The examples are invented. You can show each step on paper, with labelled tiles, by typing, speaking/AAC, a tactile line or a reader who gives you the exact prompt. Choose one A/B/C route from daily choices. Explain why a move keeps two expressions equivalent or an equation balanced. A substitution checks a proposed value. Record the given domain before interpreting a model. Drawing neatness and speed are not the mathematics.
Week 3
Day 11 · Every term in the bracket
Three identical packs contain x+4 cards each. Expand 3(x+4) by showing all groups, then substitute x=2 in both forms. For your chosen practice route, expand and check at a value. Exit: fix 2(z+6)=2z+6 and show what happens at z=1.
Day 12 · Terms keep their signs
Simplify 4x+7+2x−3 by grouping like terms. Check at x=2 in both original and short forms. Choose a route and show your regrouping. Exit: evaluate 2n+5+3n−1 at n=2 in two ways.
Day 13 · Reverse distribution
Use six equal groups to explain 6x+12 as a product with brackets. Expand your product to check. Choose a route. Exit: fill the blank in 3t+15=3(t+__), then test t=1.
Day 14 · From total to input
A fictional kit uses C=8+5n, where n is a non-negative whole number of refills. Rearrange to make n the subject. Find n when C=33 and verify by substituting in the original. Ask whether every possible C is a whole-refill total. Choose a route. Exit: explain C=8 in this model.
Day 15 · New expression transfer
Your teacher will release a new-case check after a short rehearsal. Save your first response. The check asks for your transformation steps, a verification and a careful interpretation. After that, use the Day15 routes for practice with different numbers. Exit: write one step you will inspect before trusting two forms as equivalent.
Week 4
Day 16 · Balance and substitute
Solve 3x+7=25 by doing the same operation to both sides. Check your value. Try 2y+5=12; a fraction/decimal may be the exact answer when no whole-count rule is given. Choose a route. Exit: solve and check 4z−3=9.
Day 17 · Two relations meet
Fictional plan A uses 6+4n tokens; plan B uses 18+2n for n whole batches. Find where totals match and verify in both formulas. Plot or describe A and B using (0,total) and the meeting point. Choose a route. Exit: which is lower at seven batches and by how much? Name the unit.
Day 18 · Values below a cap
A fictional poster desk uses 9+5n points for n whole posters, with at most 34 points. Write and solve an inequality. Mark its boundary on a number-line/graph board or state the allowed integers in words. Test the boundary and one value beyond it. Choose a route. Exit: at your boundary, what changes if “at most” becomes “less than”?
Day 19 · Dividing by a negative
A fictional tray has 15−3t counters after t turns, where t is a whole number from 0 through 5. Solve “more than 3 counters remain”. Verify one accepted turn and the first excluded turn. Choose a route. Exit: solve 8−2u≥0 and say what domain you are using.
Day 20 · New equation and inequality transfer
Your teacher will release a new check after a short rehearsal with other values. Show equations, inverse steps, boundary checks and what the model can/cannot say. A blank board, text or tactile route is available. Your first response is the formative evidence; Day20 routes come afterward. Exit: say one substitution you would make before using a model total.
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