New
New
Year 7

Square and cube numbers

I can explain the concept of squared and cubed numbers and calculate them.

New
New
Year 7

Square and cube numbers

I can explain the concept of squared and cubed numbers and calculate them.

Lesson details

Key learning points

  1. A square number can be represented by dots making a square.
  2. A square number is the product of two identical integers.
  3. A cube number can be made into a cube.
  4. A cube number is the product of three identical integers.

Common misconception

Students think that all numbers are square numbers as you can square any integer.

A square is the product of 2 repeated integers.

Keywords

  • Square number - A square number is the product of two repeated integers.

  • Cube number - A cube number is the product of three repeated integers.

Maybe, introduce the title of the lesson and allow students to work with manipulatives to see what prior knowledge they have. Weaker students will benefit from being able to physically rearrange them and it should help with the misconception.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
A product is the result when two or more numbers are __________ .
added
divided
Correct answer: multiplied
subtracted
Q2.
Which of the following is the product of 8 and 5?
3
12
13
Correct answer: 40
Q3.
Complete the statement. A numerical factor is __________ which exactly divides another.
a cube
a decimal
a fraction
Correct answer: an integer
a square
Q4.
Match each word to its definition.
Correct Answer:Product,The result of two or more numbers multiplied together.

The result of two or more numbers multiplied together.

Correct Answer:Square number,The product of two repeated integers

The product of two repeated integers

Correct Answer:Cube number,The product of three repeated integers

The product of three repeated integers

Q5.
Find the factors of 49
Correct answer: 1, 7 and 49
49, 98, 147, 196, ...
1, 2, 24.5 and 49
7
Q6.
Three students were given this calculation: $$ 2\times 2\times 2$$. Who is correct?
Aisha says ”the answer is 6 because 3 lots of 2 equals 6."
Lucas says "6 because 2 multiplied by 2 is 4 and this multiplied by 2 is 6."
Correct answer: Alex says "8 because 2 multiplied by 2 is 4 and this multiplied by 2 is 8."

6 Questions

Q1.
Which calculations will give a square number?
$$4 + 4 + 4 $$
Correct answer: $$4 + 4 + 4 + 4$$
Correct answer: $$4 \times 4$$
$$3 \times 4$$
Q2.
Identify the list of square numbers.
1, 2, 3, 4, 5, 6, 7, 8 …
1, 4, 7, 10, 13, ….
Correct answer: 1, 4, 9, 16, 25, 36, 49, …
1, 2, 4, 8, 16, 32, 64, …
Q3.
Identify the list of cube numbers.
1, 2, 3, 4, 5, 6, 7, 8 …
Correct answer: 1, 8, 27, 64, 125, 216, …
1, 4, 9, 16, 25, 36, 49, …
1, 3, 27, 81, 243, …
Q4.
Who is correct?
Andeep says " A square number can never be a cube number."
Correct answer: Aisha says "A square number can be a cube number."
Jacob says "All cube numbers are odd."
Q5.
The sum of a square number and cube number is 141. Work out the cube number.
An image in a quiz
1
8
27
64
Correct answer: 125
Q6.
The sum of two different square numbers and a cube number is 77. Work out the cube number.
An image in a quiz
1
8
27
Correct answer: 64