Pack B — Fluency

Mathematics

Year 7 · 7.2 Directed Numbers

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

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

BronzeQuestions 1–10

1.
Maria places 1 on a number line. She says it is 5 steps to the right of -4. Is she correct? Justify using the number line.
2.
Which is greater, -10 or -6? Justify by describing their positions on a number line.
3.
Two negative integers add to -15. Give one possible pair and justify that both numbers are negative and their sum is correct.
4.
The temperature is 5°C. It falls by 14°C. What is the new temperature? Explain which direction the fall takes you on a number line.
5.
Bob says "-7 × 5 = 35". Spot the error and give the correct answer with a reason.
6.
If 20 ÷ 4 = 5, what is 20 ÷ (−4)? Justify using the sign rules.
7.
A bank account has £30. The account holder spends £47. What is the new balance and what does the negative sign mean in context?
8.
What is the distance between -6 and 5 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 20 m below sea level (so their position is −20 m). They rise 13 m. Write a calculation and find the new position.

SilverQuestions 11–20

11.
Write in order from smallest to largest: -12, 7, -3, -8, 2.
12.
Calculate -12 + 7 + -4.
13.
Calculate -5 − (-13).
14.
Calculate -20 + 8, then subtract -5 from your answer.
15.
Calculate -5 × 4 + 26.
16.
Calculate -35 ÷ 7 − 3.
17.
The temperature starts at -7°C and falls by 9°C overnight. By midday it has risen 20°C. What is the midday temperature?
18.
Find the value of $\square$ if $\square + (-9) = -3$ .
19.
Find the midpoint of -10 and 2 on a number line.
20.
A bank account holds £20. Two payments of £31 and £12 are debited. What is the new balance?

GoldQuestions 21–30

21.
Find the LCM of 8 and 20. State whether your answer is positive or negative, and explain why.
22.
Evaluate $(-7)^2$ . Then evaluate $(7)^2$ . What do you notice?
23.
Work out $-4 \times 7 + 30 \div (-5)$ .
24.
Two integers multiply to give -24. One integer is 6. Find the other integer.
25.
Work out $(-6 + 2) \times (-3)$ .
26.
Evaluate $-(4^2) + 20$ .
27.
A submarine is at 120 m below sea level. It rises 65 m. What is its new depth? (Use a negative number to represent depth below sea level.)
28.
Find the HCF of 20 and 28. A diver records two temperatures: −(HCF)°C and +(HCF)°C. What is the difference between the warmer and colder temperatures?
29.
Evaluate $(-3)^3 + (-2)^2$ .
30.
Start with -15. Add 9. Then multiply the result by -3.

PlatinumQuestions 31–40

31.
Two negative integers multiply to give 24. Their sum is -10. Find both integers.
32.
Evaluate $(-3)^4 - (-2)^3$ .
33.
Two integers have product -30 and sum 1. Find both integers.
34.
Write 40 as a product of prime factors. Call this result $p$ . Now evaluate $p \div (-5)$ .
35.
Find the LCM of 4 and 10. Call it $n$ . Calculate $-n^2$ .
36.
A sequence begins -30, -23, -16, -9, … and increases by a constant amount each time. Find the 10th term.
37.
Solve $x^2 = 36$ . For each solution $x$ , calculate $x^2 - 6x$ .
38.
A temperature starts at -25°C. It rises by the LCM of 6 and 10 degrees. What is the final temperature?
39.
Let $a$ be negative and $b$ be negative. State whether each expression is positive, negative, or could be either: (i) $a \times b$ , (ii) $a + b$ , (iii) $a \div b$ .
40.
Evaluate $(-4)^2 - 3 \times (-7) + 20 \div (-4)$ .