Download Patterns In Mathematics Check-Up

Grade 6 Mathematics
Name:
________________________
Date: ____________________
Patterns In Mathematics
Check-Up
Our Unit 3 Test will be given on Tuesday, December 3 and will test these
outcomes:
Specific Curriculum Outcome
6PR1 Demonstrate an understanding of the relationships within tables of values to solve
problems.
6PR3 Represent generalizations arising from number relationships, using equations with
letter variables.
6PR4 Demonstrate and explain the meaning of preservation of equality, concretely and
pictorially.
Selected Response
Table of Values
Week
Money
Number Saved
1
$2
2
$5
3
$8
4
??
5
$14
6
$17
1. What is the value of the unknown term in the table of values? PR1.7 ; PR1.9
a. $11
b. $13
c. $15
d. $19
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Grade 6 Mathematics
2. What is the algebraic expression for the above table? PR1.5; PR1.8
a. 2n+1
b. 2n + 4
c. 3n - 1
d. 3n - 4
3. What is the correct expression for the following situation;
PR3.1
Colin had some strawberry Twizzles and gave Patsy two.
a. n-2
b. 2n
c. 2n +2
d. n+2
4.
Weeks Worked
Salary($)
1
25
2
52
3
77
4
102
There is an error in the above table. Identify the week in which the error
occurred.
PR1.2
a. Week 1
b. Week 2
c. Week 3
d. Week 4
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Grade 6 Mathematics
5. Which mathematical statement represents the algebraic expression 2n + 6?
PR3.2
a. Double a number
b. Six more than twice a number
c. Five more than a number
d. Six more than a number
6. What equation matches the model below? PR4.1
n
n
n
a. 3 + 4n = 10
b. 3n = 6
c. 3n + 4 = 10
d. n=4
7.
What equation is equivalent to n + 2 =6 ?
PR4.1
a. 2 + n = 8
b. n + 3 = 7
c. 2 n = 6
d. n + 4 = 8
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Grade 6 Mathematics
Match each of the following situations with the correct expression:
8. _____
Five less than double a number
a. 3n-1
9. _____
Five more than a number
b. 2n+6
10._____
Five less than a number
c. 6n-2
11._____
A number less than five
d. 5 + n
12._____
Six more than twice a number
e. 2n-5
13._____
One less than triple a number
f. 5-n
14._____
Five more than double a number
g. n-5
15._____
Two less than six times a number
h. 5+2n
Provide the next three numbers in each of these series of numbers:
16. 4,8,12,16,20, ____, _____, _____
17. 40, 37, 34, 31, , ____, _____, _____
18. 0, 1, 1, 2, 3, 5, 8, 13, , ____, _____, _____
19. 5, 8, 7, 10, 9, 12, 11, 14, 13, , ____, _____, _____
20. Sequence number _____ of these four sequences is known as the Fibonacci
sequence.
WEBSITE LINK ACTIVITY:
The Fibonacci Golden Ratio often appears in nature. Follow
the link on our class math page to read about the golden ratio of 1.618… . List four of the 15
examples here; use complete sentences so that someone who has never heard of the Fibonacci
Golden Ratio can gain some basic understanding of how this mathematical sequence appears in
nature.
The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and each number is the
sum of the two numbers that come before it. How a population of rabbits grows follows this pattern.
The number of petals in a flower consistently follows the Fibonacci sequence. The lily has three petals,
and buttercups have five petals.
If you draw a growing group of squares with
measurements that follow the Fibonacci sequence
(1,1,2,3,5,8…) and then use a compass to draw an arc in each
square, the arcs fit together to make a spiral. Spiral galaxies
like our own Milky Way have this golden spiral. Pine cones and
seed heads also spiral out from the center. Sunflower seeds grow in a spiral. Snail shells and nautilus
shells grow in spirals. These area just some of the ways that this number sequence appears in nature.
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Grade 6 Mathematics
Written Response
1.
Number of
Number of
Squares
Toothpicks
1
4
2
7
PR1.1, PR1.3.PR1.5, PR1.8
13
5
a. Complete the table filling in the missing terms.
b. Look at the table of values and the change in each variable and model it
pictorially (draw the picture).
c. Describe the pattern which identifies the number of toothpicks and
then write the rule as an algebraic expression.
Pattern Rule
Algebraic Expression
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Grade 6 Mathematics
2. a. Complete the table of values.
PR3.1, PR3.2
b. Write an algebraic expression that would help you find the number of
sides for any number of hexagons.
c. If you had 50 hexagons, how many sides would you have? Explain how you
know.
# Hexagons
# Sides
1
6
2
12
3
18
4
5
6
7
8
9
10
If I had 50 hexagons I would substitute in 50 for h (the number of hexagons). Then
I multiply 6 x 50 = 300 sides.
I can check to be sure my answer is correct by using any three numbers of
hexagons to check if I get the correct answer:
If I have 6 hexagons, then 6h = 6x6 = 36 sides, that is the same number I got in my
table pattern. If I have 8 hexagons, then 6h = 6x8 = 48 sides, that is the same
number I got in my table pattern. If I have 9 hexagons, then 6h = 6x9 = 54 sides,
that is the same number I got in my table pattern.
Now that my algebraic expression was used to confirm three of my table
pattern answers, I know that I have the correct expression.
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Grade 6 Mathematics
Patterns
Constructed Response
Name: _________________________
Date: _____________
1. The following table of values shows the number of tables in the G. C. Rowe
cafeteria. If the pattern rule for the number of chairs is ‘start at 6 and increase
by 4 each time’; complete the table.
Number of tables (n)
1
2
3
4
5
Number of chairs
6
10
14
18
22
a. Model the pattern pictorially ( 3 tables)
b. Write the rule as an algebraic expression
c. Using mathematical language describe the relationship between the
number of chairs and tables.
Two more than four times the number of tables.
OR Four times the number of tables plus two more.
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Grade 6 Mathematics
d. How many chairs would be needed to seat 30 students in the cafeteria?
How do you know?
I can use the table and keep doing my increasing pattern until I
reach or pass 30 chairs.
Number of tables (n)
1
2
3
4
5
Number of chairs
6
10
14
18
22
Answer: I would need 7 tables to seat 30 students in the cafeteria.
I can check my answer and be sure that I know I am correct by using the algebraic
expression to check.
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