Download BLM LGP 3.1 Sorting Open and Closed Questions

BLM LGP 3.1: Sorting Open and Closed Questions
Cut questions into strips and provide each group with a complete set for sorting
into “OPEN” and “CLOSED” questions.
OPEN QUESTIONS
Question:
a) Complete the following pattern.
2, 4, …, …, …, …
b) Describe your pattern using words.
c) Can you describe the pattern using an algebraic expression? Explain why
you can or cannot.
Question:
A pattern is built by adding pairs of terms to get the next term. There is a 10
somewhere between the fourth term and the tenth term. What could the
pattern be? Think of as many possibilities as you can.
Question:
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 table of values can be graphed; the x-coordinate is the position
number and the y-coordinate is the term value. Suppose the graph for a
pattern goes through (2, 3). What could the pattern be?
Question:
Draw pictures that might help someone predict the next four terms of the
pattern 1, 4, 9, 16, …
Question:
An expression involving the variable k has the value 10 when k=4. What
could the expression be?
TIPS4RM: CODE/Grade #: Unit #
June 22, 2017
1
Question:
If s=4 and t=5, these statements are true:
3(s + t) = 27
2s + 3t = 23
2t – 2s = 2
Choose values for p and q. Write three true statements using those variables.
See if a partner can figure out what your values are.
Question:
Create a variety of equations for which the solution is n=10.
a) How did you create your equations?
b) How do you know that your equation is equivalent to the equation
n=10?
Question:
a) Sketch a graph to represent the relationship between the amount of
cereal in a bowl and time, if starting to eat slowly and then speed up in
order to get to school on time.
b) How does the graph show when the person is eating slowly? Faster?
c) Why is the graph a good way to show what happened?
Question:
You are gathering data in school cafeteria from 8:00 a.m. to 3 p.m. Sketch a
graph that tells a story about the number of pop cans in a vending machine
over that time. Write a paragraph that tells the same story in words.
CLOSED QUESTIONS
Question:
The pattern rule for a sequence is “Start at 10, double the number before this
one, and subtract 1.” Write the first five numbers in the sequence.
Question:
a) Describe the rule for this sequence: 100, 99, 97, 94, 90, …
b) Write the next three numbers.
TIPS4RM: CODE/Grade #: Unit #
June 22, 2017
2
Question:
Use a table of values to find the number
of toothpicks you would need to build
the 7th figure. Explain your thinking.
Question:
What is the tenth number in this pattern:
24, 21, 18, 15, …
a) Describe your pattern using words.
b) Can you describe the pattern using an algebraic expression? Why can
you or why can’t you?
Question:
Heather wants to make 250 origami peace cranes
for a school display. She makes 12 cranes the first
day, 15 cranes the second day, 18 cranes the third
day, and so on. If she continues this pattern for 10
days, will she reach her goal of 250 peace cranes?
Question:
a) Make a scatter plot to represent this toothpick
pattern.
b) How many toothpicks would you need to make
the 9th figure in the sequence?
c) Which figure in the sequence could you make
with 22 toothpicks?
Question:
a) Which part of this pattern changes?
b) Use an algebraic expression to describe
the number of tiles in terms of the figure
number.
TIPS4RM: CODE/Grade #: Unit #
June 22, 2017
3
Question:
a) Complete the table of values for the sequence shown.
Term Number
(figure number)
Picture
Term Value (number
of squares)
2
1
2
3
4
5
b) Create an algebraic expression for the nth term of the sequence.
c) Use your algebraic expression to calculate the 30th term in the sequence.
Question:
a) Make a table of values that shows the total
number of cubes in the first five figures of
this staircase pattern.
b) Write an algebraic pattern rule.
c) Calculate the number of cubes you would
need to build the 10th figure in this staircase
pattern.
Question:
Match each algebraic equation with
the colour of its scatter plot.
a) y = 3x
b) y = 3x + 2
c) y = 3x - 2
TIPS4RM: CODE/Grade #: Unit #
June 22, 2017
4
Question:
Find the equation of the line that passes through (-4,2) and (6,2).
Question:
In a marble machine, the number of marbles inputted and outputted were
recorded. One boy put in 1 marble and got back 3 marbles. One girl put in
9 marbles and got back11 marbles and so on. Here are some other inputs
and outputs.
Input
Output
1
3
9
11
2
4
6
8
30
32
3
5
21
23
What is the rule?
Question:
The shapes shown below are made with toothpicks. Look for patterns in the
number of toothpicks in the perimeter of each shape.
Shape 1
Shape 2
Shape 3
Shape 4
a) Use a pattern from the shapes above to determine the perimeter of the
fifth shape in the sequence. Show or explain how you arrived at your
answer.
b) Write a formula that you could use to find the perimeter of any shape n.
Explain how you found your formula.
TIPS4RM: CODE/Grade #: Unit #
June 22, 2017
5