6.EE.1 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Write and evaluate numerical expressions involving whole-number exponents.

Learning Targets (I can)

• Determine order of operations.
• Express quantities with exponents.
• Write numerical expressions.
• Evaluate numerical expressions.

About the Math

• Determine order of operations.

The Order of Operations is a contrived agreement that mathematicians use for congruency. Students should first understand that agreement is needed as various results could be achieved without the agreement. For example, 4 + 7 x 8 could yield 60 (correctly) as 88 (incorrectly). Once students understand the need for common agreement, they should then acquire the order and then practice applying it. PEMDAS is a recognized acronym for order of operations. Again, understanding is needed. It may also be wise to introduce chunks of the order sequentially. That is, work with addition and subtraction before moving to expressions with all 4 operations, then to expressions with exponents, and so on. Note that students have likely had exposure to parenthesis in earlier grades due to their work with the distributive property.

• Express quantities with exponents.

Exponents express the power to which a quantity is raised. Exponents identify how many times a number is multiplied by itself. They are useful in a variety of ways. Common uses included dimensions of squares and cubes as well as powers of ten. 

• Write numerical expressions.

Situations can be represented with expressions. For example, Heather bought tickets that were $4 each. That can be expressed as 4x. Expressions can contain more than one operation. Moreover, quantities themselves can be represented with expressions. Students should be comfortable creating expressions for real-world situations as well as creating examples for a given expression.

• Evaluate numerical expressions.

Expressions are evaluated when specific values are given for an unknown(s) in an expression. Students should understand and be able to articulate that the value of an expression can change based on the value of the unknown. 

Essential vocabulary for this standard includes: exponents, base, numerical expressions, algebraic expressions, and evaluate. Visit the online dictionary Links to an external site. or  visual math dictionary Links to an external site. for vocabulary support.

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

TASKS

These tasks can be used with small group or whole group instruction.

• Do these two expressions have the same answer? Why or why not? (18 + 5) x 2 AND 18 + (5 x 2)
• Write an expression for twice the value of 3 to the third power plus 5. If evaluated, what will the expression equal? 2 (3 ³ + 5) and it will equal 64.
• Evaluate the expression 54 ÷ a + 10 - b, if a = 9 and b = 7. Now create another expression using the same values for a and b, but with a solution greater than this expression.
• Write 3 expressions that are greater than 5 x 4 ² + 8.
• Display 168 x a = b on the board. What are two different sets of values for a and b that make this statement true. If the value of a increases, how will the value of b change?
• Kisha was asked to write 8,808 in expanded form using exponents. Her response was (8 x 10 ² ) + (8 x 10 ¹ ) + (8 x 10 ⁰ ). Is Keisha’s answer correct? Justify your answer.

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Additional Tasks 

  These links provide instructional ideas connected to this standard. 

• Lesson 6.12 - Meaning of Exponents Links to an external site.(Illustrative Mathematics)
• Lesson 6.13 - Expressions with Exponents Links to an external site. (Illustrative Mathematics)
• Rectangle Perimeter 3 (Links to an external site.)  Links to an external site.(Illustrative Math)
• Watch out for Parentheses (Links to an external site.)  Links to an external site.(Illustrative Math)
• The Djinni’s Offer (Links to an external site.) Links to an external site. (Illustrative Math)
• Seven to the What?!? (Links to an external site.)  Links to an external site.(Illustrative Math)
• Sierpinski's Carpet (Links to an external site.)  Links to an external site.(Illustrative Math)
• Expressions and Equations Download Expressions and Equations (Lesson Collection)

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	6-8	Stack of Coins, Activity 10.1, Page 172 Guess My Number , Activity 10.2, Page 173 True or False Equations, Activity 10.3, Page 173 Entering Expressions, Activity 10.4, Page 175 Exploring Powers of Ten, Activity 10.8, Page 179
	Hands-On Standards	5-6	108 (Expressions with a Variable) 106 (Order of Operations)
	Nimble with Numbers	5-6	4, 17-19, 22-23, 37-38, 42-43, 49-50, 62-63
	Groundworks: Algebraic Thinking	6	57-79
	Groundworks: Reasoning with Numbers	5	112-118 (Order, Please)
	20 Thinking Questions for Pattern Blocks 20 Thinking Questions for Rainbow Cubes	6-8	38-41 50-53
	Brain-Compatible Activities for Mathematics	4-5	118-120

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• Exponent Game Download Exponent Game
  (HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

• Read, Write and Evaluate Expressions with Exponents Links to an external site.
• Write Numerical Expressions Links to an external site.
• Expressions and Equations Links to an external site.
• Read, Write and Evaluate Numeric Expressions with Exponents Links to an external site.
• Use Order of Operations to Write Expressions of a Given Value Links to an external site.
• Express Quantities Using Exponents Links to an external site.

Learning Targets

• Determine order of operations.
• Express quantities with exponents.
• Write numerical expressions.
• Evaluate numerical expressions.

Learning targets identify what students should be able to do.  This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks (3-5) Download Rubric for Tasks (3-5)