Download Unit 2 Multiplying and Dividing Rational Numbers Days: 1 – 11

Unit 2 Multiplying and Dividing Rational Numbers
Days: 1 – 11
Mathematics
Grade: 7th
Standard: Standard: 7.NS.2a Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational
numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the
properties of operations, particularly the distributive property leading to products such as (-1)(-1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.2b Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero divisor) is a
rational number. If p and q are integers, then –(p/q) = -p/q = p/-q. Interpret quotients of rational numbers by describing real-world
contexts.
7.NS.2c Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2d Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or
eventually repeats.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.1
1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
The
Number System
Grade: 7
Domain:
Cluster: Apply and extend previous
understandings of multiplication and
division of fractions to multiply and
divide rational numbers.
Make sense of
problems and
persevere in solving
them.
Reason abstractly
and quantitatively.
Knowledge Target
(Prerequisite Skill or Underpinning)
Construct viable
arguments and
critique the
reasoning of others.
Model with
mathematics.
Reasoning Target
(Mastery)
Use appropriate
tools strategically.
Attend to precision.
Performance Skill Target
(Mastery)
Target
Type:
Look for and make
use of structure.
K, R
Look for and express
regularity in repeated
reasoning.
Product Target
Recognize that the process for multiplying Apply the properties of operations, particularly
fractions can be used to multiply rational distributive property, to multiply rational
numbers including integers.
numbers.
Know and describe the rules when
multiplying signed numbers.
Interpret the products of rational numbers by
describing real-world contexts.
Explain why integers can be divided
except when the divisor is 0.
Interpret the quotient of rational numbers by
describing real-world contexts.
Describe why the quotient is always a
rational number.
Apply properties of operations as strategies to
multiply and divide rational numbers.
Know and describe the rules when
dividing signed numbers, integers.
Recognize that –(p/q) = -p/q = p/- q.
Solve real-world mathematical problem by
adding, subtracting, multiplying, and dividing
rational numbers, including complex fractions.
Identify how properties of operations can
be used to multiply and divide rational
numbers (such as distributive property,
multiplicative inverse property,
multiplicative identity, commutative
property for multiplication, associative
property for multiplication, etc.)
Convert a rational number to a decimal
using long division.
Explain that the decimal form of a rational
number terminates (stops) in zeroes or
repeats.
Add rational numbers.
Subtract rational numbers.
Multiply rational numbers.
Divide rational numbers.
Formative Pre-assessment
Student Learning Target
Formative Assessment
Unit 2 Multiplying and Dividing Rational Numbers
Days: 1 – 11
Mathematics
Day 1:
I can use the properties of operations to
multiply integers. (K)
Day 2:
I can convert improper fractions to mixed
numbers and vice versa. (K)
Day 3:
I can use the properties of operations to
multiply rational numbers. (K)
Day 4:
I can use the properties of operations to divide
integers. (K)
Grade: 7th
Day 1:
Please describe and give two examples of multiplying positive and negative integers.
If the product of two integers is -50 and one of the integers was -5 what is the other integer?
Day 2:
1.
2.
7/5 =
2½ =
Day 3:
1.
2.
3.
1/5 x 4/7=
3½ x 2¾ =
2.45 x 6.8 =
Day 5:
Day 4:
I can use the properties of operations to divide
Please describe and give two examples of dividing positive and negative integers.
rational numbers including complex fractions.
*Fractions (K)
Day 5:
Day 6:
1. 4/5 / 3/2 =
I can use the properties of operations to divide
rational numbers.
2. 4x2/2x9 =
*Long Division (K)
3. The square root of 18 is between which two whole numbers?
Day 7:
I can use properties of operations to multiply
and divide fractions and decimals in order to
solve real world mathematical problems. (R)
Day 8:
I can convert between all forms of rational
numbers using various strategies including long
division and place value.
*mental math, place value, long division,
factors in the denominator (K)
Day 6:
12.456 / 4.5 =
Day 7:
1.
2.
Day 9:
I understand that the decimal form of a rational
number will either repeat or terminate. Irrational Day 8:
numbers do neither. (K)
1.
Day 10:
2.
I can identify rational numbers as numbers that
3.
can be represented by a fraction. I know that a
rational number cannot have a zero as a
Day 9:
denominator. (K)
Day 11:
The bill for the dinner was $80.00. One of the diners had a coupon for $25.00 toward
the dinner. The five diners then split the remaining bill equally. How much did each
diner have to pay?
A piece of wood that is 9 feet long is cut in half lengthwise. Each half is half is then
cut lengthwise into 6 congruent pieces of wood. What is the length of each of the
twelve small pieces of wood?
Change the following decimal to fraction using mental math. 0.8 =
Change the following fraction to a decimal using factors of 100. 1/5 =
Change the following fraction to a decimal using long division. 1/8 =
I can use place value to round decimal
numbers in order to solve real world and
mathematical problems. (R)
Using the nested Venn diagram explain your understanding of rational and irrational numbers.
Day 10:
1.
2.
Use long division to convert 1/7 into a decimal and determine how many places the
repeating block goes until it begins to repeat.
Determine if the numbers are rational or irrational.
1.3
2 2/3
5.432124678 -6/7
Day 11:
Before 2000, stocks on the New York stock exchange were listed with fractional values. Now
they are listed with a decimal to the nearest penny. In 1999, a stock’s value changed by 10/32.
What would its change in value be, using today’s value system, to the nearest penny?
Critical Content Vocabulary
Suggested
Strategies/Activities
Instructional Resources