Comparing, Adding and Subtracting Integers

Compare −12 and −7 using <, > or =. Then state which integer has the greater magnitude.

Order 4, −9, −1 and 0 from least to greatest. Briefly justify the position of −9.

Evaluate −8+5 and describe the movement on a number line.

Evaluate 7−(−6). Explain why the result is greater than 7.

Which has the greatest magnitude: −11, 9, −7 or 10? Explain your choice using absolute value.

A student says “−5 is greater than +2 because 5 is bigger than 2.” Explain the error, write the correct inequality, describe where both numbers lie on a number line, explain sign versus magnitude, and give one real-world example using negative values.

Order −14, 6, −2, 0 and −9 from least to greatest. Explain the ordering using a number line, explain why negative numbers further left are smaller, discuss magnitude, and give one context where ordering integers matters.

Evaluate −7−(−12). Rewrite the expression, solve using number-line reasoning, explain why subtracting a negative increases the value, show a symbolic method, and compare the two methods.

Evaluate −15+(−8). Represent the movement on a number line, solve, explain what “adding a negative” means, and give a bank-balance or temperature context that matches the calculation.

A hiker starts at elevation +3, descends 12 units, ascends 5 units, then descends 4 units. Write the signed operations, find the final elevation, describe the number-line journey, explain how signs represent direction, and explain why integers suit elevation modelling.