Pack A — Fluency

Mathematics

Year 7 · 7.2 Directed Numbers

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
Maria places -2 on a number line. She says it is 3 steps to the right of -5. Is she correct? Justify using the number line.
2.
Which is greater, -7 or -3? Justify by describing their positions on a number line.
3.
Two negative integers add to -12. Give one possible pair and justify that both numbers are negative and their sum is correct.
4.
The temperature is 3°C. It falls by 10°C. What is the new temperature? Explain which direction the fall takes you on a number line.
5.
Bob says "-6 × 4 = 24". Spot the error and give the correct answer with a reason.
6.
If 18 ÷ 3 = 6, what is 18 ÷ (−3)? Justify using the sign rules.
7.
A bank account has £20. The account holder spends £35. What is the new balance and what does the negative sign mean in context?
8.
What is the distance between -4 and 7 on a number line? Show your method.
9.
Sam says "negative × negative = negative". Is Sam correct? Give an example and a counter-example if needed.
10.
A diver is at 15 m below sea level (so their position is −15 m). They rise 8 m. Write a calculation and find the new position.

SilverQuestions 11–20

11.
Write in order from smallest to largest: -9, 4, -1, -6, 0.
12.
Calculate -8 + 5 + -3.
13.
Calculate -2 − (-9).
14.
Calculate -14 + 6, then subtract -3 from your answer.
15.
Calculate -4 × 3 + 15.
16.
Calculate -24 ÷ 6 − 2.
17.
The temperature starts at -3°C and falls by 8°C overnight. By midday it has risen 14°C. What is the midday temperature?
18.
Find the value of $\square$ if $\square + (-6) = -2$ .
19.
Find the midpoint of -8 and 4 on a number line.
20.
A bank account holds £15. Two payments of £23 and £7 are debited. What is the new balance?

GoldQuestions 21–30

21.
Find the LCM of 12 and 18. State whether your answer is positive or negative, and explain why.
22.
Evaluate $(-5)^2$ . Then evaluate $(5)^2$ . What do you notice?
23.
Work out $-3 \times 5 + 18 \div (-6)$ .
24.
Two integers multiply to give -15. One integer is 5. Find the other integer.
25.
Work out $(-8 + 3) \times (-2)$ .
26.
Evaluate $-(5^2) + 30$ .
27.
A submarine is at 80 m below sea level. It rises 35 m. What is its new depth? (Use a negative number to represent depth below sea level.)
28.
Find the HCF of 18 and 24. A diver records two temperatures: −(HCF)°C and +(HCF)°C. What is the difference between the warmer and colder temperatures?
29.
Evaluate $(-2)^3 + (-1)^2$ .
30.
Start with -12. Add 8. Then multiply the result by -2.

PlatinumQuestions 31–40

31.
Two negative integers multiply to give 36. Their sum is -13. Find both integers.
32.
Evaluate $(-2)^4 - (-3)^3$ .
33.
Two integers have product -20 and sum -1. Find both integers.
34.
Write 36 as a product of prime factors. Call this result $p$ . Now evaluate $p \div (-4)$ .
35.
Find the LCM of 4 and 6. Call it $n$ . Calculate $-n^2$ .
36.
A sequence begins -25, -19, -13, -7, … and increases by a constant amount each time. Find the 10th term.
37.
Solve $x^2 = 25$ . For each solution $x$ , calculate $x^2 - 5x$ .
38.
A temperature starts at -18°C. It rises by the LCM of 4 and 6 degrees. What is the final temperature?
39.
Let $a$ be negative and $b$ be positive. State whether each expression is positive, negative, or could be either: (i) $a \times b$ , (ii) $a + b$ , (iii) $a \div b$ .
40.
Evaluate $(-3)^2 - 4 \times (-5) + 18 \div (-6)$ .