8.1.1: Going Around the Curve
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1 8.1.1: Going Around the Curve Experiment A A particular mould grows in the following way: If there is one blob of mould today, then there will be 4 tomorrow, 9 the next day, 16 the next day, and so on. Model this relationship using linking cubes. Find the relationship between the side length and the number of cubes. What type of relationship do you think exists between the side length and the number of cubes? 1. Build the following sequence of models, using the cubes. Side Length of Cubes 0 0 TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 1
2 8.1.2: Going Around the Curve Experiment B Jenny wants to build a square pool for her pet iguana. She plans to buy tiles to place around the edge to make a full play area for her pet. Model the relationship, comparing total play area (pool combined within the edging) to the side length of the pool, using linking cubes. Find the relationship between the side length of the pool (shaded inside square) and the total play area. What type of relationship do you think exists between the side length and the play area? Note: The pool is the shaded square, the tiles are white. Side Length Total Play Area 1 TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 2
3 8.1.3: Going Around the Curve Experiment C A particular mould grows in the following way: If there is one blob of mould today, then there will be 3 tomorrow, and 6 the next day. Model this relationship using linking cubes. Find the relationship between the number of cubes in the bottom row and the total number of cubes. What type of relationship do you think exists between the number of cubes in the bottom row and the total number of cubes? of Cubes Total in the Bottom of Cubes Row TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 3
4 8.1.4: Going Around the Curve Experiment D Luisa is designing an apartment building in a pyramid design. Each apartment is a square. She wants to know how many apartments can be built in this design as the number of apartments on the ground floor increases. Model this relationship, using linking cubes. Find the relationship between the number of cubes in the bottom row and the total number of cubes. What type of relationship do you think exists between the number of cubes in the bottom row and the total number of cubes? of Cubes Total in the Bottom of Cubes Row 0 0 TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 4
5 8.1.5: Going Around the Curve Experiment E Liz has a beautiful pond in her yard and wants to build a tower beside it using rocks. She is unsure how big she will make it and how many rocks she will need. She is particularly concerned to have the nicest rocks showing. Model the relationship comparing the length of the base to the number of visible rocks using linking cubes. Find the relationship between the number of cubes on the side of the base and the total number of unhidden cubes. What type of relationship do you think exists between the length of the side of the base and the number of visible cubes? Length of Side of Base Total of Unhidden Cubes TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 5
6 TIPS4RM: Grade 10 Applied: Unit 4 Graphical Models and Solutions 6
5.1.1: Going Around the Curve
5.1.1: Going Around the Curve Experiment A A particular mould grows in the following way: If there is one blob of mould today, then there will be 4 tomorrow, 9 the next day, 16 the next day, and so on.
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