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:
- one block, two blocks and three blocks for toddlers;
- four blocks, five blocks and six blocks for elementary school children;
- seven blocks, eight blocks and nine blocks for older children, 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 the faces of the blocks in the towers. All visible
square faces on all towers must be decorated.
If they want two students to decorate one square face, how many
students are needed to decorate the tower built with 23 blocks?
Resources and Materials :
- interlocking cubes
- blank table of values
- scientific calculators
Group students into teams and ask them to choose a strategy that will help them determine the answer to this question. Remind them to record their steps as they work in order to present their strategy to the class.
Students use a strategy and model of their choice to solve the problem. The teacher circulates among the teams and asks questions to three teams who have been 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 of Learning
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 : L’@telier - Ressources pédagogiques en ligne (atelier.on.ca).