Understanding Number — Practice Worksheet — Understanding Number: Integers, Place Value, Primes & Fractions

Part A — Integers on a number line

Positive and negative integers describe everyday situations such as temperature, money owed, or floors below ground. On a number line, numbers get smaller as you move left and larger as you move right. Zero sits in the middle and separates the negatives from the positives.

A number line from minus 5 to plus 5 with zero centred; negatives in red on the left and positives in green on the right, with minus 3 and plus 4 highlighted. — Use a number line to compare and order integers.

Q1. Write the integer shown by each described point:

(a) 4 to the left of 0: (b) 2 to the right of 0: (c) 1 to the left of −2:

Q2. Order each set from lowest to highest:

(a) 6, −3, 0, −7, 2

(b) −1, −9, 4, −4, 8

(c) −10, 10, −5, 5, 0

Q3. A diver is at −8 m and a bird is at +5 m. Which is further from sea level (0)? Explain how the number line helps you decide.

Q4. Fill in <, > or =:

(a) −3 2 (b) −7 −4 (c) 0 −1 (d) −6 −6

Q5. Real-world integers. Write an integer for each situation:

(a) 5°C below zero: (b) a lift going to floor 3 below ground:

(c) a $20 debt: (d) 12 m above sea level:

Part B — Place value, primes, fractions & percentages

This part connects four ideas from the lesson: multiplicative place value (each place is 10 times the place to its right), square, prime and composite numbers shown as arrays, ordering fractions, and linking common percentages to fractions and decimals.

Place value

Q1. In 4.62, the 6 is in the place and is worth . The 2 is worth .

Q2. What happens to the digit 5 when 5.0 becomes 50 (how many times larger)? What about 5.0 → 0.5?

Square, prime & composite

Q3. Draw the array for 9 as a square number. Why is 9 square?

Q4. Sort into prime or composite: 7, 12, 13, 15, 21, 23.

Q5. Explain why 1 is neither prime nor composite.

Ordering fractions

Q6. Order from smallest to largest: 1/2, 1/4, 3/4, 1/8.

Answer:

Q7. True or false: 2/4 = 1/2. Explain.

Percentages, fractions & decimals

Q8. Complete the table.

Percentage	Fraction	Decimal
50%	1/2	0.5
25%	1/4
10%		0.1

Q9. Find 25% of 80 and 10% of 60.

Part C — Square, prime & composite numbers

Build each number as a rectangle of counters to reveal its type. A prime makes only one row; a square number makes a perfect square; a composite makes more than one rectangle.

Q1. Classify each number as square, prime or composite. Sketch an array to justify each: 4, 11, 15, 16, 23, 25, 36.

Q2. List all the prime numbers between 1 and 20.

Answer:

Q3. Find a number under 30 that is both square and even.

Q4. Explain why 1 is not a prime number.

Q5. Challenge. 49 is a square number. What is √49? Draw its array.

Part D — Fractions & percentages

Common conversions to know by heart: 1/4 = 0.25 = 25%; 1/2 = 0.5 = 50%; 3/4 = 0.75 = 75%; 1/10 = 0.1 = 10%. Rename fractions to a common denominator before ordering them.

Q1. Order from smallest to largest: 1/2, 1/4, 3/4, 1/8.

Q2. Order these mixed numerals: 1 1/2, 1 1/4, 2, 3/4.

Q3. Complete the table.

Fraction	Decimal	Percentage
1/2
	0.25
		10%
3/4

Q4. Which is larger: 50% of a pizza or 3/8 of the same pizza? Explain.

Q5. Exit ticket. Write one integer, one prime number, and one fraction equal to 50%.