[Solutions are shown after the activities]
TASK 1: What do you See?
EXTENSIONS
Build a new growing pattern
Ask students to build their own growing pattern and complete a table of values.
Algebraic expressions
The train patterns below represent linear equations students may study in grades 8-9:
- y = 3x + 3
- y = x + 1
- y = 2x + 1
TASK 2: Complete the graph
TASK 3: What is different?
EXTENSION
Model and then ask students to investigate the simulation at https://imaginethis.ca/mathncode/sims-growpatt.html
TASK 4: How does the pattern grow?
SOLUTIONS
TASK 1: What do you see?
What students might see:
1. Growing patterns on train cars
Students may notice the growing patterns of blue and pink blocks on train cars.
Give students link cubes, or chart paper and dabbers. Ask students to reproduce the patterns.
- How do the patterns grow?
- What changes? What stays the same?
- What would be on the 5th train car?
- On the 10th? On the 100th?
2. Bar graphs
Students may notice the bar graphs made of blue and pink pebbles.
Give students link cubes, or chart paper and dabbers. Ask students to reproduce the bar graphs. What creates growth? The blue or pink pebbles? (Students will revisit this in Activity 3.)
TASK 2: Complete the graph
Young students love to work with large numbers. Don’t hesitate to ask them how may blocks might be needed to build the 1000th stage.
TASK 3: What is different?
Both bar graphs represent the pattern shown below.
The pink pebbles are on top of the blue pebbles in the first bar graph, and vice versa in the second bar graph.
This helps students see that it is the blue pebbles (whose number varies or increases) that make the pattern grow at each stage.
TASK 4: How does the pattern grow?
This pattern represents the growth of bacteria, which grow by dividing themselves in two.
So, 2 bacteria lead to 4, which lead to 8, which lead to 16.
This doubling pattern, shown in green on the right, is called exponential growth. Its algebraic expression is 2x, where x is the stage number.
Dr. Lindi Wahl, applied mathematician at Western University, builds and discusses this growing pattern in the 5th video, How Bacteria Grow, at https://imaginethis.ca/lindi-wahl.
Next
Coding puzzles … https://learnx.ca/mt/coding-growing-patterns