Unit 2
Expressions of Integers
Expressions of Integers
Notebook:
In this class, we will be using the language of math to communicate. Speaking math takes practice.
An expression is a mathematical phrase (part of a sentence) made up of two things:
values and operations.
Values can be constants (numbers that stay the same) or variables, (usually letters that stand for numbers).
Operations are the verbs of math: the most used are addition, subtraction, multiplication and division.
Addition expressions are used when you are gathering up objects or values.
If you have two oranges and you get three more oranges, you can gather all the oranges together to get five oranges.
Addition is gaining, gathering, rising, up, up, UP!
If you have two oranges and you get three more oranges, you can gather all the oranges together to get five oranges.
Addition is gaining, gathering, rising, up, up, UP!
Subtraction expressions are used when you lose or give away objects or values.
If you have five oranges and four of them fall out of your grocery bag on the way home, you have only one orange left.
Subtraction is losing, taking away, down,
down,
down.
If you have five oranges and four of them fall out of your grocery bag on the way home, you have only one orange left.
Subtraction is losing, taking away, down,
down,
down.
And now, we come to magical multiplication. Multiplication is how we humans understand the universe. We have done amazing things with multiplication!
Multiplication is repeated addition.
8 + 8 + 8 + 8 + 8 + 8 = 6(8)
Multiplication is repeated addition.
8 + 8 + 8 + 8 + 8 + 8 = 6(8)
Division expressions are used when you want separate a whole into equal parts.
If Mr. Barnes wanted to evenly distribute Skittles to each of his students, he would need to use division.
Division is the basis for many themes we will use this year: Ratios, Rational Numbers, Percents, Proportional Thinking... We've already used it to find the mean in Unit 1. Division is everywhere.
If Mr. Barnes wanted to evenly distribute Skittles to each of his students, he would need to use division.
Division is the basis for many themes we will use this year: Ratios, Rational Numbers, Percents, Proportional Thinking... We've already used it to find the mean in Unit 1. Division is everywhere.
Classwork & Homework:
--Big Ideas
--EngageNY
State Test Practice:
California Standards:
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
CCSS.Math.Content.6.EE.A.2.a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
CCSS.Math.Content.6.EE.A.2.b
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
CCSS.Math.Content.6.EE.A.2.c
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
CCSS.Math.Content.6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
CCSS.Math.Content.6.EE.A.2.a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
CCSS.Math.Content.6.EE.A.2.b
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
CCSS.Math.Content.6.EE.A.2.c
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
CCSS.Math.Content.6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..