Integer Operations in Action

Overview

In this first lesson of a three-lesson unit, students model addition and subtraction of integers using number lines, two-color counters, and real-world situations. They connect subtraction to adding the opposite and explain their reasoning using patterns and mathematical language.

Learning intentions

Students will be able to:

• Represent integer addition and subtraction with counters and horizontal number lines.
• Explain that adding a positive moves right and adding a negative moves left.
• Rewrite subtraction as addition of the opposite.
• Interpret integer sums and differences in real-world contexts.

Success criteria

• I can model an integer operation with counters or a number line.
• I can solve an integer addition or subtraction problem accurately.
• I can explain why subtracting an integer is equivalent to adding its opposite.
• I can describe what an integer answer means in a real-world situation.

Curriculum links

• Number — apply and extend understanding of addition and subtraction to rational numbers.
• Number — understand sums as movement a distance in a positive or negative direction on a number line.
• Number — identify opposites as additive inverses whose sum is zero.
• Number — rewrite subtraction as adding the additive inverse and use properties of operations.

Lesson structure (40 minutes)

1. 0–5 min · Hook and activate prior knowledge. Open with the opening temperature-change visual showing a thermometer at 3°F followed by a 5-degree drop. Ask, “What operation describes the change, and where would the temperature land?” Students make an estimate, discuss with a partner, and mark a starting point and movement on a mini number line. Briefly review that positive numbers are to the right of zero and negative numbers are to the left.

2. 5–12 min · Model addition on a number line. Use the number-line modeling slides to model (3+(-5)), starting at 3 and moving 5 units left. Then model ((-4)+6), moving 6 units right from -4. Emphasize that the first number identifies the starting location and the second number identifies the movement. Students draw arrows for both examples and state whether the answer is greater or less than the starting number.

3. 12–20 min · Build with integer counters. Display the counter instructions in the counter-modeling slides and give pairs two-color integer counters, with one color representing positive and the other negative. Students model (4+(-2)), ((-3)+(-4)), and ((-5)+7). Establish that one positive and one negative counter form a zero pair. Students remove zero pairs, combine the remaining counters, and record each equation. Pause after the final example for students to explain why zero pairs do not change the value.

4. 20–27 min · Discover subtraction as adding the opposite. Present (5-(-3)) and ((-2)-4) on the subtraction investigation slides. First, students model each expression by starting with the first number and removing the second quantity when possible. When removal is not possible, they add zero pairs to create the needed counters. Students then compare the models with (5+3) and ((-2)+(-4)). Guide them to state the rule: (p-q=p+(-q)). Ask, “What is the opposite of the number being subtracted, and how does the movement change?”

5. 27–35 min · Partner practice and contexts. Distribute the integer operations practice worksheet. Students solve problems involving number lines, counters, and contexts such as temperature, elevation, and bank-account changes. Partners must solve at least four problems and explain one using the sentence frame, “I started at ___, moved ___ units ___, so the result is ___.” Circulate and check that students reverse the sign of the subtracted integer rather than simply changing the final answer’s sign. Ask selected pairs to share different representations.

6. 35–40 min · Check for understanding and close. Return to the summary and exit-question slides. Students complete an individual exit ticket: solve (-6-(-4)), represent it on a number line, and explain why it can be rewritten as (-6+4). Add the real-world prompt: “A hiker is at an elevation of -2 meters and climbs 7 meters. What does the answer mean?” Collect responses and preview that the next lesson will use integer-operation strategies more efficiently.

Resources

• One teacher slide deck covering the hook, number-line models, counter directions, subtraction investigation, practice prompts, and closure
• One-page integer operations practice worksheet
• Two-color integer counters, approximately 20 per pair
• Mini whiteboards or notebook paper
• Pencils and colored pencils
• Projector or interactive display
• Individual number-line strips
• Exit-ticket slips or notebook paper

Assessment

• During modeling, ask students to identify the starting number, direction, and distance before calculating.
• During partner practice, use questioning and observation to check counter models, zero-pair reasoning, and correct rewriting of subtraction.
• Use the exit ticket to assess computation, number-line representation, explanation of additive inverses, and interpretation of a real-world sum.

Differentiation

• Provide pre-drawn number lines, labeled positive and negative counters, and the sentence frame for students who need support. Allow students to physically move on a floor number line before recording.
• For students who need language support, pair visual models with the terms “start,” “move,” “opposite,” “positive,” and “negative,” and rehearse explanations orally before writing.
• For students with dyslexia, attention needs, or fine-motor needs, use large-print number lines, uncluttered worksheet formatting, read directions aloud, and permit verbal explanations.
• Challenge early finishers to create two different real-world situations for ( -3-(-8) ), solve them, and justify why both situations have the same mathematical structure.