Back to Exercise: Types of Numbers: Composite, Square, Cubic, and Triangular

Exercises: Types of Numbers — Composite, Square, Cubic, and Triangular

Work through each section in order. Show your work where indicated.

Grade 7·19 problems·~30 min·Uganda NCDC Primary 7 Mathematics·lesson·patterns-02

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Recall / Warm-Up

List the factors of 12. Using the number of factors, how should 12 be classified?

Prime — it has exactly two factors.

Composite — it has more than two factors.

Neither prime nor composite.

Compute $7^2$ .

Fluency Practice

Which of these numbers is prime?

$15$

$21$

$23$

$27$

$Four growing square dot arrays of 1, 4, 9, and 16 dots, showing the square-number pattern$

The dot arrays below grow as $1 \times 1$ , $2 \times 2$ , $3 \times 3$ , $4 \times 4$ . What is the next square number in the sequence 1, 4, 9, 16, ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ?

What are the first four cubic numbers?

$1, 4, 9, 16$

$1, 8, 27, 64$

$3, 6, 9, 12$

$1, 3, 6, 10$

$Four growing triangular dot arrangements of 1, 3, 6, and 10 dots$

The dot triangles below show $T_1, T_2, T_3, T_4$ with 1, 3, 6, 10 dots. What is the fifth triangular number, $T_5$ ?

Use $T_n = \frac{n(n+1)}{2}$ to decide: is 28 a triangular number?

Yes — $T_7 = \frac{7 \times 8}{2} = 28$ .

No — no whole number $n$ gives $T_n = 28$ .

Yes — $28 = 4 \times 7$ , so it is triangular.

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