write each as an expression. Test every expression with a number you choose to see that it fits the words.
Practice
1
Write “9 more than y”.
y + 9.
2
Write “6 less than m”.
m − 6.
3
Write “the product of 8 and k”.
8k.
4
Write “3 times n, minus 2”.
3n − 2.
5
Rana writes “4 less than n” as 4 − n. Test with n = 10 and correct her.
4 less than 10 is 6. The right expression is n − 4, because 10 − 4 = 6.
