Lesson Overview

This grade 7 integer operations lesson plan uses two-colour counters to help students build a concrete understanding of adding and subtracting integers before moving to symbolic notation. The lesson is designed for a 75-minute block and aligns with the Number strand in most provincial math curricula, including Ontario’s Grade 7 Mathematics curriculum and BC’s Math 7 learning standards.

The central idea is simple: students who can physically manipulate counters to show why (+3) + (−5) = −2 will have a much easier time making sense of the rules they’ll apply later in algebra. The counter model gives the abstract a concrete home.

Learning Goal

Students will use two-colour counters to model addition and subtraction of integers, and connect those physical models to written number sentences using standard algebraic notation.

Success Criteria

  • I can use red and yellow counters to represent positive and negative integers.
  • I can model integer addition and subtraction with counters and explain what my model shows.
  • I can identify and remove zero pairs to simplify a counter model.
  • I can write a number sentence that matches my counter model and check it using a number line.

Materials

  • Two-colour counters (red/yellow), approximately 20 per student or pair. These are available from most school supply catalogues; plastic poker chips work just as well.
  • Printed or digital integer mat (a simple T-chart labeled “Positive” and “Negative”)
  • Mini whiteboards or plain paper for recording number sentences
  • Number lines posted or printed (integers from −10 to +10)
  • Projector or interactive whiteboard for whole-class modelling
  • Optional: virtual manipulatives from the Math Learning Center for students working on tablets

Hook

Open with a quick real-world scenario Canadian students recognize. Ask: “It’s January in Winnipeg. The temperature is −4°C at noon. By 9 p.m. it drops another 6 degrees. What’s the temperature now?” Give students 60 seconds to talk to a partner, then take a few answers.

Most students will get −10 by intuition or a number line sketch. Tell them that today they’ll learn a physical model that explains exactly why that answer works, and how it connects to the math symbols they’ll use in every future unit that involves negative numbers.

Direct Instruction

Introduce the two colours: yellow = positive, red = negative. Hold up one yellow counter and one red counter side by side. Ask students what happens when you have one positive and one negative. Introduce the term zero pair: one yellow plus one red always equals zero, and zero pairs can be removed from the mat without changing the value.

Model three examples on the projector, building each one with counters before writing the number sentence:

  1. (+4) + (−2): Place 4 yellow, 2 red. Remove 2 zero pairs. 2 yellow remain. Write: (+4) + (−2) = +2.
  2. (−3) + (−4): Place 3 red, then 4 more red. No zero pairs. 7 red remain. Write: (−3) + (−4) = −7.
  3. (+2) − (+5): Place 2 yellow. You need to take away 5 yellow, but only 2 are there. Add 3 zero pairs to get enough yellow. Remove 5 yellow. 3 red remain. Write: (+2) − (+5) = −3.

That third example is the critical one. Taking away more than you have is the exact moment students typically get lost, and the counter model makes the logic visible. Narrate every step aloud.

Guided Practice

Give each pair of students a set of counters and an integer mat. Call out four expressions one at a time, projected on the board. Students build the model, record the number sentence on their whiteboard, and hold it up before you reveal the answer.

  • (+5) + (−3)
  • (−6) + (+2)
  • (−1) − (−4)
  • (+3) − (+7)

Circulate and watch for two common errors: students forgetting to add zero pairs before subtracting, and students confusing which colour represents which sign. Address these as a group if you see them coming up more than once.

Independent Practice

Students complete a set of eight integer expressions on their own, recording both the counter model (sketched as circles, shaded for red) and the matching number sentence. Include a mix of addition and subtraction, and end with two word problems in Canadian contexts (temperature changes, below-sea-level elevations, or yardage gains and losses in a CFL game).

A good independent practice worksheet can be built quickly, or you can find printable integer activities in the teaching resources section of this site.

Consolidation

Bring the class back together for the last 10 minutes. Ask one student to come up and model an expression they found tricky. Then pose this question to the group: “Can you write a rule in words for what happens when you subtract a negative number?”

Guide students toward the idea that subtracting a negative is the same as adding a positive. Let them articulate it themselves using what they saw with the counters. Write their class-generated rule on the board and leave it posted for the next few lessons.

Differentiation

Students Who Need More Support

Keep the number range small (integers between −5 and +5) and focus only on addition before introducing subtraction. Provide a colour-coded reference card showing a yellow circle = +1 and a red circle = −1, plus a worked example of removing a zero pair. Pairing these students with a strong partner during guided practice also helps, as long as both students are building and recording.

Students Ready for Extension

Challenge students to write their own word problems that require integer subtraction, then swap with a classmate to solve. You can also introduce expressions with three or more integers, such as (−4) + (+6) − (−2), and ask students to predict the answer before building. A further extension is to ask students to generalize: what patterns do they notice that let them skip the counters entirely?

Multilingual Learners

The physical counter model is a strong support here because understanding doesn’t depend on reading a word problem first. Provide vocabulary cards with the key terms (integer, zero pair, positive, negative, expression) in both English and the student’s home language if possible. Sentence frames like “I placed ___ yellow counters because…” help students participate in discussion without the pressure of open-ended verbal responses.

Assessment

Use the whiteboard check-ins during guided practice as a quick formative read on the whole class. For individual assessment, collect the independent practice and look specifically at the sketched models alongside the number sentences. A student whose sketch matches but whose notation is wrong has a different gap than a student whose notation is right but whose sketch makes no sense.

If you want a brief exit ticket, three questions work well: one addition of a positive and a negative, one subtraction that requires zero pairs, and one open-ended prompt asking students to explain zero pairs in their own words.

Follow-up Lessons

  • Lesson 2: Connecting the counter model to a vertical number line, then a horizontal one. Students practise moving from the concrete model to a purely symbolic process.
  • Lesson 3: Multiplying integers. Start again with the counter model (repeated addition of negative groups) before introducing the sign rules.
  • Lesson 4: Dividing integers and connecting multiplication and division as inverse operations, using fact families that include negative numbers.
  • Lesson 5: Order of operations with integers. Students apply BEDMAS to expressions involving negative numbers, building on the operational fluency from lessons 1 to 4.

You can browse sequenced lesson ideas for the full integer unit in the teaching lessons section.

Frequently Asked Questions

What if I don’t have physical counters in my classroom?
Virtual manipulatives work well. The Math Learning Center’s Number Pieces app is free and runs in a browser. You can also have students use two different colours of sticky notes, coins with tape on one side, or even beans painted red on one side.

How long should I stay with the counter model before moving to purely symbolic work?
Most grade 7 students are ready to transition after two or three lessons with the concrete model, but keep counters available at the back of the room throughout the unit. Students often return to them when a new operation type is introduced, and that’s a healthy sign of self-regulation, not a gap.

Does this lesson align with provincial expectations?
The content fits Number strand expectations across most Canadian provinces. Ontario’s 2020 math curriculum addresses integer operations in Grade 7 under Number, and BC’s curriculum lists operations with integers as a core competency in Math 7. Check your specific provincial ministry site for exact expectation codes, as they vary by province. You can find links organized by province at thecanadianteacher.com/links/by-province/.

My students already know the “rules” for integers. Why should I use counters?
Knowing the rules and understanding why they work are different things. Students who only know rules tend to apply them inconsistently when the expressions get more complex. A few days with counters helps students build the mental model they’ll need when integers appear inside algebraic equations later in grades 8 and 9.

Continue the Conversation

Have a variation on this lesson that worked well for your class? Want to share a Canadian context that clicked better than temperature examples? Head over to The Canadian Teacher Forum and post in the Grade 7 Math thread. Other teachers across the country are working through the same unit right now and are always glad to swap ideas.