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Expressions and Equations 6-8 / Week 07 / Puzzle Day
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Week 07 · Two Quantities That Change Together

Puzzle Day

Puzzle Day: guess my rule
// Inputs, outputs and the rule machine
⏱ about 20 min

Puzzle Day: Guess My Rule

Saturday morning the orange box sits in the middle of the kitchen table, slot facing the family.

"Puzzle Day," Raven says. "Everyone takes a turn as rule keeper. The rest of us feed inputs and guess."

Rocket slides in a 4. A 10 comes out. He slides in a 6. A 14 comes out.

"What do you notice about the jump?" Raven asks. "Input up 2, output up 4," Rocket says. "Times 2. Then plus 2."

Nova hovers above the box, her light on the output card. "Check it with a third input before you shout," she says.

Rocket slides in a 10. Out comes 22. "Times 2 plus 2!" Nova hums. "Now you keep the rule."

  1. Two quantities change together. The one you choose is independent, and the one that follows is dependent.
  2. A function is a rule that gives exactly one output for every input.
  3. A table, ordered pairs (input first), a graph and an equation are four views of one rule.
  4. d = 4t: distance depends on time, 4 meters for every second, and (0, 0) is on the line.
  5. Read a rule from a table: the output change per step gives the multiplier, and the start gives the plus.
◇ FAMILY GUESS MY RULE
Set the box on the table. The rule keeper hides a rule in the notebook, like × 3, + 8 or × 2 + 2.
Each guesser feeds one input card. The keeper sends out the output card. Record every pair in a table.
After four pairs, each guesser writes the rule as an equation. Check it against every row before announcing.
Plot the pairs on graph paper, input across and output up. Do they line up?
Swap roles until everyone has kept a rule. Try one rule with a head start.
For a grown-up
This week your student named independent and dependent variables and wrote rules as equations like d = 4t.
Ask them to explain how they can tell × 2 + 2 from + 6 using two inputs. The jump in the output tells the multiplier.
A grown-up cuts the box slots. Cards and beans stay away from children under three and pets.
Safety first
A grown-up does any cutting. Scissors only.
Keep cards and small counters away from children under three and pets.
PUZZLE DAY CHECK
  • Read the question.
  • Tap your answer.
The box gave (4, 10), (6, 14), (10, 22). Which equation is the rule?
The rule is × 2 + 2. What comes out when 7 goes in?
Grandpa's machine: (1, 9), (2, 10), (3, 11), (4, 12). Is the output a function of the input?
A guesser chooses an input card, and the keeper's output follows the rule. Which is the independent variable?
Puzzle Day checkTrue or false?
Two inputs are always enough to be sure of a rule.?
In (4, 10), the input is 4.?
A rule with a head start, like × 2 + 2, is a function.?
WHY THIS EXERCISEChecking a guess against every row is what makes a rule trustworthy.
Draw the family's best round: the table of pairs, the graph and the rule written on the box.

Great puzzling, crew. Next week: slope, the steepness of a line, measured on a ramp.

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