Integers Foundations

Overview

Students begin Unit 1, “Mastering Integers Together,” by exploring what integers are and how positive and negative numbers represent quantities in everyday situations. They learn to locate integers on a number line and describe their meaning using language such as “greater than,” “less than,” and “opposite.”

Learning intentions

• Students will be able to explain what integers are and identify examples of positive and negative numbers.
• Students will locate and order integers on a number line.
• Students will connect integers to real-world contexts (e.g., temperature, elevation, money owed).
• Students will use integer language to justify where a number is placed on a number line.

Success criteria

• I can correctly classify numbers as positive, negative, or zero.
• I can place an integer at the correct position on a number line.
• I can compare two integers and explain which is greater or less.
• I can describe the meaning of integers in a context sentence.

Curriculum links

• Uses the number system and number sense: integers and their order.
• Represents integers in multiple ways, including on a number line.
• Applies reasoning to explain relationships between numbers (greater/less, opposites).

Lesson structure (40 minutes)

1. 3 min – Launch and hook

• Display three short scenario cards: “temperature is −4°C,” “elevation is +12 m,” and “you owe −$15” (or “owing $15”).
• Ask: “What do the plus and minus signs tell us?” Briefly collect ideas and confirm today’s focus: integers represent quantities below/above a reference point.

2. 7 min – Direct teaching: what integers are

• Define integers as the set of whole numbers with their opposites, including zero: …, −3, −2, −1, 0, 1, 2, 3, …
• Model how to interpret a minus sign as “below”/“less than zero” and a plus sign as “above”/“more than zero.”
• Emphasize opposites: numbers that are the same distance from 0 but on opposite sides (e.g., +6 and −6).

3. 10 min – Guided practice on the number line

• Draw a number line on the board with equal intervals between integers (include negative and positive regions).
• Model placing −3, 2, and −1 by counting equal steps from 0.
• Use guided questions:
• “Where is −3 compared to 0?”
• “Is −1 closer to 0 than −4? How do you know?”
• Students do a think-pair-share for two placements, then teacher checks: the class agrees on the correct position and explains the counting strategy.

4. 8 min – Comparisons and ordering

• Write pairs on the board: (−5, −2), (−1, 3), (0, −4), (2, 2).
• Teach a simple comparison strategy: the number line shows that numbers further right are greater.
• Students complete “greater/less” statements in their notebooks using sentence frames:
• “−5 is less than −2 because it is to the left.”
• “3 is greater than −1 because it is to the right.”
• Quick whole-class check for misconceptions (e.g., mistaking “bigger number means bigger value” when negatives are involved).

5. 6 min – Context-to-integer task (independent)

• Give each student a short handout (or board slide) with 4 prompts:
• 1 temperature: −7°C
• 1 elevation: +9 m
• 1 money situation described as “owing $12”
• 1 statement where students must choose the correct integer: “Bank account balance changed by ___ dollars (below/above zero).”
• Students write the integer and a one-sentence meaning (e.g., “−7°C means 7 degrees below zero.”).
• Teacher circulates and uses prompts: “What reference point are you using?” “Is it above or below zero?”

6. 4 min – Exit ticket and closure

• Exit ticket (done individually):
• a) Place −2 on a provided number line (or mark its position).
• b) Write which is greater: −3 or −1.
• c) Give meaning for −4 in a context chosen from two options: temperature or elevation.
• Collect and quickly scan for common errors: incorrect placement, reversed comparison, missing meaning.

Resources

• Number line diagrams (printed or projected), clearly showing equal intervals
• Scenario cards or slide (temperature, elevation, money owed)
• Student notebooks and pencils
• Short practice sheet with placement, comparison, and context prompts
• Exit ticket slips with a simple number line and two written questions
• Teacher-made anchor chart title: “Integers on a Number Line”
• Optional: coloured counters or integer tiles for physical placement on the number line

Assessment

• Formative checks during guided practice: student explanations of counting steps and left/right reasoning.
• Independent context task: whether students correctly match scenarios to integers and accurately describe meaning.
• Exit ticket: accuracy placing integers, correct comparison, and clear one-sentence context interpretation.

Differentiation

• Support:
• Provide a partially completed number line with 0 and one positive/one negative tick already labeled.
• Offer sentence frames for explanations: “I know because it is to the left/right of 0.”
• Use an extra example orally before independent work and allow pair support for the first prompt.
• Extension:
• Add a challenge prompt: “Write two integers that are opposites and explain what they have in common.”
• Ask students to order three integers given in mixed form (e.g., 1, −3, −1) and justify ordering.
• EAL:
• Use visuals (number line and context images) and keep wording consistent across prompts.
• Allow oral explanation before writing; provide translated scaffolds only if available in the classroom.
• SEN:
• Reduce the number of items on the context worksheet (e.g., 3 prompts instead of 4) while keeping the same skill focus.
• Offer step-by-step guidance for placing integers (identify 0, then count equal intervals).