Expressions and Equations The Relationships of the Operations Common Core: Engage New York 6.EE.1, 6.EE.2, 6.EE.3 and 6.EE.4

Lesson 5: Special Notations of Operations Focus Standard: 6.EE.A.2c Write, read, and evaluate expressions in which letters stand for numbers. 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 =3 and =62 to find the volume and surface area of a cube with sides of length =1/2.

What does 6.EE.A.1 cover? Write and evaluate numeric expressions involving whole-number exponents.

What does 6.EE.A.2 cover? Write, read, and evaluate expressions in which letters stand for numbers a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract from 5” as 5−. 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. 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 =3 and =62 to find the volume and surface area of a cube with sides of length =1/2.

What does 6.EE.A.3 cover? Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+) to produce the equivalent expression 6+3; apply the distributive property to the expression to produce the equivalent expression 6(4+3); apply properties of operations to ++ to produce the equivalent expression 3.

What does 6.EE.A.4 cover? 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 ++ and 3 are equivalent because they name the same number regardless of which number stands for.

Table of Contents DateTitlePage 2/6/14NEW Focus 8- Algebraic Expression Scale and ChartFresh Left 2/6/14F8 Engage NY Lesson 1 – Add and subtract Relationship Fresh Left 2/7/14F8 Engage NY Lesson 2 – Multiplication and Division Relationship Fresh Left 2/10/14F8 Engage NY Lesson 3- Multiplication and Addition Relationship Fresh Left 2/11/14F8 Engage NY Lesson 4- Division and Subtraction Relationship Fresh Left 2/18/2014F8 ENY L5- ExponentsFresh Left

Focus 8 Algebraic Expression Learning Goal I am able to work with numerical expressions and use letters to represent unknowns in problem solving situations, investigate and apply properties of operation in numerical contexts, such as the associative, distributive, and commutative properties. I can build on my understanding of inverse operations to solve algebraic expressions.

Today, my learning target is to…

MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.

Lesson Notes & Preparation Lesson Notes In 5th grade, students are introduced to exponents. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10 (5.NBT.A.2). In this lesson, students will use new terminology (base, squared, and cubed), and practice moving between exponential notation, expanded notation, and standard notation. The following terms should be displayed, defined, and emphasized throughout Lesson 5: base, exponent, power, squared, and cubed.

Opening Exercises (2 minutes)- As you evaluate these expressions, pay attention to HOW you arrived at your answers.

Socratic Discussion (15 mins) How many of you solved the problems by “counting on”? That is, starting with 4, you counted on 4 more each time (5,6,7,,9,10,11,,13,14,15,...) If you did not find the answer that way, could you have done so? Yes, but it is time-consuming and cumbersome. Addition is a faster way of “counting on.” How else could you find the sums using addition? Count by 4, 9, or 10. How else could you solve the problems? Multiply 4 times 10; multiply 9 times 5; multiply 10 times 5. Multiplication is a faster way to add numbers when the addends are the same.

Socratic Discussion

Student Practice #1-5 (5minutes) Record your answer in your math workbook.

Student Practice- Record your answer in your math workbook.

SP #1-5 Answers

Student Practice #6-8 (4 minutes) Record your answer in your math workbook. The base number can also be a fraction. Convert the decimals to fractions in Examples 7 & 8 and evaluate. Leave your answer as a fraction. Remember how to multiply fractions!

SP#6-8 ANSWERS The base number can also be a fraction. Convert the decimals to fractions in Examples 7 & 8 and evaluate. Leave your answer as a fraction. Remember how to multiply fractions!

Thursday- 5 th Period Start Here

Student Practice #9-10 (1 minute) Record your answer in your math workbook.

Squared vs. Cubed There is a special name for numbers raised to the second power. When a number is raised to the second power, it is called squared. Remember that in geometry, squares have the same two dimensions: length and width. For >0, 2 is the area of a square with side length. What is the value of 5 squared? 25 What is the value of 7 squared? 49 What is the value of 8 squared? 64 What is the value of 1 squared? 1 There is also a special name for numbers raised to the third power. When a number is raised to the third power, it is called cubed. Remember that in geometry, cubes have the same three dimensions: length, width, and height. For >0, 3 is the volume of a cube with edge length. What is the value of 1 cubed? 1×1×1=1 What is the value of 2 cubed? 2×2×2=8 What is the value of 3 cubed? 3×3×3=27

Thursday- 1 st, 2 nd Period START HERE!

Exercises #1-4 (8minutes) Record your answer in your math workbook. 2. Write “five cubed” in all three forms (exponential form, written as a series of products, standard form) 3. Write “fourteen and seven tenth squared” in all three forms. 4. One student thought two to the third power was equal to six. What mistake do you think they made and how would you help them fix their mistake?

Exercises #1-4 ANSWERS

Closing (2 min) We use multiplication as a quicker way to do repeated addition if the addends are the same. We use exponents as a quicker way to multiply if the factors are the same. Carefully write exponents as superscripts to avoid confusion.

Student Exit Ticket for Lesson 5 Exponents Complete the Handout and Turn In for a GRADE

Exit Ticket - Lesson 5 ANSWERS

Today, I achieved my learning target by…

MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.

The End of Lesson 5 Exponents