Download 6th Grade – Day 1

The First Ten Days – 6th Grade MEAP Review
Day 2
Focus:
Find prime factorizations of whole numbers
N.MR.05.07
Understand fractions as division statements; find equivalent fractions
N.ME.05.10
N.ME.05.11
Express, interpret, and use ratios; find equivalences
N.MR.05.22
N.ME.05.23
Vocabulary:
composite numbers, equivalent fractions, equivalent ratios, exponent, exponential notation,
factors, fraction, least common denominator, prime factorization, prime numbers, ratio,
square numbers, whole numbers.
Connection: Yesterday, as you recall, we worked on multiplication and division of whole
numbers and the understanding of division of whole numbers. Today we will start by
reviewing factor trees and move into decimal, fraction, and percentage review.
Teaching Point 1:
Prime Numbers
A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or
itself. The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ....
http://www.mathsisfun.com/prime-composite-number.html
http://www.mathsisfun.com/prime_numbers.html
Factors
"Factors" are the numbers you multiply together to get another number:
Prime Factorization
"Prime Factorization" is finding which prime numbers you need to multiply together to get
the original number.
Example 1
What are the prime factors of 12? It is best to start working from the smallest prime
number, which is 2, so let's check:
12 ÷ 2 = 6
But 6 is not a prime number, so we need to factor it further: 6 ÷ 2 = 3
And 3 is a prime number, so: 12 = 2 × 2 × 3
As you can see, every factor is a prime number, so the answer must be right - the
prime factorization of 12 is 2 × 2 × 3, which can also be written as 22 × 3.
Example 2
What is the prime factorization of 147? Can we divide 147 evenly by 2? No, so we
should try the next prime number, 3: 147 ÷ 3 = 49
Then we try factoring 49, and find that 7 is the smallest prime number that works:
49 ÷ 7 = 7
And that is as far as we need to go, because all the factors are prime numbers.
147 = 3 × 7 × 7 = 3 × 72
Why?
A prime number can only be divided by 1 or itself, so it cannot be factored any
further!
Every other whole number can be broken down into prime number factors.
There is only one (unique!) set of prime factors for any number.
http://www.mathisfun.com/numbers/prime-factorization-tool.html
Teaching Point 2:
Equivalent Fractions
Equivalent Fractions have the same value, even though they may look different. Example:
These fractions are really the same: ½= 2/4= 4/8
Why are they the same? When you multiply or divide both the top and bottom by the same
number, the fraction keeps its value. The rule to remember:
What you do to the top of the fraction
you must also do to the bottom of the fraction!
So, here is why those fractions are really the same:
×2
×2
1
2
=
×2
2
4
=
×2
4
8
And visually it looks like this:
1/2
2/4
4/8
=
=
Here are some more equivalent fractions, this time by dividing:
÷3
÷6
18
36
6
12
1
2
÷3
÷6
By dividing until we can't go any further, then we have simplified the fraction.
A Chart of Fractions: http://www.mathsisfun.com/numbers/fraction-decimal-chart.html
Understand Fractions as Division Statements
Quick Definition: An Improper fraction has a
numerator (top number) larger than or equal to
the denominator (bottom number),
such as 7/4
Also means 7 ÷4=
7/4
(seven-fourths or seven-quarters)
A Fraction (such as 7/4) has two numbers:
Numerator
Denominator
The top number is the Numerator.
The bottom number is the Denominator, or the number of parts the numerator is divided into.
Three Types of Fractions:
Proper Fractions: The numerator is less than the denominator
Examples: 1/3, 3/4, 2/7
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: 4/3, 11/4, 7/7
Mixed Fractions:
A whole number and proper fraction together
Examples: 1 1/3, 2 1/4, 16 2/5
Connections: We will recall the interconnectedness between fractions, decimals, and
percentages by talking about when we might need to express a fraction as a decimal, or a
percentage as a fraction, or visa versa. We will also think about different ways to express
ratios and find equivalent ratios.
Teaching Point 3: Define what a ratio is and three different ways to express a ratio. Explain
what an equivalent ratio is and when and where you would use one.
Active Engagement 1: (Play Memory)
1. As a group, define a ratio.
2. Pair the students up. Have the students come up with ratios in the room (5 boys to 4
girls, 10 blue chairs to 5 green chairs, etc.).
3. Students will record the ratios in the three different formats and an equivalent ratio on
big grid paper provided by the teacher.
4. Have the students cut the grid into individual squares and flip over
Students will play Memory with the grid pieces.
Web Support:
Visual Fractions http://www.visualfractions.com/
National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vLibrary.html
Fraction & Decimal review http://www.quia.com/jg/65724.html
Arcademic Skill Builders http://www.arcademicskillbuilders.com/
Eratosthenes' Sieve http://www.hbmeyer.de/eratosiv.htm
Day 2 – MEAP Released Items
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which expression shows the price factorization of 36?
a.
b.
c.
d.
____
2. For which number is
the prime factorization?
a. 48
b. 36
c. 24
d. 18
3. Which fraction has the same meaning as
?
a.
____
b.
c.
d.
____
4. Which statement means the same as ?
a.
b.
c.
d.
3 minus 8
8 divided by 3
3 divided by 8
3 multiplied by 8
____
5. Which shape below appears to be exactly
shaded?
a.
b.
c.
d.
____
6. Pat needs to use
cup of sugar and
cup of flour to make a recipe. Which size measuring cups
would hold these exact amounts?
a.
cup for the sugar and cup for the flour
b.
c.
d.
cup for the sugar and
cups for the sugar and
cup for the sugar and
cup for the flour
cups for the flour
cup for the flour
____
7. Which of the following is equivalent to ?
a.
b.
c.
d.
____
8. In John’s class,
of the students had pizza for lunch. What percent of the students had pizza for
lunch?
a. 12%
b. 20%
c. 50%
d. 75%
____
9. In a bag of marbles, 0.25 of the marbles are green. What percent of the marbles are green?
a. 0.25%
b. 2.5%
c. 25%
d. 250%
____ 10. Ralph bought a package of assorted colored paper, of which
of the papers are blue. What percent
of the papers are blue?
a. 4%
b. 40%
c. 52%
d. 75%
____ 11. Which percent is equivalent to
a.
b.
c.
d.
10%
12%
20%
80%
____ 12. Exactly
a.
b.
c.
d.
?
0.05%
1%
5%
20%
of the students in Mr. Bank’s class have a bird. What percent of his student have a bird?
____ 13. In a class of 25 students, 10 ran a race in nine minutes or less. What percent of the students ran the
race in nine minutes or less?
a. 5%
b. 10%
c. 25%
d. 40%
____ 14. Mr. Kuo ordered sandwiches to serve at the school open house. He ordered 50 cheese, 35 vegetable,
40 ham, and 60 turkey sandwiches. The clean-up committee found 9 cheese, 5 vegetable, 6 ham, and
7 turkey sandwiches left over. According to the ratio of sandwiches left over to sandwiches ordered,
which was the most popular type of sandwich?
a. ham
b. turkey
c. cheese
d. vegetable
____ 15. For every 6 boys in Mrs. Getty’s class, there are 7 girls. Which shows three correct ways to express
the ratio of boys to girls?
a.
; 7:6; 7 to 6
b.
c.
d.
; 6:13; 6 to 13
; 6:7; 6 to 7
; 13:6; 13 to 6
Day 2 - 6th Grade First Ten Days
Answer Section
MULTIPLE CHOICE
1. ANS: A
OBJ:
STA: N.MR.05.07
2. ANS: A
OBJ:
STA: N.MR.05.07
3. ANS: A
OBJ:
STA: N.ME.05.10
4. ANS: C
OBJ:
STA: N.ME.05.10
5. ANS: D
OBJ:
STA: N.ME.05.10
6. ANS: A
OBJ:
STA: N.ME.05.11
7. ANS: D
OBJ:
STA: N.ME.05.1
8. ANS: C
OBJ:
STA: N.MR.05.22
9. ANS: C
OBJ:
STA: N.MR.05.22
10. ANS: B
OBJ:
STA: N.MR.05.22
11. ANS: C
OBJ:
STA: N.MR.05.22
12. ANS: C
OBJ:
STA: N.MR.05.22
13. ANS: D
OBJ:
STA: N.MR.05.22
14. ANS: B
OBJ:
STA: N.ME.05.23
15. ANS: C
OBJ:
STA: N.ME.05.23
Find price factorization of #s, show exponentially
Find price factorization of #s, show exponentially
Understand and show fractions as a statement of division
Understand and show fractions as a statement of division
Understand and show fractions as a statement of division
Compare two fractions using common denominators
Compare two fractions using common denominators
Express fractions and decimals as percentages
Express fractions and decimals as percentages
Express fractions and decimals as percentages
Express fractions and decimals as percentages
Express fractions and decimals as percentages
Express fractions and decimals as percentages
Express ratios in the forms a to be, a:b, a/b
Express ratios in the forms a to b, a:b, a/b