Download Grade 7- Chapter 4

Grade 7- Chapter 4
Goals: Key Understandings: Students will understand that…
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There are equivalent forms for any real number.
The results of an operation depend on the types of numbers involved. Multiplying and
dividing fractions is sometimes counter-intuitive.
Essential Questions:
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What is the relationship between the position of a number on the number line and the
value of the number?
 How does identifying the types of numbers in an operation help in determining the
reasonableness of the result?
Students will know that…
Students will be able to…
 One number is divisible by another if it
 Use the divisibility rules to identify the
can be divided evenly by that number
factors of a given number. (4-1)
with no remainder.
 List positive factors for various
 We have divisibility rules that allow us
numbers.
to tell if a number would be divisible.
 List factor pairs for various numbers.
(pp. 178+179)
 A factor is a number that can be divided
into another evenly.
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You can use exponents to show
repeated multiplication.
A power has two parts: a base, the
number you will be multiplying, and an
exponent, the number of times you will
be multiplying the base. Ex: 43 = 4*4*4
You can extend PEMDAS to include
simplifying exponents as needed.
Ex: (-5)2 = -5* -5 OR +25; while -52 =
-( 5*5) OR -25. The exponent affects
only that which it is directly adjacent to.
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Rewrite expressions using exponents
instead of repeated multiplication. (4-2)
Simplify terms with exponents using
PEMDAS.
Evaluate terms with exponents using
PEMDAS.
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A prime number is a number which
can only be multiplied by itself and
one. Ex: 13 = 13*1
A composite number has more than
two factors. Ex: factors of 24= 1, 2, 3,
4, 6, 8, 12, and 24.
You can write a composite number as
a product of its prime factors. Ex: 24 =
2 * 2* 2* 3 or 23* 3. This is called prime
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Identify prime and composite numbers
and justify. (4-3)
Use a factor tree to determine the
prime factorization of various numbers
then write using exponential notation.
Use prime factorization to identify the
GCF for two numbers.
Venn diagrams can be used to
illustrate common factors.
Grade 7- Chapter 4
factorization.
 Greatest common factors or GCF’s are
the largest factors that 2 numbers
have in common. These can be used
to simplify fractions.
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 Equivalent fractions represent the
same portion of the whole, but may be
written differently. Ex: 2/4 = ½.
 You can simplify fractions by dividing
the numerator and denominator by the
same common factor. Ex: With 10/12
you can divide the numerator and
denominator by 2 to get 5/6.
 You can find equivalent fractions with
common denominators for adding or
subtracting by multiplying the
numerator and denominator by the
same number. Ex: With 2/8 + ¾ you
can multiply the numerator and
denominator in ¾ by 2 to get 6/8.
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 You can use tree diagrams or nets to
account for all possibilities.
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 A rational number is any number that
you can write in the form a/b where a
and b are integers and b is not zero.
 All numbers have a distinct position on
the real number line.
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 When multiplying powers with the same
base, just add the exponents. Ex: 23 *
24 = 27 because 23= 2*2*2 and 24=
2*2*2*2; so altogether we are
multiplying 2 by itself 7 times, or 27.
 When raising a power to a power,
multiply the exponents. Ex: (23)2 =
(2*2*2) *(2*2*2) or 26.because you’re
multiplying 2 six times.
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Find equivalent fractions by multiplying
(to find common denominators) or
dividing (to simplify). (4-4)
Simplify fractions by using the divisibility
rules.
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Solve problems by accounting for all
possibilities using a tree diagram, net,
or chart. (4-5)
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Write equivalent fractions using positive
and negative integers. (4-6)
Find, graph, and position fractions on a
number line and in an ordered list.
Evaluate fractions containing variables
then simplify.
Identify rational numbers which lie
between two given quantities.
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Simplify exponential expressions
containing powers with the same base.
(4-7)
Simplify powers of powers.
Compare exponential expressions.
Evaluate exponential expressions using
graphing calculators.
Grade 7- Chapter 4
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 When dividing exponential expressions
containing the same base, just subtract
the exponents. Ex: 23/ 22 means 2*2*2/
2*2 which equals 2/1 or 21.
 Any number to the zero power is equal
to 1. Ex: 20= 1; 100 = 1
 Any base raised to a negative power is
the reciprocal. Ex: 10-2 = 1/100 because
it means 1/10* 1/10. While b3 / b9 = b-6
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Scientific notation allows you to write
very large or very small numbers using
powers of ten. Ex: 189,750,000 =
1.8975 * 108; while 0.00001897 =
1.8975* 10-5.
Standard notation does not include
powers of ten. Ex: 1.5 * 102 = 150 in
standard notation.
Remember: when multiplying powers
with the same base, just add the
exponents. Ex: 23 * 24 = 27 because 23=
2*2*2 and 24= 2*2*2*2; so altogether
we are multiplying 2 by itself 7 times, or
27.
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Simplify rational expressions with
exponents by dividing powers with the
same base. (4-8)
Simplify expressions with integer
exponents (zero or negative).
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Translate numbers from scientific
notation to standard notation or back
again. (4-10)
 Compare and order numbers written in
scientific notation.
 Multiply numbers written in scientific
notation by combining the exponents.
 Use calculators to multiply numbers
written in scientific notation.
Learning Plan
Day
Section / Objectives
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Q1
Q2
Q3
Capstone Activity- Performance Task
(Project)
Homework
Grade 7- Chapter 4
12
Chapter Review
13
Chapter Test
Goals: Key Understandings: Students will understand that…

There are equivalent forms for any real number.
The results of an operation depend on the types of numbers involved. Multiplying and
dividing fractions is sometimes counter-intuitive.
Essential Questions:
 What is the relationship between the position of a number on the number line and the
value of the number?
 How does identifying the types of numbers in an operation help in determining the
reasonableness of the result?
 How can we use a number line to solve problems?
