C1.3 Determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns.
Activity 1: Climbing Walls
Before Learning
Present students with the following scenario:
Volunteers from a local association responsible for installing youth playground equipment in city parks recently built towers out of large cement blocks to be used as climbing walls, and there are towers for all ages:
- Toddler Tower consists of rows with one block, two blocks and three blocks;
- Elementary School Children Tower consists of rows with four blocks, five blocks and six blocks;
- Older Children Tower consists of rows with seven blocks, eight blocks and nine blocks, and so on up to 25 blocks.
Using interlocking cubes, invite students to build the towers. Have them record the number of visible square faces on all sides of the tower in a table of values. (Remember that the face on top of the highest cube is also visible.)
Active Learning
Add to the situation:
Park officials have chosen students from our school to decorate all the visible square faces of the blocks on the towers.
If two students are needed to decorate one square face, how many students are needed to decorate the tower built with 23 blocks?
Resources and Materials:
- interlocking cubes
- table of values template
Group students into teams to answer the question using a strategy of their choice. Reinforce for students to show their work so it can be used when they present to the class.
Circulate among the teams and identify the teams that are using different models to solve the problem.
Note: The functional relationship is the following: the number of faces (f) is the number of cubes on which we see 4 faces (c × 4) plus the top face of the tower (+ 1)
\(f = c \times 4 + 1\)
Or
\(f = 4c + 1\)
Consolidation
Each team presents its representation of the relationship and explains it.
Extension Questions:
- If the time required to decorate one side is 10 minutes, how long would it take to decorate a tower having 5 blocks?
- If you have 3 hours, how many sides can you decorate?
- The estimated cost of materials to decorate 4 faces is $10. What is the cost of materials to decorate a tower of 8 blocks?
- If our class has $100, which tower can we decorate?
- If we increase the amount of money available to buy decorating materials to $200, how many small towers can we decorate?
Source: translated from L’@telier - Ressources pédagogiques en ligne (atelier.on.ca).