Week 05 · Inequalities
Puzzle Day
Puzzle Day: Walk the line
// More than, less than, and a whole set of answers on the number line
⏱ about 20 min
Puzzle Day: Walk the Line
Saturday morning, Raven checks every strip of tape on the floor number line. "Puzzle Day. Family edition."
"I read a rule, you walk to a number that fits," Rocket says. "Then we test it. Then you read one for me."
"What do you notice about the hardest cards?" Raven asks, shuffling them. "They have two steps."
"Then we undo first," Rocket says, "and the ribbon shows where everyone can stand."
Nova hovers by the 0, her light warm. "Circle first, ribbon second, test third," she says. "Hints only."
Rocket picks up the ribbon. "Hints only," he agrees. Nova hums. "That includes the boundary."
- An inequality uses >, <, ≥ or ≤ and has infinitely many solutions.
- More than is >, less than is <, at least is ≥, at most is ≤.
- Graph it with a circle at the boundary and an arrow in the direction that works. Open circle for > and <, filled for ≥ and ≤.
- Solve px + q > r by undoing on both sides, the added number first, then the multiplied one.
- Test a solution by substitution, and check that the boundary is in or out.
◇ WALK THE LINE WITH YOUR FAMILY
Tape a number line from 0 to 12 on the floor and press every strip flat.
Write six rule cards: two with more than or fewer than, two with at least or at most, two with two steps.
Read a card. Your family member walks to a number that fits and tests it aloud.
Lay the circle and the ribbon, then swap roles. For a two-step card, undo first and find the boundary together.
Keep a tally of how many numbers were tested before someone stood on the boundary by mistake.
Write six rule cards: two with more than or fewer than, two with at least or at most, two with two steps.
Read a card. Your family member walks to a number that fits and tests it aloud.
Lay the circle and the ribbon, then swap roles. For a two-step card, undo first and find the boundary together.
Keep a tally of how many numbers were tested before someone stood on the boundary by mistake.
For a grown-up
This week your student wrote inequalities like x ≥ 8, graphed them and solved two-step ones like 4x + 3 > 15.
Ask them why x > 4 has infinitely many solutions and what the open circle means. Both answers should mention the boundary.
Tape stays flat, no running on the line, and the ribbon stays on the floor.
Ask them why x > 4 has infinitely many solutions and what the open circle means. Both answers should mention the boundary.
Tape stays flat, no running on the line, and the ribbon stays on the floor.
Safety first
Press every strip of tape flat so no one trips. Shoes on in the garage, and clear the path first.
Walk, never run or jump, between numbers.
The ribbon stays on the floor, never around anyone's neck or hands.
Small paper circles and beans stay away from children under three and pets.
Walk, never run or jump, between numbers.
The ribbon stays on the floor, never around anyone's neck or hands.
Small paper circles and beans stay away from children under three and pets.
PUZZLE DAY CHECK
- Read the question.
- Tap your answer.
Each player brings at least 6 cards. Which inequality says that?
Which inequality does this number line show?Which values of x make 3x + 1 > 10 true?
Which value of x makes x ≤ 4.5 true: 4, 5, 6?
Draw your family number line with one two-step card solved: the circle, the ribbon and the numbers people stood on.
Great walking, crew. Next week the balance comes back with two steps to undo.