Please respond to the discussion below using RISE model.

For this integration, I'd anchor a civics/economics lesson in a City Council Budget Simulation in which students act as council members closing a mid-year budget gap while funding a youth program. The math goal is explicit: students use integer operations and name the relevant properties for commutative, associative, distributive, identity, and inverse to justify each budget move. I'd open with a two-minute advance organizer: a quick slide contrasting revenues (+) and expenses (-) and the objective, "We will balance a budget and justify each move with an integer property" (Burden & Byrd, 2019, Chapter 7). In a brief guided demo (about three minutes), I'd model how a refund (-$6) cancels a fee (+$6) to highlight the additive inverse, and how adding $0 changes nothing to surface the identity property (Burden & Byrd, 2019, Chapter 7).

Students then move into heterogeneous cooperative groups for 15-20 minutes. Each team receives line-item cards (e.g., +8, -3, -5, +4, -2) and a set of policy levers. They must (a) justify an across-the-board 10% cut with the distributive property by showing ; (b) reorder revenue/expense entries to argue that the net balance is unchanged (commutative/associative properties of addition); and (c) bundle three small cuts before adding a grant to argue associativity.

To support thinking, groups produce artifacts such as color-coded number lines and "Original vs. Reordered" T-charts such as nonlinguistic representations, and they work in defined roles (facilitator, recorder, checker, presenter) to ensure equal participation and individual accountability (Burden & Byrd, 2019, Chapter 6; Chapter 7). During a five-minute policy pitch, each team presents one balanced plan; the speaker must name the property used in a key step, and peers pose one clarifying question such as leveraging cues and questioning to deepen understanding (Burden & Byrd, 2019, Chapter 7). A quick exit ticket closes the lesson: "City B applies a 15% cut to (12 - 4). Show two paths and circle the property that proves they match."

Throughout, I'll layer ELL and differentiation supports like sentence stems (e.g., "Our net remains/changes because ___ property..."), manipulatives/visuals, and brief, criterion-based feedback during walk-around conferencing to keep guidance timely and corrective; structured cooperative roles and clear tasks further promote access and accountability (Burden & Byrd, 2019, Chapter 6; Chapter 7). This approach works because it is problem-based and collaborative, and it weaves graphic organizers, cues/questions, and timely feedback to boost understanding and engagement while making integer properties authentic to civic decision-making (Burden & Byrd, 2019, Chapters 6-7).