DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 1: Number Classification, Integers and Mental Number Skills

Number Classification, Integers and Mental Skills

Build reliable number sense so later algebra and statistics do not collapse under weak arithmetic.

Junior Maths Book 1 pages 3-188 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 3-18

Classify numbers, use mental strategies, calculate with integers, factors, multiples, HCF, LCM and order of operations.

AI explanation

The AI teacher treats number classification as a language for describing structure. Integers are taught on a number line, while HCF and LCM are shown through factor lists and prime-factor thinking.

  1. 1First identify the type of number: prime, composite, square, cube, triangular, integer, even or odd.
  2. 2For integer calculations, picture movement on a number line.
  3. 3For HCF, look for the greatest shared factor.
  4. 4For LCM, look for the first shared multiple.
  5. 5Order of operations protects the meaning of an expression.

Animated teaching

See the method

A number line compares integers, then factor cards and multiple cards sort into HCF and LCM columns.

Integer number line showing movement-8-4048move right for addition
Factors divide a number exactly
Multiples are made by repeated groups
HCF divides both numbers
LCM is reached by both lists

Why this method works

  • A number line turns positive and negative values into positions, so comparison becomes visual.
  • HCF and LCM work because factors divide numbers while multiples are built from repeated groups.
  • Order of operations removes ambiguity: everyone reads the same expression in the same way.

Common mistakes

  • Treating 1 as a prime number.
  • Thinking -12 is greater than -5 because 12 is larger than 5.
  • Finding a common factor when the question asks for a common multiple.
  • Working strictly left to right when multiplication or brackets should come first.

Multiple methods

  • HCF can be found by listing factors or by using prime factors.
  • LCM can be found by listing multiples or by using prime factors.
  • Integer questions can be solved by rules, number lines or checking with real contexts such as temperature.

Worked examples

HCF and LCM

Find the HCF and LCM of 18 and 24.

Method: List factors and multiples, then compare.

  1. 1.Factors of 18 are 1, 2, 3, 6, 9, 18.
  2. 2.Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
  3. 3.The greatest common factor is 6.
  4. 4.Multiples of 18 are 18, 36, 54, 72.
  5. 5.Multiples of 24 are 24, 48, 72.

Answer: HCF = 6 and LCM = 72

Directed numbers

Calculate -7 + 12 - 5.

Method: Move on the number line.

  1. 1.Start at -7.
  2. 2.Move 12 places right to 5.
  3. 3.Move 5 places left to 0.

Answer: 0

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Which number is prime?

Question 2

Find the LCM of 8 and 12.

Question 3

Calculate 5 - 3 x 4.

Review prompt

Explain the difference between a factor and a multiple using one example.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

Two bells ring every 18 minutes and 24 minutes. They ring together at 9:00. When will they next ring together?

Hint: Find the LCM of 18 and 24, then add that many minutes to 9:00.