Download Which big idea do you think is highlighted

LGP BLM 1.2 (VERY DRAFTY – NOT FORMATTED YET)
Which big idea(s) do you think are highlighted by each question?
Q Number
1.
Question
The study of the
mathematical structure of
patterns is a foundation to
algebraic reasoning.
Big Idea 1
(written out)
Big Idea 2
(written out)
Big Idea 3
(written out)
Big Idea 4
(written out)
1. Consider the linear growing pattern that begins with 2, 5, 8.
a) How do you know that 11 is the next term?
b) How do you know that 107 is a term in this pattern?
c) Did you find the answers to parts a and b in the same way?
2. How do you know that the 100th term in the linear growing pattern 5, 9, 13,
17, … is 401?
3.
4.
2.
The mathematical structure of
a linear growing pattern (e.g.,
numeric, graphical,
geometric, algebraic) can be
represented in different ways.
5.
1. Which of the representations makes it easier for you to see that the rate of
growth is 4 tiles at a time.
Merge Big Ideas 2 and 3
Different representations
highlight different
characteristics and can serve
different purposes.
2.
1. Which of the above representations would you use to tell someone the
number of tiles in position 100.
3. Jaclyn found 6n –1 written on the board when she came into class.
On her table were pattern blocks, toothpicks, and interlocking cubes.
Use one of these materials to represent the first three terms of the
pattern created by the general term 6n –1. Explain why you chose this
representation.
4.
4.
Linear growing patterns can
be distinguished from other
patterns by the way they
grow.
1. Here are three patterns, which two do you think are most alike and why?
a. 3, 5, 7, 9, …
b. 3, 6, 9, 12, …
c. 3, 6, 10, 15, …
2. How are linear growing patterns different than other types of growing
patterns.
3. A pattern starts with 4 and the fifth number is 24. What could the in-between
numbers be?
4, __, __, __, 24.
5.
Two pieces of information
about a linear growing pattern
can be sufficient information
to fully describe the pattern.
1. A linear growing pattern has the number 1000 as one of its terms
can you tell it grows quickly or slowly? What other piece of
information could help you answer the questions.
2. Roll a six-sided die <picture> to determine the first term in your growing
number pattern. Roll again to determine the amount to add to each term. If
your friend was using a 12-sided die, how might your patterns be the same
or different?
Others
1. A number pattern can be described by a table of values. The first number tells the position of the number in
the pattern, and the second number is the pattern value. For example, the pattern 2, 4, 6, 8, …. Is
described by:
1
2
2
4
3
6
4
8
5
10
6
12
Then the tale of values can be graphed; the x-coordinate is the position number and y-coordinate is the
term value. Suppose the graph for a pattern goes through (2, 3). What could the pattern be?
Draw pictures that might help someone predict the next four terms of the pattern 1, 4, 9. 16, …
Make a linear growing pattern using blue and yellow tiles.
Create a linear growing pattern that begins with 3, 5, …. Represent the pattern in different ways.
The third term in a linear growing pattern is 6. What could the pattern be?
In a group of people, each person shakes hands with each other person exactly once. How many
handshakes will there be if there are 3 people? 4 people? 11 people?
7. Choose two numbers. Call them p and q. A pattern’s rule is: multiply the term number by p and add q. Can
the 100th term be 900 greater than the 10th term? If so, how? If not, why not?
8. A student company charges a $5 flat fee plus $3 per window to wash windows.
a. How much more would someone pay to have 35 windows washed than 24 windows?
b. Might someone have to pay exactly $87 to have their windows washed? Explain.
9.
2.
3.
4.
5.
6.