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Expressions and Equations 6-8 / Week 09 / Puzzle Day
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Week 09 · Linear Functions

Puzzle Day

Puzzle Day: graph stories
// Rate of change, starting value, and graphs that tell a story
⏱ about 20 min

Puzzle Day: Graph Stories

Saturday morning Raven tapes a big sheet of graph paper to the kitchen wall. "Puzzle Day. Graph stories."

"One person tells a short story about a walk or a jug," Rocket explains. "Everyone else sketches the graph."

Raven starts. "I walk to the mailbox at a steady pace. I stop to read a card. Then I jog home."

"What do you notice about the middle part?" she asks. "Flat," Rocket says. "Distance does not change while you read."

Nova hovers beside the wall, her light on the sketches. "Now the other way," she says. "Here is a graph. Tell its story."

She shows a straight line falling from 12 to 0. "The draining jug!" Rocket says. Nova hums. "Or a candle, or a walk home."

  1. A linear function is y = mx + b: m is the rate of change and b is the initial value. Its graph is a straight line.
  2. Compare two functions in any form by finding each rate of change and initial value.
  3. Not every function is linear. The perimeter of a square, 4s, is linear. The area, s², bends.
  4. From two points: rate = rise ÷ run, then step back to x = 0 for the start.
  5. Describe a graph from left to right: increasing or decreasing, linear or not, and where it is flat.
◇ FAMILY GRAPH STORIES
Take turns telling a short story about a walk, a filling cup or a draining jug. Everyone else sketches the graph.
Compare the sketches. Agree on where the graph should climb, fall or stay flat.
Then reverse it: one person draws a graph, and the others tell its story in words.
Pick one steady part of a story and give it numbers. Write its rule y = mx + b with a rate and a start.
Hang the best story and its graph on the Puzzle Post wall.
For a grown-up
This week your student compared linear functions by rate of change and initial value and described graphs in words.
Ask them to tell the story of a straight line that falls from 12 to 0 in two different ways.
Water stays over a tray or the sink. Plastic jugs only, and spills are wiped at once.
Safety first
Tape graph paper to a wall, not the floor, so no one trips. Water work stays over a tray or the sink.
Plastic cups and jugs only. Wipe spills at once.
PUZZLE DAY CHECK
  • Read the question.
  • Tap your answer.
Raven jogs home and her distance from home falls. Is that part of her graph increasing or decreasing?
Nova's graph falls from (0, 12) to (6, 0). What is its rate of change?
Cup A rises 2 cm a minute from 3 cm. Cup E's graph passes through (0, 5) and (4, 9). Which has the greater initial value?
A speeding-up walker gave (0, 0), (1, 2), (2, 6). Do these points lie on one straight line?
Puzzle Day checkTrue or false?
A flat part of a distance graph means the walker has stopped.?
A graph falling from 12 to 0 could be a draining jug.?
A speeding-up walker makes a straight line.?
WHY THIS EXERCISETelling a graph's story in words is the skill that makes every graph readable.
Draw the graph of Raven's walk to the mailbox: steady out, a flat stop, then a steeper jog home.

Great storytelling, crew. Next week: solving linear equations, with envelopes on both sides of the balance.

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