Download 6patternsa - Logan Elm Schools

Grade 6
Patterns, Functions & Algebra Answers
Open Response Question 9
Use the picture below to answer question 9.
1
Marion wants to rent a canoe to go out on a lake. The cost is $2.00 plus $1.50 for each
hour.
a. Make a table showing how much it would cost to rent a canoe for 1, 2, 3, and 4
hours.
b. Using numbers, symbols, and the variable n, write an expression for how much it
would cost to rent the canoe for n hours.
c. Marion has $14.00. What is the greatest number of hours she can rent the canoe?
Show your work or explain how you found your answer.
Scoring Guide
Score
Description
4
Student demonstrates comprehensive understanding of a pattern in a real life
situation by consistently identifying correct extensions of the pattern,
generalizing the pattern using an algebraic expression, and finding and
explaining a solution to a problem related to the pattern.
3
Student demonstrates general understanding of a pattern by identifying the
correct
extension(s), generalizing the problem, and finding and explaining a solution to
a problem related to the pattern with minor errors.
2
Student shows basic understanding of the concept of the pattern by identifying
correct extension(s) and/or generalizing the pattern.
1
Student shows minimal understanding of the pattern.
0
Response is incorrect or contains some correct work that is irrelevant to the skill
or concept being measured.
Blank No response
2
3
4
Open Response Question 23
Daniel has invented a new game with its own money system. The money system has the
following three coins:
To challenge his friends to find the relationship among the values of the coins, he gave
them the following three coins:
Clue 1:
Clue 2:
is the same as
is the same as
a. Use Clue 1 to find how many rectangles are worth the same as 1 triangle.
Use words or pictures to explain your reasoning.
b. Use Clues 1 and 2 to find how many triangles are worth the same as 1 circle.
Use words or pictures to explain your reasoning.
c. If 1 rectangle is worth 15 cents in U.S. money, what is the value in U.S. money of
the other two coins?
Explain how you found your answer.
Scoring Guide
5
Score
Description
4
Student demonstrates thorough understanding of models of simple linear
situations by correctly solving equations represented by models, accurately
explaining the process, and evaluating the expressions for given values.
3
Student demonstrates general understanding of simple linear situations by
solving equations, explaining the process, and evaluating the expressions for
given values, with only one minor error.
2
Student shows basic understanding of the concept of simple linear situations by
solving equation(s), and/or the expression(s) for given values.
1
Student shows minimal understanding of the simple linear situations.
0
Response is incorrect or contains some correct work that is irrelevant to the skill
or concept being measured.
Blank No response
6
7
8
9
10
11
Question 31
A booth at the State Fair is offering pony rides for children. The table below shows the
relationship between the number of rides a child takes and the cost of the rides.
Pony Rides
Number
Cost
1
$2.00
2
$2.50
3
$3.00
4
$3.50
5
?
10
?
a. If the pattern continues in the same way, what is the cost for 5 rides and the cost
for 10 rides?
b. Francie had $5.50 to spend. What is the greatest number of rides she could
take? Explain how you found your answer.
c. Write an expression using n to show the cost of n rides.
Scoring Guide
12
Score
Description
4
The response shows a comprehensive understanding of linear equations and how
to solve them and represent them with rules and words.
3
The response shows a general understanding of linear equations and how to
solve them and represent them with rules and words.
2
The response shows a basic understanding of linear equations.
1
The response shows a minimal understanding of linear equations.
0
The response is incorrect or contains some correct work that is irrelevant to the
skill or concept being measured.
Blank No response.
2002 MCAS
Grade 6 Mathematics
Question # 31 - Score Point 4
13
14
15