Integers explained for parents (Australia)

Homework says integers, positive and negative integers, or order these on a number line - and Australian parents wonder whether that is the same as "negative numbers" or a whole new topic. In primary classrooms, integers are the family of whole numbers that includes zero and the negatives: … −3, −2, −1, 0, 1, 2, 3 …. Teachers often use everyday pictures - temperature, lift floors, scores - before they ask children to name which side of zero a number sits on.

This guide owns the integer set / family language for Year 5–Year 6 (Year 4 light bridge): positive and negative naming, ordering on a number line, oral "which side of zero?", and light everyday contexts. Deep below-zero meaning, "how far below zero?", and comparing negatives (closer to zero is greater) live on negative numbers explained (live) - link there when homework is mainly about left-of-zero sense. Positive comparing and place sense: comparing numbers and place value (live). Grid plotting: coordinates explained (live). Year maps: Year 4–Year 5–Year 6 maths. Not a negative-numbers deep dive, not algebra solving equations, not order-of-operations teach-through, and not decimals or fractions.

The big idea: the whole-number family including negatives

An integer is a whole number that can be positive, negative, or zero. Spoken calmly: "Integers are the counting numbers, their opposites on the other side of zero, and zero itself."

• Positive integers - 1, 2, 3, 4 … (sometimes written +1, +2 when the class wants the plus sign clear).
• Zero - neither positive nor negative; the meeting point on the number line.
• Negative integers - −1, −2, −3 … (left of or below zero).

Together they make the integer family. Fractions such as ½ and decimals such as 0.3 are not integers - they sit between whole marks. You do not need set-theory language at the kitchen table. One clear picture of a line with marks on both sides of zero is enough.

At home: draw −5 to 5, circle the whole set, and say: "These marks are all integers. Half would sit between 0 and 1 - that is a different topic."

Positive and negative language (without drowning in symbols)

Children need two calm labels before they can talk about the family:

• Positive - on the familiar side of zero (right / above on most classroom lines).
• Negative - on the other side (left / below).

Echo the class phrase: "positive three" / "negative three" or "plus three" / "minus three". The written minus before a digit (−3) is a label of which family member, not yet a long "take away" calculation.

Keep the contrast with negative numbers explained clear: that page owns what it means to sit below zero and how far. This page owns naming the set and putting family members in order once both sides are in view.

Oral cue: which side of zero?

Many Australian classrooms ask a simple sorting question first:

• "Which side of zero?" → positive side, negative side, or on zero.
• "Is this an integer?" → yes for whole marks on either side; no for halves and tenths (say lightly).

Example: 4 is on the positive side. −2 is on the negative side. 0 sits on the meeting point.

Use the oral cue when a sheet mixes positives and negatives. It stops children treating every minus as "take away" before they have named the place. When the sheet then asks how far below or which negative is greater, tip to the negative numbers guide and keep a number line on the table.

Ordering integers on a number line

Once both sides are named, order is the next calm skill.

On a horizontal line, numbers increase as you move right. So a typical least-to-greatest run might look like:

−4, −1, 0, 2, 5

Oral check: "Start furthest left (least), walk right toward the greatest." Vertical thermometer-style lines increase up - same idea, different drawing.

Positive-only more/less language still lives on comparing numbers explained. When the mix includes negatives and the sticky point is "is −5 greater than −2?", use the negative-numbers page's closer to zero is greater story - do not invent a new slogan here.

At home: shuffle sticky notes −3, −1, 0, 2, 4. Child lines them up and says which side of zero each sits on before naming least and greatest.

Everyday pictures: temperature, lifts, and scores (light)

Abstract integer words land better after one concrete story. Keep these light - meaning and family language, not finance courses or full negative-operation drills.

Temperature. Marks above and below zero on a fridge or weather app. "Three degrees below zero" → −3; "two above" → 2. Ask which side of zero first.

Lift / car-park floors. Ground as 0, basement −1, −2, upper floors positive. "Which side of ground?" maps to "which side of zero?"

Scores and "above / below" talk. A game score that can dip below zero, or a simple "above / below target" chart, can show positive and negative integers as positions relative to a zero mark. Keep it short and calm.

These stories teach family membership and order. Deep below-zero compare and distance: negative numbers. They are not a reason to drill add/subtract-negative algorithms or secondary algebra here.

Not the same as negative numbers, algebra, or order of operations

This page owns integer family language, which side of zero, and ordering on a line - not those deep dives.

• Negative numbers explained (live) - below-zero meaning; how far below; comparing negatives.
• Comparing numbers explained (live) - more / less / greater for positives.
• Coordinates explained (live) - ordered pairs / first-quadrant grids; light only when axes show left of / below zero.
• Place value explained (live) - tens and ones for positives.
• Algebra explained (live) - mystery number / missing number; not this page.
• Order of operations explained (live) - BODMAS / BIMDAS; light link only.

At home: (1) name the integer family; (2) ask which side of zero; (3) order a short mixed list on a line. Skip full negative-operation algorithms, decimals/fractions deep dives, and algebra "solve for x" here.

Year by year: where integers show up

Year 4 (light bridge) - firmer number lines and positive compare; integer / negative words may tease via thermometer talk if the class dips in (Year 4 maths; AC Year 4).

Year 5 - clearer integers on a number line; positive and negative language; locate and order with everyday contexts (Year 5 maths; AC Year 5).

Year 6 - fluent order across both sides of zero; confident "which side of zero?"; operations with negatives only if the class requires them - still not a full secondary integers course here (Year 6 maths; AC Year 6).

Australian Curriculum Mathematics (version 9) builds number-line and integer ideas across upper primary. At home: one correct family-and-order story beats a page of silent ticks with mixed-up signs.

Home games that do not feel like worksheets

Which side? Call numbers (−4, 0, 3, −1). Child points left, on zero, or right and says positive / negative / zero.

Order the cards. Shuffle −5, −2, 0, 1, 4; line least to greatest; name each side of zero aloud.

Thermometer sticky. Vertical −5 to 5; place stickies; ask which side first, then tip to negative numbers if the sheet asks how far below or which is greater.

Lift ride. Label Ground = 0, B1 = −1, Level 2 = 2. Call floors; child sorts by side of ground.

Integer or not? (light). Flash 7, −3, ½, 0, 2.5. Child sorts "integer" vs "not yet on this page" - keep fractions/decimals as a calm "different guide later," not a lecture.

Keep games under ten minutes. If evenings fray - homework without tears.

A simple weekly home routine

1. 1. Two minutes of oral - "which side of zero?" for three marks on a scrap line.
2. 2. Five minutes of order - one mixed list of five integers; always show the line.
3. 3. Three minutes of a story - temperature, lift, or score; if the sheet digs into below-zero compare, open negative numbers beside you.

Stop while friendly. Frequency beats duration. Foundations: place value; comparing numbers; year maps Year 4–6 above.

Common mix-ups (and kinder fixes)

Thinking "integers" only means negatives. Fix: "Integers include positives, zero, and negatives - the whole-number family on both sides of zero."

Treating every minus as take-away. Fix: "Here the minus labels which side of zero; take-away can wait."

Skipping the line and memorising slogans. Fix: always point and say which side before you order.

Mixing this page with the negative-numbers deep dive. Fix: family and order here; below-zero distance and negative-vs-negative compare there - negative numbers.

Jumping to algebra or BODMAS too early. Light tip only to algebra or order of operations if the sheet shows those - then return to the integer line.

Tears over a long signed worksheet. Three careful family-and-order stories beat twenty rushed ticks - homework without tears, maths anxiety.

Wider worry: Is my child behind in maths?; calm signals: when to worry about maths.

How this links to other guides

• Negative numbers explained for parents - below-zero meaning, how far, comparing negatives (live; sibling deep dive)
• Comparing numbers explained for parents - more / less / greater for positives (live)
• Coordinates explained for parents - ordered pairs / first-quadrant grids (live)
• Place value explained for parents - tens and ones for multi-digit positives (live)
• Algebra explained for parents - mystery / missing number (live; not this page)
• Order of operations explained for parents - which operation first (live; light link only)
• Year 4–Year 6 maths (Year 5)
• Maths Help hub - more parent guides

Ask the teacher: "For integers homework, should we keep a number line on the table and say which side of zero before we order the list?"

FAQ

What are integers?

Whole numbers including zero and negatives - the family … −3, −2, −1, 0, 1, 2, 3 …. Fractions and decimals between those marks are not integers.

Is zero an integer?

Yes. Zero is an integer that is neither positive nor negative - the meeting point on the number line.

Are negative numbers the same as integers?

Negative numbers are the integers less than zero. Integers names the whole family (positives, zero, and negatives). For below-zero meaning and compare, see negative numbers explained.

What does "which side of zero" mean?

It asks whether a number sits on the positive side, the negative side, or on zero - before distance or greater/less questions.

When do Australian children meet integers?

Often more formally in Year 5–Year 6, with Year 4 bridging from number lines and positive compare. Follow the class method.

Does this page teach algebra or adding negatives?

Algebra mystery numbers: algebra explained (light tip only). Full add/subtract-negative algorithms: not this page - family language, which side of zero, and order first. Below-zero deep dive: negative numbers.

A calm next step

When the integer family (positives, zero, and negatives) is clear, "which side of zero?" comes before order, and a short mixed list lines up calmly on a number line - and you want a wider number-skill snapshot at home - Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths for practice that can meet number-line ideas at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.