Step 1 of 10
Start
Find the minimum hidden in the words.
Meaning first
A candidate receives at least 125 votes.
You sold 3 gardens Monday + 4 Tuesday. Reach at least 10.
Basketball: 24 points + 2 per basket. Reach at least 46.
Spot floor
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Build total
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Solve
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Check
Number line · locate the floor
The filled gate opens at the minimum
Shading shows every allowed value. A filled endpoint means the boundary value counts too.
Vote threshold number lineAT LEAST 125
all shaded values are allowed
124unshaded
125filled = included
126shaded
124 is unshadedbelow 125 → blocked
● 125 is filledequal to 125 → allowed
126 is shadedabove 125 → allowed
125 is allowed because the phrase says “at least 125,” not “more than 125.”
124 is too small. The allowed side continues right toward larger values.
votes ≥ 125
The endpoint tells you whether 125 counts
v > 125open circle · 125 excluded
v ≥ 125filled circle · 125 included
Build one total toward the floor
Everything you sell belongs in one total. The minimum goal belongs on the other side.
Each club member should sell at least 10 herb gardens. You sold 3 on Monday and 4 on Tuesday. Let x be the number you can sell next.
at least 10 gardens→≥ 10
3Monday sales
4Tuesday sales
10minimum goal
0 gardensprogress railGOAL 10+
Mon 3
Tue 4
need 3
extra
Seven are sold already. Three more lands exactly on the goal.7 + 3 = 10 ✓
Add every sale into one total
3 + 4+x≥10
already soldnext salesminimum
Free x, then test the threshold
The symbol stays ≥ because we subtract a positive amount from both sides.
3 + 4 + x ≥ 10
Combine the known sales: 3 + 4 = 7
7 + x ≥ 10
− 7 from both sides
x ≥ 3
You may sell 3, 4, 5, ... gardens. Three is the minimum, not the only answer.
7 + 2 = 9below the goal ✕
7 + 3 = 10boundary counts ✓
7 + 4 = 11above also works ✓
Your turn: reach Casey’s score
Let b be the number of two-point baskets. Build the score, choose the minimum symbol, then find the least whole number of baskets.
Fill: current score, points per basket, minimum symbol, goal score, and least baskets.
✎
Solve on your whiteboard
Let b be baskets. Write the score inequality, solve it, and test the boundary. Submit when your work is ready.
Work submitted. The score ticket is unlocked.
The score ticket proves 11 baskets
Each line preserves the same inclusive minimum from the story.
Casey’s minimum-score ticket
readcurrent 24 · rate 2 · goal 46
Add every point into one total
model24 + 2b ≥ 46
− 24 from both sides
remaining2b ≥ 22
÷ 2 points per basket
minimumb ≥ 11 baskets
boundary24 + 2(11) = 46 ✓
below floor24 + 2(10) = 44 ✕
Reliable model: starting amount + rate × number of units ≥ the minimum goal.
Minimum language mastered
At least, no less than, and greater than or equal to all open the same inclusive minimum gate.
≥floor included
Read from the story: put the changing total on one side, the minimum on the other, and include equality at the filled boundary.
Spot floor wordsBuild one totalSolve the boundaryTest one below