New
New
Year 7

# Problem solving with factors, multiples, squares and cubes

I can use my knowledge of factors, multiples, squares and cubes to solve problems.

New
New
Year 7

# Problem solving with factors, multiples, squares and cubes

I can use my knowledge of factors, multiples, squares and cubes to solve problems.

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## Lesson details

### Key learning points

1. Knowledge of factors and multiples can be used to solve problems
2. Knowledge of squares and cubes can be used to solve problems
3. Knowledge of squares, cubes, multiples and factors can used to solve problems

### Common misconception

Real life measurements aren't always integers. Use of integers can give more a practical application

e.g. find the largest with 200 blocks, the cbrt(200) is not an integer so we use 5 x 5 x 5 =125

### 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

• Multiple - A multiple is the product of a number and an integer

• Numerical factor - A numerical factor is a factor that is an integer

As a warm up activity to revisit squares, cubes, factors and multiples go around the class asking students to give an example which has not already been said. Allow the use of a calculator so that students are able to give their answers quickly.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
What does LCM stand for?
Correct Answer: lowest common multiple, Lowest Common Multiple
Q2.
Sam makes two towers of blocks. One uses blocks that are 15 cm high, the other has blocks that are 12 cm high. What height will the towers first be the same height? Is this an LCM or HCF problem?
Correct Answer: HCF, highest common factor
Q3.
Sam makes two towers of blocks. One uses blocks that are each 15 cm high, the other has blocks that are 12 cm high. What height will the towers first be the same height?
Correct Answer: 60 cm, 60cm, 60 centimetres, 60
Q4.
Aisha has 20 white flowers, 45 red flowers and 30 yellow flowers. Aisha wants to make identical bunches. What is the greatest number of bunches they can make?
2
3
4
Q5.
Laura goes to a club every 6 days, Andeep goes to the same club every 10 days and Lucas goes every 15 days. They all went today. How many days will it be until they all go on the same day again?
This is an HCF problem
Correct answer: This is an LCM problem
Q6.
Laura goes to a club every 6 days, Andeep goes to the same club every 10 days and Lucas goes every 15 days. They all went today. How many days will it be until they all go on the same day again?
Correct Answer: 30, thirty, 30 days, thirty days

## Exit quiz

### 6 Questions

Q1.
The product of two repeated integers is called a __________.
multiple
cube number
factor
Q2.
True or false? All integers are square numbers.
True, you can square any integer.
Correct answer: False, not all integers can be written as the product of two repeated integers.
Q3.
What are the dimensions of the largest square you can make with 90 counters?
7 by 7
8 by 8
10 by 10
Q4.
Which of the following is both a square number and a cube number?
4
8
36
Q5.
Which of the following is not written as a product of prime factors?
$$2^3$$
$$3^4\times7$$
Correct answer: $$5^2\times9$$
$$11^3\times13\times19^2$$
Q6.
Which of the following are a correct answer to a string of consecutive numbers that satisfies: even, prime, composite, square
20, 21, 23, 24
Correct answer: 22, 23, 24, 25
Correct answer: 6, 7, 8, 9
12, 13, 14, 15